Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true?

Firm A and B are two airlines. If the two airlines must decide simultaneously, what is the Nash equilibrium prediction for this game if the government offers a $30 subsidy to airlines that serve this route?

fill in the blank.

(b) If you are sure that the other hunter will hunt hare, what is the best thing for you to do? - HUNT HARE

(c) Does either hunter have a dominant strategy in this game? - NO

(d) Is (Hunt Stag, Hunt Stag) a Nash equilibrium of this game? - YES

(e) Is (Hunt Stag, Hunt hare) a Nash equilibrium of this game? - NO

(f) Is (Hunt Hare, Hunt Stag) a Nash equilibrium of this game? - NO

(g) Is (Hunt Hare, Hunt Hare) a Nash equilibrium of this game? - YES

If they choose actions simultaneously, what are their Nash equilibrium strategies?

(b)Suppose that you are player A. If the other player keeps, what is your payoff if you contribute? - $8

(c)Suppose that you are player A. If the other player contributes, what is your payoff if you keep? - $18

(d) Suppose that you are player A. If the other player contributes, what is your payoff if you contribute? - $16

(e) Is (Contribute,Contribute) a Nash equilibrium of this game?- FALSE

(f) Is (Contribute,Keep) a Nash equilibrium of this game? - FALSE

(g) Is (Keep,Contribute) a Nash equilibrium of this game? - FALSE

(h) Is (Keep,Keep) a Nash equilibrium of this game? - TRUE

**= [a]. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p**is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

If they choose actions simultaneously, what are their Nash equilibrium strategies?

does this game have a dominant strategy (write "Yes" or "No")?

Is (Swerve, Swerve) a Nash equilibrium of this game (write "Yes" or "No")?

Is (Swerve, Don't Swerve) a Nash equilibrium of this game?

Is (Don't Swerve, Swerve) a Nash equilibrium of this game (write "Yes" or "No")?

Is (Don't Swerve, Don't Swerve) a Nash equilibrium of this game (write "Yes" or "No")?

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true if we predict a Nash equilibrium will result from their strategic interaction?

**=_______-. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p**is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

**=____ and p2**=_____.

If there is an additional pollution cost ca per unit produced, what is the DWL in the market if the government decides to impose a specific tax collected from the producer of ca per unit.

If there is an additional pollution cost ca per unit produced, what is the DWL in the market.

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)-3000-10p.

The industry output is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)-3000-10p.

The price is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)-3000-10p.

The total amount of consumer surplus is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)-3000-10p.

The total amount of producer surplus is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

the industry output:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

The price is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

The total amount of consumer surplus is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

The total amount of producer surplus is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

The total welfare is:

Each of these firms is identical in every aspect to each other firm in the industry. The industry is a constant cost industry such that each firm produces at a constant cost where C(q)=120q and where the market demand is Q(p)=3000-10p.

The dead weight-loss is:

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

The monopolist output:

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

the monopolist price is:

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

The total amount of consumer surplus is

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

The total amount of producer surplus is:

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

The total welfare is:

The industry is a constant cost industry where c(q)=120q and where the market demand is Q(p)=3000-10p.

The dead weight loss is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

The aggregate production is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

the price is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

The total amount of consumer surplus is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

The total amount of producer surplus isL

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

The total welfare is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

The DWL is:

The industry is a constant cost industry where C(q)=120q and where the market demand is Q(p)-3000-10p. Suppose the government intervenes the market and splits the monopoly into two firms with cost of C1(q)=120q and C2(q)=120q.

the welfare gain/loss to society from this intervention is:

if (top,right) is a Nash strategy equilibrium, then we know that: c ≥____ and _____≥ b.

If (top, right) is a Nash equilibrium then it must be a dominant strategy equilibrium (true/false)

if (top,left) is an equilibrium in strictly dominant strategies, then we know that: a>____, b>____, ____>g, and ____>h.

if (top,left) is a Nash equilibrium, then how many of the above strict inequalities must be satisfied (numeric answer, i.e., 0, 1, 2, 3, or 4)? ____

If (top, left) is an equilibrium in strictly dominant strategies then it must be a Nash equilibrium (write "T" if true, or "F" if false). ____

Specified Answer for: aNOSpecified Answer for: bNOSpecified Answer for: cYESSpecified Answer for: dYESSpecified Answer for: eNO

d

f

35

A.) has 0 Nash equilibrium (in pure strategies)

B.) has 1 Nash equilibrium (in pure strategies)

C.) has 2 Nash equilibria (in pure strategies)

D.) has 3 Nash equilibria (in pure strategies)

E.) has more than 3 Nash equilibria (in pure strategies)

A.) a - 2bQ

B.) a

C.) 2bQ

D.) a - bQ/2

E.) a - bQ

**= [a] and p2**= [b].

b.= 35

A.) produces more than the competitive outcome.

B.) produces the same units as the competitive outcome.

C.) produces less than the competitive outcome.

D.) has zero profits.

E.) has the same profits as what would have in a competitive market.

A.) sells at a price higher than its marginal cost at q*.

B.) sells at a price lower than its marginal cost at q*.

C.) sells at a price the same as its marginal cost at q*.

D.) sells at a price lower than the competitive price.

E.) sells at the same price as the competitive price.

A.) a strictly dominated action

B.) a best response

C.) a strictly dominant action

D.) a worst response

E.) a dynamic response

A.) a strictly dominant action

B.) a strictly dominated action

C.) a dominated action

D.) a strict action

E.) a dynamic action

A.) increase price by $4.

B.) increase price by $8.

C.) leave its price unchanged.

D.) increase price by $12.

E.) increase price by $5.

A.) the firm must lower price if it wishes to sell more output.

B.) the demand for the firm's output is perfectly elastic.

C.) the firm can sell all of its output at any price.

D.) the firm is a price taker.

E.) the firm has no supply curve.

A.) True

B.) False

A.) True

B.) False

Fill in the blank:

(a) does this game have a dominant strategy (write "Yes" or "No")? [a]

(b) Is (Swerve, Swerve) a Nash equilibrium of this game (write "Yes" or "No")? [b]

(c) Is (Swerve, Don't Swerve) a Nash equilibrium of this game (write "Yes" or "No")? [c]

(d) Is (Don't Swerve, Swerve) a Nash equilibrium of this game (write "Yes" or "No")? [d]

(e) Is (Don't Swerve, Don't Swerve) a Nash equilibrium of this game (write "Yes" or "No")? [e]

b. No

c. Yes

d. Yes

e. No

A.) (No Bonus, Loaf)

B.) (Bonus, Loaf)

C.) (No Bonus, Work)

D.) (Bonus, Work)

E.) there is no Nash equilibrium in this game.

(a) If you are sure that the other hunter will hunt stag, what is the best thing for you to do (write either "Hunt Stag" or "Hunt Hare")? [a]

(b) If you are sure that the other hunter will hunt hare, what is the best thing for you to do (write either "Hunt Stag" or "Hunt Hare")? [b]

(c) Does either hunter have a dominant strategy in this game (write "Yes" or "No")? [c](d) Is (Hunt Stag, Hunt Stag) a Nash equilibrium of this game (write "Yes" or "No")? [d]

(e) Is (Hunt Stag, Hunt hare) a Nash equilibrium of this game (write "Yes" or "No")? [e]

(f) Is (Hunt Hare, Hunt Stag) a Nash equilibrium of this game (write "Yes" or "No")? [f]

(g) Is (Hunt Hare, Hunt Hare) a Nash equilibrium of this game (write "Yes" or "No")? [g]

b. Hunt Hare

c. No

d. Yes

e. No

d. No

e. Yes

A.) 21

B.) 58

C.) 2646

D.) 882

E.) 1764

A.) 58

B.) 21

C.) 2646

D.) 882

E.) 1764

A.) Confess

B.) Don't confess

C.) There is no strictly dominant action for Player 1

D.) Both Confess and Don't Confess are strictly dominant actions for

Player 1

E.) Strictly dominant actions are the derivative of the subgame perfect quantal equilibrium.

A.) (Don't confess, Don't confess) is a Nash equilibrium and an equilibrium in strictly dominant strategies.

B.) (Don't confess, Don't confess) is a Nash equilibrium, but not an equilibrium in strictly dominant strategies.

C.) (Don't confess, Don't confess) is not a Nash equilibrium, but is an equilibrium in strictly dominant strategies.

D.) (Don't confess, Don't confess) is neither a Nash equilibrium nor an equilibrium in strictly dominant strategies.

E.) None of the above statements is correct.

A.) Q=96, Q=96)

B.) (Q=96, Q=64)

C.) (Q=96, Q=48)

D.) (Q=48, Q=48)

E.) (Q=64, Q=64)

A.) 200

B.) 300

C.) 600

D.) 400

E.) 100

A.) a higher payoff than any other action the player can use for every possible action of the other players.

B.) a lower payoff than any other action the player can use for every possible combination of the other players.

C.) the same payoff as any other action the player can use for every possible combination of the other players.

D.) a lower or the same payoff as any other action the player can use for every possible combination of the other players.

E.) a lower payoff than any other action the player can use for one possible combination of the other players.

A.) the strictly dominated action may be selected.

B.) the strictly dominated action will not be selected.

C.) the strictly dominated action may or may not be selected.

D.) the strictly dominated action must be selected.

E.) the strictly dominated profile will outperform the market.

A.) Perfect first-degree price discrimination

B.) Imperfect first-degree price discrimination

C.) Second-degree price discrimination

D.) Third-degree price discrimination

E.) None of the above

A.) Perfect first-degree price discrimination

B.) Imperfect first-degree price discrimination

C.) Second-degree price discrimination

D.)Third-degree price discrimination

E.) None of the above

A.) consumers internalize the consequences of their pricing/consumption decisions.

B.) firms internalize the consequences of their pricing/production decisions.

C.) neither agents nor firms can affect prices.

D.) only firms are price takers.

E.) consumers do not maximize utility and firms do not maximize profits.

A.) is a market in which production is controlled by a small number of firms.

B.) takes prices as given.

C.) does not maximize profits.

D.) is a firm that controls 100% of the production of a certain good.

E.) does not induce a deadweight loss.

A.) Produces a quantity that maximizes its profits.

B.) Produces a quantity that maximizes its marginal revenue.

C.) Produces a quantity that maximizes its marginal profit.

D.) Usually breaks even.

E.) Produces a quantity that maximizes its revenue.

A.) charging price equal to marginal cost.

B.) by setting marginal profit equal to marginal cost.

C.) by charging price equal to average cost.

D.) by setting MR(q)=MC(q) at a q for which p(q) is at least AVC(q)

E.) by setting marginal revenue equal to marginal profit at a q for which p(q) is at least AVC(q)

A.) MR(q)=(dP(q)/dq)q+Q(q)

B.) MR(q)=(dP(q)/dq)p+P(q)

C.) MR(q)=(dP(q)/dq)p+Q(q)

D.) MR(q)=(dQ(q)/dq)p+Q(q)

E.) MR(q)=(dP(q)/dq)q+P(q)

A.) 2646

B.) 58

C.) 21

D.) 882

E.) 1764

A.) Q=48

B.) Q=64

C.) Q=96

D.) both Q=48 and Q=64

E.) There is no strictly dominated action.

A.) 1764

B.) 21

C.) 882

D.) 2646

E.) 441

A.) -1.5

B.) -2

C.) -1.2

D.) -2.5

E.) -2.2

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true if we predict a Nash equilibrium will result from their strategic interaction?

A.) Only firm A will enter the market

B.) Only firm B will enter the market

C.) Neither firm will enter the market

D.) Firm A and firm B will both enter the market

E.) The outcome of the game is unpredictable (i.e., there is no Nash equilibrium for this game).

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true?

A.) Firm B does not have a dominant strategy

B.) Firm A does not have a dominant strategy

C.) Neither firm entering is a Nash equilibrium

D.) Both firms entering is a Nash equilibrium

E.) The outcome of the game is unpredictable

A.) $2

B.) $1

C.) $1.50

D.)$3

E. $2.50

A.) price elasticity of demand

B.) price elasticity of supply

C.) the firm's cost function

D.) slope of the demand curve

E.) shape of the marginal cost curve

A monopolist?

A.) Produces a quantity less than its production at the Bertrand competition outcome when there is another competitor with lower costs (when both have constant MC).

B.) Produces a quantity greater than its production at the Bertrand competition outcome when there is another competitor with equal marginal costs (when both have constant MC).

C.) Produces a quantity that is greater than the competitive outcome.

D.) Never makes a positive profit.

E.) Produces a quantity that is generally less than the competitive outcome.

A.) Yes

B.) No

A.) -1.25

B.) -0.2

C.) -0.8

D.) -5

E.) 0.8

A.) p(q)=100-3q

B.) p(q)=50-2q

C.) p(q)=50-q

D.) p(q)=100-2q

E.) p(q)=100-q

Fill the blank:(a) if (top,right) is a Nash strategy equilibrium, then we know that: c ≥ [a] and [b]≥ b.(b)

If (top, right) is a Nash equilibrium then it must be a dominant strategy equilibrium (write "T" if true, or "F" if false). [c]

b.) d

c.) F

A.) economic profit

B.) economic revenues

C.) economic costs

D.) prices

E.) units produced

A.) Under the first-degree price discrimination, consumer surplus is equal to zero.

B.) Under the first-degree price discrimination, producer surplus is maximized.

C.) Under the first-degree price discrimination, social welfare is minimized.

D.) Under the first-degree price discrimination, the dead-weight loss is zero.

E.) Under the first-degree price discrimination, the total welfare is higher than that under the profit-maximizing single price scheme.

Firm A and B are two airlines. If the two airlines must decide simultaneously, what is the Nash equilibrium prediction for this game if the government offers a $30 subsidy to airlines that serve this route?

A.) Both firms will enter and make a positive profit.

B.) Firm A will decide not to enter since firm B will

C.) Firm B will decide not to enter since firm A will

D.) Neither firm will have a dominant strategy

E.) Neither firm entering is a Nash equilibrium

A.) 32

B.) 256

C.) 64

D.) 1296

E.) 72

Perfect competition increases prices compared to the monopoly outcome.

A.) True

B.) False

A.) B produces a higher payoff than A independently of what the other players do.

B.) B produces a lower payoff than A independently of what the other players do.

C.) B produces the same payoff as A independently of what the other players do.

D.) B produces a lower or the same payoff as A independently of what the other players do.

E.) A produces a higher payoff than B independently of what the other players do.

A.) p(q)=500-(1/2)q

B.) p(q)=1000-2q

C.) p(q)=500-2q

D.) p(q)=1000-q

E.) p(q)=500-q

A.) a strictly dominant action

B.) a strictly dominated action

C.) a best response

D.) a worst response

E.) a dynamic response

A.) (U, L)

B.) (U, R)

C.) (D, L)

D.) (D, R)

A.) Q=48

B.) Q=64

C.) Q=96

D.) both Q=48 and Q=64

E.) There is no strictly dominated action.

A.) Confess.

B.) Don't confess.

C.) There is no strictly dominant action for Player 1.

D.) There is no strictly dominant action for Player 2.

E.) There is no strictly dominant action for both Player 1 and Player 2.

[a] units of output?

[b] Her profit will be?

b.) 6900

A.) Candidate A has a strictly dominant strategy.

B.) Candidate B does not have a strictly dominant strategy.

C.) The game does not have an equilibrium in strictly dominant strategy.

D.) (medium, medium) is a Nash equilibrium.

E.) None of the above.

Consider the following game. Two players are put in separate rooms. Each player is given $10. The player can use this money in either of two ways. He can "keep" it or he can "contribute" it to a public fund. Money that goes into the public fund gets multiplied by 1.6 and then divided equally between the two players. If both contribute their $10, then each gets back $20x1.6/2=$16. If one contributes and the other does not, each gets back $10x1.6/2=$8 from the public fund so that the contributor has $8 at the end of the game and the non-contributor has $18-his original $10 plus $8 back from the public fund. If neither contributes, both have their original $10. The following is the payoff table for this game. (The following is a description of the table: Rows are labeled by player A's actions and columns are labeled with player B's actions. From top to bottom, A's actions are "Contribute" and "Keep". From left to right, B's actions are "Contribute" and "Keep". Payoffs, in dollars, are as follows: The first row is (16,16) and (8,18); the second row is (18,8) and (10,10).) (PICTURE)

(a) Suppose that you are player A. If the other player keeps, what is your payoff if you keep (do not include the dollar sign in your answers)? $ [a]

(b)Suppose that you are player A. If the other player keeps, what is your payoff if you contribute? $ [b]

(c)Suppose that you are player A. If the other player contributes, what is your payoff if you keep? $ [c]

(d) Suppose that you are player A. If the other player contributes, what is your payoff if you contribute? $ [d]

(e) Is (Contribute,Contribute) a Nash equilibrium of this game (answer "T" if true, or "F" if false)? [e]

(f) Is (Contribute,Keep) a Nash equilibrium of this game (answer "T" if true, or "F" if false)? [f]

(g) Is (Keep,Contribute) a Nash equilibrium of this game (answer "T" if true, or "F" if false)? [g]

(h) Is (Keep,Keep) a Nash equilibrium of this game (answer "T" if true, or "F" if false)? [h]

b.) 8

c.) 18

d.) 16

e.) F

f.) F

g.) F

h.) T

(a) if (top,left) is an equilibrium in strictly dominant strategies, then we know that: a> [a], b> [b], [c]>g, and [d]>h.

(b) if (top,left) is a Nash equilibrium, then how many of the above strict inequalities must be satisfied (numeric answer, i.e., 0, 1, 2, 3, or 4)? [e]

(c) If (top, left) is an equilibrium in strictly dominant strategies then it must be a Nash equilibrium (write "T" if true, or "F" if false). [f]

b.) d

c.) c

d.) f

e.) 0

f.) T

A monopolist sells in two states. The demand function in state 1 and 2 respectively is Q1(p1)=50 - p1 and Q2(p2)=90-1.5p2. The monopolist produces at a constant marginal cost of 10. If a government regulation prevents the monopolist from charging different prices in the two states, then the profit maximizing price will be p

**= [a]. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p**is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

A.) True

B.) False

A.)-i

B.) -(i+n)

C.) -(e+h+m+l+s)

D.) -(e+h+i+m+n+l+s)

E.) -(e+h+i)

a) y=5-2x

b) y=5+4x

c) y=5-4x

d) y=10-8x

e) y=2-4x

a) 6

b) 8

c) 3

d) 7

e) 5

a) F(10,2)= 5

b) F(10,2)= 4

c) F(10,2)= 10

d) F(10,2)= 20

e) F(10,2)= 2

a) 40, the average of 0 and 80.

b) 0 because is marked late by the system.

c) 10

d) It could be 0 or 80, depending on the student's ability to convince the instructor to waive the deadline.

e) 80 because the student did not enter any new answer after the deadline.

a) f(x,y)=min{3x,2y}

b) f(x,y)=3x+2y

c) f(x,y)=min{2x,3y}

d) f(x,y)=min{2x2,3y2}

e) f(x,y)=x+y

a) (0,3)

b) (3,0)

c) (0,5)

d) (5,0)

e) (5,5)

a) f(x,y)=3x+2y.

b) f(x,y)=2x+3y.

c) f(x,y)=x2y

d) f(x,y)=min{x,y}

e) f(x,y)=xy2

a) B

b) D

c) C

d) A

e) F

a) 5

b) 10

c) 1.5

d) 1.07

e) 3

a) An X shaped set

b) An L shaped set

c) A straight line

d) Half a circle

e) A bell shaped curve

a) C'(n)= 4n^(-1/2)+3n^(2)

b) C'(n)= 2n^(-1/2)+6n^(2)

c) C'(n)= 2n^(-1/2)+12n

d) C'(n)= 2n^(-1/2)+6n

e) C'(n)= 2n^(-1/2)+3n

a) 1

b) n+1, where n is the number of products that the student can buy (including pizza).

c) It's impossible to determine.

d) 2

e) 0

a) A'(n)=0.30

b) A'(n)=-30/n^(2)

c) A'(n)=35

d) A'(n)=1

e) A'(n)=30/n^(2)

a) C=3n+9

b) C=3n+3

c) C=6n-9

d) C=9n-3

e) C=9n+3

a) dF/dL(1,2)= 12

b) dF/dL(1,2)= 128

c) dF/dL(1,2)= 48

d) dF/dL(1,2)= 32

e) dF/dL(1,2)= 64

a) A(n)=n+C(n)

b) A(n)=5/n+C(n)/n

c) A(n)=(30+5n)/n

d) A(n)=(5+5n)/n

e) A(n)=n+2+C(n)/n

a) 2

b) 3

c) 1

d) 4

e) 0

a) dF(L,K)/dL=(8/3)L^(1/3)K^(-1/3)

b) dF(L,K)/dL= (4/3)L^(2/3)K^(2/3)

c) dF(L,K)/dL= (8/3)L^(1/3)K^(1/3)

d) dF(L,K)/dL= (4/3)L^(2/3)K^(-2/3)

e) dF(L,K)/dL=(8/3)L^(-1/3)K^(1/3)

a) 8

b) 7

c) 10

d) 5

e) 35

a) dF/dK(L,K)= 4LK^(3)

b) dF/dK(L,K)= 8LK^(3)

c) dF/dK(L,K)= 12L^(2)K^(2)

d) dF/dK(L,K)= 8L^(2)K^(3)

e) dF/dK(L,K)= 8L^(3)K^(3)

a) (1,4)

b) (3^(1/2),2)

c) (2^(1/2),3)

d) (3^(1/2),3)

e) (2^(1/2),2)

a) C'(n)=53

b) C'(n)=50n

c) C'(n)=3n

d) C'(n)=3

e) C'(n)=53

a) -9/10

b) -8/10

c) 0

d) -1/10

e) 9/10

a) D(a)=100*a

b) D(m,a)=0.1

**m+100**a

c) D(m,a)=0.1

**m-100**a

d) D(m,a)=100

**a-0.1**m

e) D(m)=2m.

**m+100**a

Confess Don't Confess

Confess 1,1 5,0

Player 1:

Don't Confess 0,5 3,3

In the following prisoner's dilemma problem, the equilibrium in strictly dominant action is

Confess Don't Confess

Confess 1,1 5,0

Player 1:

Don't Confess 0,5 3,3

In the following prisoner's dilemma problem, the strictly dominant action

**for Player**1 is

Q= 96 Q=64 Q=48

Q=96 $0,$0 $3.1, $2.0 $4.6,$2.3

Firm 1: Q=64 . $2.0, $3.1 $4.1 $4.1 . $5.1, $3.8

Q=48 $2.3, $3.6 . $3.8, $5.1 . $4.6, $4.6

In the following game, the strictly dominated action for Firm 1 is:

Under the first-degree price discrimination, consumer surplus is equal to zero.

Under the first-degree price discrimination, producer surplus is maximized.

Under the first-degree price discrimination, social welfare is minimized.

Under the first-degree price discrimination, the dead-weight loss is zero.

Under the first-degree price discrimination, the total welfare is higher than that under the profit-maximizing single price scheme.

ENTER DO NOT ENTER

ENTER 10,-20 50,0

Firm A:

DO NOT ENTER 0,40 0,0

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true?

ENTER DO NOT ENTER

ENTER 10,-20 50,0

Firm A:

DO NOT ENTER 0,40 0,0

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true if we predict a Nash equilibrium will result from their strategic interaction?

**= [a]. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p**is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

Movies Football

Movies 3,2 1,0

Girl:

Football 0,1 2,3

In the following battle of sexes game, is there a strictly dominant action?

Work . Loaf

Bonus 1,2 -1,3

Lori:

No bonus . 3,-1 0,0

If they choose actions simultaneously, what are their Nash equilibrium strategies?

Q= 96 Q=64 Q=48

Q=96 $0,$0 $3.1, $2.0 $4.6,$2.3

Firm 1: Q=64 . $2.0, $3.1 $4.1 $4.1 . $5.1, $3.8

Q=48 $2.3, $3.6 . $3.8, $5.1 . $4.6, $4.6

If we assume that strictly dominated action are not selected, then the combination that survives the iterative elimination of strictly dominated actions in the following game is?

Negative externality results in over-production.

Negative externality results in efficiency loss.

Positive externality results in under-production

.

Positive externality results in efficiency loss.

Internalizing positive externality results in efficiency loss.

Drunk driving jeopardizes public safety.

Your neighbor's dog keeps barking at night so that you cannot sleep.

Air pollution emitted by motor vehicles is detrimental to public health.

Recycling reduces landfills.

You drink too much coffee and cannot sleep at night.

U & B L& R

100, -1

If we assume no strictly dominated is selected then the combination that survives the iterative elimination is

Medium Low High

Each has 3 levels of campaign spending which is correct?

B) 6900

Producing _____ levels of output (a)

Her profit will be _______ (b)

a > __ , B > ____, ____>g and ____ > h

2) 8

3) 18

4) 16

A-D: Suppose you are player a

1) if other player keeps what is your payoff you keep

2)If other player keeps what is your payoff you contribute

3) If other player contributes, what is your payoff if you keep?

4) If other player contributes what is your payoff if you contribute:?

by setting marginal revenue equal to marginal profit at a q for which p(q) is at least AVC(q)

**= [a]. (Hint: The monopoly serves both markets if the optimal price is below 50; assume that p**is at most 50 and solve for the monopoly that maximizes profits with the aggregate demand; confirm that the solution is below 50).

[b] 6900

**=[a] and p2**=[b].

[b] 35

A monopolist (1) produces less than the competitive outcome, (2) sells at a price higher than the competitive price, (3) sells at a price higher than its marginal cost at q

**and (4) has higher profits than what would have in a competitive market (q**is different from the competitive quantity).

The monopolist maximizes economic profit.

Marginal revenue is less than price because a monopolist faces a downward sloping demand function.

The government induces even a higher DWL by imposing taxes.

A monopoly is a firm that controls 100% of the production of a certain good. It internalizes the consequences of their pricing and production decisions.

Since R(q)=P(q)q then MR(q)=(dP(q)/dq)q+P(q).

p(q)=500-(1/2)q; it is calculated from Q(p)=1000-2p, by finding p in terms of q.

The maximal price at which the monopoly can sell q units is exactly the price at which the agents would demand q units. Thus, q=50-p/2. Thus, p(q)=100-2q.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000. We know that -(1/Eown-price)=(P-MC)/P=(300-100)300=200/300=2/3. Then, Eown-price=-3/2=-1.5.

If p(q) = a - bq then Revenue = pq = aq- bq2. Therefore, MR = a - 2bq.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000.

Since p(q)=50-q/4, then MR(q)=50-q/2. Since MC is constant and equal to 14, then MC(q)=MR(q) implies 50-q/2=14. Thus, q=72. Thus, p(72)=32. Profit=Revenue-Cost=32

**72 - 14**72

(P-MC)/P=-(1/Eown-price), then (P-1)/P=-(1/(-2))=1/2. Thus, 2P-2=P, and P=2.

Competition reduces DWL, so increases aggregate welfare.

Since (P-MC)/P=-(1/Eown-price), then when Eown-price=-1, we have that P-MC=P, and MC=0. Since MR=MC for the monopolist, we have that MR=0.

(P-MC)/P=-(1/Eown-price). Then, -(1/Eown-price) =(50-10)/50=4/5. Thus, Eown-price=-5/4=-1.25.

Since Q(p)=70-p, then P(q)=70-q. Thus, MR(q)=70-2q. The monopolist maximizes profits by setting MR(q)=MC(q). MC before tax is 5. Therefore, without tax q=65/2 and p=(70-65)/2. After the tax, MC(q)=13. Therefore, the quantity produced q'=57/2 and the price p'=(70-57)/2. Thus, p'-p=4.

Competitive prices are lower than monopoly prices.

A monopoly can charge a price over marginal cost when consumers are not perfectly elastic

Government provides s per unit. Since the monopoly produces q2 units, then the government has a deficit of s*q2. That is, d+k+j.

Producer surplus is the net area above the MC and below the horizontal line at p1.

Consumer surplus is the net area above the horizontal line at p1 and below Q.

Total welfare is CS+PS+G=a+b+n+d+e+f+g+h+i+j+k-(d+j+k)=a+b+n+e+f+g+h+i.

Total welfare with subsidy is CS+PS+G=a+b+n+d+e+f+g+h+i+j+k-(d+j+k)=a+b+n+e+f+g+h+i. Total welfare without is: a+b+n+e+f+g. The difference is: h+i.

Producer surplus is the net area above the MC and below the horizontal line at p2.

Consumer surplus is the net area above the horizontal line at p2 and below Q.

Monopoly produces at the quantity in the intersection between MC and MR. They produce q1.

Total welfare is CS+PS=a+b+n+e+f+g.

Monopoly produces at the quantity in the intersection between MC and MR. The MC is reduced to c-s when the government provides the subsidy. They produce q2.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

We know that the monopolist maximizes its profits by setting MR1=MC=MR2. We also know that MR=p(1+1/e1) where e1 stands for the elasticity of demand in market 1. Thus, 4/3=8(1+1/e2), which leads to e2=-1.2.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42. The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

The price at which the monopolist is able to sell q units is P(q)=100-2q. Then, Revenue(q)=(100-2q)q, and marginal revenue is MR(q)=100-4q. If MR=MC, we have that 100-4q=16. Thus, q=21. The monopolist charges a price P(21)=100-2(21)=58. Profit is Revenue-Cost=P(q)q-c(q) where q is the amount that maximizes the monopolist profit, i.e., 21. Then, Profit is 58(21)-16*(21)=882. If the monopolist is able to perfectly price discriminate (firs-order price discrimination), it is able to capture all the consumer surplus at the competitive equilibrium. Since there is no fixed cost, the perfectly discriminating monopoly's profit is equal to this consumer surplus. The competitive outcome is where demand intersects supply, i.e. the MC curve. Since MC is flat, the equilibrium price is 16 and the equilibrium quantity Q(16)=42 (this is also the amount produced by the perfectly discriminating monopolist). The profit of the monopolist in the competitive equilibrium is zero (pays 16 to produce a good it sells at 16). The CS is the triangle determined by the demand and the horizontal line at the level of 16. This triangle has base 42 and height (100-16). Its area is 42(100-16)/2=1764. Thus, the perfectly discriminating monopolist profit is 1764.

A monopolist (1) produces less than the competitive outcome, (2) sells at a price higher than the competitive price, (3) sells at a price higher than its marginal cost at q

**and (4) has higher profits than what would have in a competitive market (q**is different from the competitive quantity).

A monopolist (1) produces less than the competitive outcome, (2) sells at a price higher than the competitive price, (3) sells at a price higher than its marginal cost at q

**and (4) has higher profits than what would have in a competitive market (q**is different from the competitive quantity).

The monopolist maximizes profits by setting marginal profit equal to 0. Since marginal profit=MR-MC, this is equivalent to setting MR=MC.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000. We know that -(1/Eown-price)=(P-MC)/P=(300-100)300=200/300=2/3. Then, Eown-price=-3/2=-1.5.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000.

we know that P(q)=500-(1/2)q; thus revenue is R(q)=p(q)q=(500-q/2)q; thus, MR(q)=500-q. Then, MR=MC, implies 500-q=100. Thus, q=400 and the monopoly produces 400 units. Monopoly price is 500-400/2=300. Monopoly profit is 400(300-100)=400(200)=80000.

a. by setting MR(q)=MC(q) at a q for which p(q) is at least AVC(q)

b. charging price equal to marginal cost.

c. by charging price equal to average cost.

d. by setting marginal revenue equal to marginal profit at a q for which p(q) is at least AVC(q)

e. by setting marginal profit equal to marginal cost.

a. Produces a quantity that maximizes its revenue.

b. Produces a quantity that maximizes its profits.

c. Produces a quantity that maximizes its marginal profit.

d. Usually breaks even.

e. Produces a quantity that maximizes its marginal revenue.

a. Produces a quantity greater than its production at the Bertrand competition outcome when there is another competitor with equal marginal costs (when both have constant MC).

b. Produces a quantity that is greater than the competitive outcome.

c. Produces a quantity that is generally less than the competitive outcome.

d. Never makes a positive profit.

e. Produces a quantity less than its production at the Bertrand competition outcome when there is another competitor with lower costs (when both have constant MC).

True

False

True

False

True

False

a. MR(q)=(dQ(q)/dq)p+Q(q)

b. MR(q)=(dP(q)/dq)p+P(q)

c. MR(q)=(dP(q)/dq)p+Q(q)

d. MR(q)=(dP(q)/dq)q+Q(q)

e. MR(q)=(dP(q)/dq)q+P(q)

a. MR(q)=p+p/e

b. MR(q)=p+pe

c.MR(q)=p/e

d. MR(q)=p-pe

e. MR(q)=p-p/e

True

False

Is it possible that this is the COST function when both L and K are variable of a production function that satisfies the law of decreasing marginal returns of labor?

Then, the Marginal cost function associated with this production is:

Is this the graph of a linear production function when capital is fixed?

From the following, which can be the graph of L(q,K), i.e., the labor necessary to produce q units?

Is this the graph of a production function f(L,K)=Amin{L,K} for some constant A>0, when capital is fixed?

If the output price is equal to $12, then the firm maximizes profits by producing?

If the output price is equal to $16, then the firm's maximal profits is?

If the output price is equal to $30, then the firm maximizes profits by producing

If the output price is equal to $30, then the firm's maximal profits is?

If the output price is equal to $34, then the firm maximizes profits by producing?

What is this firm's fixed cost?

Is the law of diminishing marginal returns of labor satisfied for this production function (if the graph of all production functions when capital is fixed looks like this, i.e., concave)?

The Marginal Product of Labor is the slope of the production function when K is fixed. When the graph of this functions are concave, the Marginal Product of Labor is always decreasing as L increases. Thus the law of diminishing marginal returns of labor is satisfied for this production function.

From the graph we know that for the corresponding K:

The marginal product of labor is the slope of the graph of the production function when capital is fixed; in this case the slope is higher at L1 than at L2, and is higher at L2 than at L3; the only true relation from the possible answers is MPL(L1,K)>MPL(L2,K).

From the following options, which one can be the production function of this restaurant?

The production function with K fixed is a line. The only functions that generate lines from the options are f(L,K)=50(L+K), f(L,K)=50L, ad f(L,K)=7LK. We know that neither f(L,K)=50L nor f(L,K)=7LK are the choice, for otherwise the graph would go through (0,0). If K is fixed at 2, then the graph of f(L,2) is exactly the one in the problem.

Denote by APL(L,K)=f(L,K)/L the average product of labor (here f is the production function of the firm). From the graph we learn that for the corresponding K:

APL(5,K)=f(5,K)/5=200/5=40. APL(L,K) is the slope of the line that interpolates the production function and the origin; it is increasing for small L.

Can we say that the production function satisfies the law of decreasing marginal returns of labor?

(it is constant and equal to the slope of the production function when K is constant).

f(1,2)=40(1)+200(2)=440.

If L=100, K=40, and M=100, then f(100,40,100)=100+402+4(100)=2100

The firm is operated for some L and K such that 5LK=100. If inputs are tripled, the firm produces 5(3L)(3K)=9(5LK)=9(100)=900. So production increases (900-100)/100x100%=800%.

The firm is operated for some L and K such that 5L1/3K2/3=100M. If inputs are doubled, the firm produces 5(2L)1/3(2K)2/3=2(5L1/3K2/3)=2(100M)=200M. So production doubles, i.e., it increases (200M-100M)/100Mx100%=100%.

APL is f(L,K)/L. In this case (30L+600)/L, which is 30+600/L. No matter what L is, this figure is more than 30. Thus, it is never 10.

**2.5 / 2.5 pts**

Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.)

Denote by APL(L,K)=f(L,K)/L the average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K:

APL(L,K) is the slope of the line that interpolates the production function when for K fixed and the origin; for L1, this line is flatter than the tangent to the production function at L1; thus, APL(L1,K)<MPL(L1,K); none of the other relations are true.

If f(2L, 2K)= 2f(L, K), we say the firm has constant returns to scale

For a Cobb-Douglas production function f(L, K)= ALaKb, f satisfies increasing returns to scale if and only if a+b>1 (please see lecture notes).

f(2L,2K)=3(2L) a (2K) 1-a = 2a21-a f(L,K)=2f(L,K). Then, f(2L,2K)=2f(L,K). The function is a Cobb-Douglas function with alpha=1 and beta=1-alpha. Since alpha+beta=1 then it satisfies constant returns to scale.

f(2L,2K)=100(2L)(2K)=4f(L,K). Then, f(2L,2K)>2f(L,K). Alternatively, the function is a Cobb-Douglas function with alpha=1 and beta=1. Since alpha+beta=2>1 then it satisfies increasing returns to scale.

(x less of capital, 1 more of labor = same production).

MRTSLK(L,K) is the amount of capital that the firm can substitute with one unit of labor so the production remains constant. That means that in this particular problem if the firm substitutes one unit of labor for two of capital the production remains constant. Thus, substituting two units of labor for one unit of capital increases production.

For a Cobb-Douglas production function f(L, K)= ALaKb, f satisfies constant returns to scale if and only if a+b=1 (please see lecture notes). Then, this is so if b=1/3.

Marginal profit is zero at an interior profit maximizer (i.e., greater than 0 production); thus, if marginal product is >0 at 1000, then 1000 is not profit maximizing.

From the following options, which can be the labor necessary to produce 40 units for this firm? (Hint: you need to understand what decreasing marginal returns of labor is).

From the graph we know that the labor to produce 40 units is between 100 and 200. Suppose that the amount of labor necessary to produce 40 units is x. Notice that the graph shows that the marginal product of labor is decreasing as L increases. This means that x has to satisfy three conditions. First (40-23)/(x-100)<=23/100. This equation says that the increase from 100 to x gives per unit a contribution that is not more than that we have for the first 100 units. You can check that x=120, 140, 160 all violate this. Second, (42-40)/(200-x)<=(42-23)/(200-100). This equation says that the increase from x to 200 gives per unit a contribution that is not more than that we have for the second 100 units. You can check that x=195 violates this.

Since the firm has strictly increasing returns to scale, then the cost per unit decrease with volume produced. Let L and K the amounts of inputs used by the firm to produce 500 units. Then, f(2L,2K)>2(500)=1000. Thus, the firm can produce more than 1000 units at a cost of $200,000.00. Thus, the cost to produce 1000 units is necessarily less than $200.000.00.

Since the firm has strictly decreasing returns to scale, then the cost per unit cannot decrease with volume produced. Suppose on the contrary that producing 1000 units costs less than $200,000.00, say c. Let L,K be the combination of factors used by the firm to do this. Then, (0.5L) and (0.5K) produce more than f(L,K), that is f(L,K)<2f(0.5L,0.5K). Thus, f(0.5L,0.5K)>1000/2=500. But, 0.5L and 0.5K cost 0.5c. Since c<$200,000.00, then 0.5c<$100.000.00. Thus, the firm would be able to produce 500 units for less than $100,000.00. Thus, this cannot be the cost of 500 units. Thus, the only possible option is the amount that is greater than $200,000.00.

Accounting profits only include accounting costs, which can be different from economic costs. For instance, completely depreciated physical capital does not generate depreciation expense. This capital has an economic cost, for it can be rented or sold.

If a production function satisfies constant returns of scale, its cost function is linear. That is, cost can be calculated by means of proportions. Thus, if 100 units cost $200,000.00, 500 units cost $1,000,000.00.

Then, the Average cost function associated with this production is:

MC=AC are both constant.

From the following, which can be the graph of L(q,K), i.e., the labor necessary to produce q units?

The graph of L(q,K) is obtained by rotating the graph of f when K is fixed and flipping it. This produces

Economic Profit = Revenue - Economic Cost

If the output price is equal to $12, then the firm maximizes profits by producing?

The horizontal line at p=12, intersects MC when q<100. But at q, such that p<AVC(q). Thus the firm produces q=0.

If the output price is equal to $8, then the firm maximizes profits by producing?

The horizontal line at p=8, does not intersect MC. Thus the firm produces q=0.

If the output price is equal to $10, then the firm maximizes profits by producing?

The horizontal line at p=10, intersects MC when q=50. But at q=50, p<AVC(50). Thus the firm produces q=0.

Could this be a marginal cost function for a firm participating in a market in which there is free-entry?

The marginal cost of this firm is increasing. A firm participating in a market in which there is free entry has constant marginal cost.

Could this be a marginal cost function for a firm participating in a market in which there is free-entry?

A firm participating in a market in which there is free entry has constant marginal cost.

If the output price is equal to $21, then the firm maximizes profits by producing?

The horizontal line at p=21, intersects MC when 100<q<120. At such a q, p>AVC(q). Then, the firm produces 100<q<120.

If the output price is equal to $16, then the firm maximizes profits by producing?

The horizontal line at p=16, intersects MC when q=100. At q=100, we have that p=AVC(q). Thus the firm produces either q=0 or q=100.

If the output price is equal to $34, then the firm maximizes profits by producing?

The horizontal line at p=34, intersects MC when q>120. At such a q, p>AVC(q). Then, the firm produces q>120.

Could this be a cost function for a firm participating in a market in which there is free-entry?

The marginal cost of this firm is increasing. A firm participating in a market in which there is free entry has constant marginal cost.

What is this firm's fixed cost?

C(q)=F+VC(q). Then, AC(q)=F/q+AVC(q). At q=100, 34=F/100+16. Then, F=1800.

If the output price is equal to $30, then the firm's maximal profits is?

The horizontal line at p=30, intersects MC when q=120. At q=120, we have that p>AVC(q). Thus the firm produces q=120. Profit(q)=q(p-AC(q))=120(30-30)=0.

if K=2, then f(L,4)=40L+400.

f(10, K) f(5, K)

Can we say that the production function satisfies the law of decreasing marginal returns of labor?

Yes, eventually the marginal return of labor decreases (becomes zero after L=10).

APL is f(L,K)/L. If K=1, then APL is 5L1/2/L=5/L1/2. Thus, APL=1 if L1/2=5, or equivalently L=25.

The function is a Cobb-Douglas function with alpha=1/2 and beta=1/3. Since alpha+beta=5/6<1 then it satisfies decreasing returns to scale. Free entry would require constant returns to scale.

If the firm substitutes one unit of labor for x units of capital, then production remains constant. (x less of capital, 1 more of labor = same production)

If the output price is equal to $30, then the firm maximizes profits by producing?

The horizontal line at p=30, intersects MC when q=120. At such a q, p>AVC(q). Then, the firm produces q=120.

What is the quantity that maximizes the firm's profits when price is 12?

The horizontal line at level p=12 intersects S at q=300. Then the optimal production of the firm is 300.

If the output price is equal to $16, then the firm's maximal profits is?

The bundle that is most to the north east is the one that has the most of each commodity, i.e., (3,7).

(3,5) is to the north east of (2,4), because it contains more of each of the two commodities. Each of the other alternatives contains a lower amount of one of the commodities.

With two commodities, say x and y, in which we draw x in the horizontal axis and y in the vertical axis, a bundle (x,y) contains x of the first commodity and y of the second commodity. Thus, bundle (100,80) has 100 units of food, which is the largest amount of food among these bundles; (99,150) has 100 units of transportation, which the maximum among these bundles.

With two commodities, say x and y, in which we draw x in the horizontal axis and y in the vertical axis, a bundle (x,y) contains x of the first commodity and y of the second commodity. Thus, bundle (100,80) has 100 units of food, which is the largest amount of food among these bundles; (99,150) has 100 units of transportation, which the maximum among these bundles.

The bundle that is most to the south west is the one that has the least of each commodity, i.e., (1/2,1/3).

Think of sodas a being represented in a horizontal axis and slices of pizza on the vertical. The two bundles in the statement are (1,2) and (2,1). Since (1,2) is at least as good as (2,1) but the opposite is not true, then (1,2) is preferred to (2,1). Since these bundles are not related by order, i.e., one is not greater-greater than the other, there is no implication for more is better here. Indeed, even if the bundles were related by order and there was no violation of more is better, we would not be able to say the property is satisfied in general, because we would not know if somewhere else there is a violation of it.

Calculate the utility of the given bundles. There is only one whose utility is greater than the utility of (40,5).

Utility has no meaning on its own. The meaning of utility is only to compare between bundles. It is possible that U(0,0)<U(1,1). For instance U(0,0)=-1000. So Ronald may prefer (1,1) to (0,0).

This utility function says that a is preferred to b and b is preferred to c. There is only one utility function in the options provided that says the same.

Calculate the utility of each of the alternatives and only one has the same utility as (40,5).

Evaluate the utility of each option and the one with greatest utility will be the preferred basket.

The bundles that are indifferent to (2, 0) for Natalia are such that U(2,0)=6=3x+2y. Thus, y=3-3x/2. If (x,y) gives utility 7 to Gina, then V(x,y)=7=4x+2y. This means that if a bundle gives utility 7 to Gina and is indifferent to (2,0) for Natalia, 7=4x+2(3-3x/2). This means that x=1 and y=3-2(1)/2=3/2.

For instance Georgos is indifferent between (0,1) and (1,0). Thus, Georgos finds (1,0) at least as good as (0,1). Evdekia, on the other hand, finds (1,0) is NOT at least as good as (0,1).

Mark's utility at (2,1) is 8. This his indifference curve has equation 8=x3y. Thus, y=8/x3.

Calculate the utility of each of the alternatives and only one has the same utility as (4,0).

Both sisters have linear preferences. Thus their indifference curves are line. Take for instance the point (1,1). The equation of Natalia's indifferce curve through (1,1) is 5=3x+2y, and the equation of Gina's indifference curve through (1,1) is 6=4x+2y. Thus for Natalia y=5/2-3x/2 and for Gina y=3-2x. Thus, Gina's indifference curves are steeper: the slope is more negative. The only point in Gina's indifference curve through (0,0) is (0,0). The utility of Natalia in her indifference curve through (3,2) is 13. Thus, (0,0) is not on Natalia's indifference curve through (0,0).

they are identical. Suppose that (x1,y1) is at least as good as (x2,y2) for Elena. Then 6x1+8y1=6x2+8y2. Then, 3x1+4y1=3x2+4y2. This means that Tuna finds (x1,y1) is at least as good as (x2,y2). One can see that the symmetric statement is also true. If Tuna finds (x1,y1) is at least as good as (x2,y2), then Elena finds the same. Thus, Elena and Tuna will have the same answers to all "at least as good" questions.

More-is-worse for Jan Claude. In the same way that we saw in class that more-is-better implies indifference curves are thin and never cross, one can see that more-is-worse implies the same.

Since Mr. Butcher's MRS of coffee for tea is constant, we can measure it at any point. Suppose that he is consuming (c,t). MRStc is the maximal amount of tea that he is willing to give up to consume one additional cup of coffee. This means that the utility of (c,t) is the same as the utility of (c+1,t- MRStc). Since we have the utility function, we know then that 2c+t=2(c+1)+t-MRStc. This can be simplified to MRStc=2. Note that this is intuitive. Mr. Butcher gets 2 units of additional utility for an additional cup of coffee. He gets the same additional utility from 2 cups of tea. So he is willing to give up 2 cups of tea for one cup of coffee and his utility remains constant.

As Michael eats more smores, it is easier to substitute smores for hamburgers.

MRS of tea for coffee is 3/4 and the ratio of prices is 1. Thus, if we draw an x vs y representation of the problem with tea in x and coffee in y we see that the agent's indifference curves are flatter than the budget constraint. Thus, the agent consumes only of good y, i.e., coffee.

Since MRS food for clothing is 5/7, the maximal amount of clothing that he is willing to give up in order to consume 1 unit more of food is 5/7. Then, the maximal amount of clothing that he is willing to give up in order to consume 3 units more of food is 3*5/7=15/7.

25

**3+2**10=85. Then, James can afford this bundle.

The budget constraint is pxx+pyy=Income. Here it is: 10x+15y=30. Simplifying, 2x+3y=6.

The slope of the budget constraint is initially -px/py=-1. Then it becomes -2px/3py. That means is less negative and the line is flatter.

The slope of the budget constraint is -px/py=-10/15=-2/3.

The budget constraint is pxx+pyy=Income. Here, 20x+12y=100. Simplifying we get 10x+6y=50.

-px/py=-2/5.

Is x such that 2x+3*0=25, i.e., 25/2.

The slope of the budget constraint is initially -px/py. Then it becomes -1.5px/1.5py= -px/py. Thus, the slope stays the same. The budget constraint shrinks, because prices increase. Thus, it is not true that the budget constraint will be unchanged.

The slope of the budget constraint is -px/py=-20/12=-5/3.

The y intercept is where Ellie consumes all her income on good y, i.e., Income/py=25/15=5/3. One can also find the equation of the budget constraint and find its intercept.

Jon may be constrained to buy only products available at amazon. Even though his income would increase with the card, his unrestricted utility maximization may require he buys part of the $1000 in commodities not available in Amazon. For instance, he may need this money to help him pay school. Note that getting the card and selling it would give him less than $1000.

Jane's utility function is of the Cobb-Douglass form. Using the formula for utility maximization we find that in College Station Jane consumes (2000,800). Thus her salary in Dallas is 12000. Again using the formula for utility maximization we find that she consumes (1000,1600) in Dallas with the new salary. Thus her utility changes from 1280000000 to 2560000000. Increases 100%.

If B is the maximizer in budget the constraint that passes through B and C, then B is better than any other point inside the triangle determined this budget line. Thus, all the points in the budget line that passes through A and B, that are to the left of B are worse than B. Thus, the agent will never choose them in this budget constraint.

Victor's utility function is of the Cobb-Douglass form. Using the formula for utility maximization for this type of utility, we find that in College Station victor consumes (2500,500). Thus his salary in Dallas is 9000. Using again the formula for utility maximization, we find that he consumes (2250, 565,5) in Dallas with the new salary. Thus his utility changes from 1250000 to 1265625. Increases 1.25%.

The ratio of prices is equal to 10/5=2, the absolute value of the slope of the budget line (y=20/5-10/2x); moreover, MRSxy is equal to 5/2=2.5; then, the agent's indifference curves are steeper than his/her budget constraint; then the agent consumes all her income in good x, i.e., 20/10=2 units.

**,y**) be the optimal consumption of money of the agent when her income is W (here W is positive) and the price of x is twice the price of y. Suppose that prices remain constant but the agent's income increases by 50%. Then,

An inferior good is exactly the opposite of a normal good. Thus a normal good cannot be inferior.

What is the value of W in the curve shown in the figure?

Let Qx(px,py,W) and Qy(px,py,W) be the agent's consumption of x and y when prices are px and py and income is W, respectively. Since the preferences satisfy more is better, consumption is always in the budget line. Thus, px Qx(px,py,W)+py Qy(px,py,W)=W. This means Qx(px,py,W)=W/px- py Qy(px,py,W)/px. This means Qx(px,py,W)=W/px- (py /px) [3W/(px+3py)]=W/(px+3py). From the information in the demand curve we know that 70=W/(1+3py) and 56=W/(2+3py). Thus, 70+210 py=W and 112+168py=W. Then, 70+210 py=112+168py. Then, py=1 and W=70+210=280.

Then the demand of good x for prices px and p'y and income Y is:

The demand of good x for prices px and p'y and income Y is the x component of the utility maximizer for the second budget constraint, i.e., (4,0.6). Thus, Qx(px,p'y,Y)=4.

Then the demand of good x for prices p'x and p'y and income Y is less than 3?

The demand of good x for prices p'x and p'y and income Y is the x component of the utility maximizer for the budget line that has intercepts Y/p'x and Y/p'y. All the points on this budget line are t the south-west of (3,2).

Can we conclude that good x is a Giffen good for some market situation?

A good is Giffen when demand increases when its price increases. This change corresponds here to go from the first budget line to the third budget line. Consumption of x goes from 3 to 1. Thus, we cannot conclude that x is Giffen.

An increase in Y always causes an increase in Qx. The demand for the good is normal for this range of income.

Let px and py be the initial market prices. Before the change Juan is spending (2/3)W in good x. Thus, he is consuming (2/3)W/px of good x. Juan's expenditure in the second market situation is: ypy+xpx/2, where he consumes x and y. If the consumption of x does not decrease when the price of x is cut by half, the total expenditure is more than 2/3W+(2/3)(W/px)(px/2)=W, because Juan would spend more than 2/3W in good y, and at least (2/3)(W/px)(px/2) in good x. Then, in order to buy more than 2/3 of his income in good y when the price of x is cut by half, Juan needs to buy less of x. Since the price of x dropped, x is a Giffen good.

Jane has preferences that satisfy *more is better*. Jane’s demand of good y as a function of prices px and py and income W is given by 3W/8py. What is Jane’s consumption of x when px=1, py=3, and W=32.

Let x

**and y**be Jane's consumption when px=1, py=3, and W=32. Observe that y

**=3W/8py=3**32/8

**3=4. Then, Since (x**,y

**) is on the budget line, then pxx**+pyy

**=W. Then, x**=W/px-(py/px)y*=32/1-(3/1)4=20.

Then the demand of good y for prices p'x and p'y and income Y is less than 2?

The demand of good y for prices p'x and p'y and income Y is the y component of the utility maximizer for the budget line that has intercepts Y/p'x and Y/p'y. All the points on this budget line are t the south-west of (3,2).

Can we conclude that good y is a Giffen good for some market situation?

A good is Giffen when demand increases when its price increases. This change corresponds here to go from the first budget line to the second budget line. Consumption of y goes from 2 to 0.6. Thus, we cannot conclude that y is Giffen.

Since u(x,y)=x+2y then the agent either consumes all his/her income in x or all his/her income in y. This depends on the relation of MRSxy and MRTxy. Thus, we have to know px, py and W to determine demand of x.

We can conclude that:

The consumption of x decreases when the price of x decreases: x is a Giffen good.

We can conclude that:

The consumption of x decreases when the price of x decreases: x is a Giffen good. All Giffen goods are inferior at some market situation.

Then the demand of good x for prices px and py and income Y is:

The demand of good x for prices px and py and income Y is the x component of the utility maximizer for the first budget constraint, i.e., (3,2). Thus, Qx(px,py,Y)=3.

There are Giffen goods.

3W/8py=3

**32/8**3=4.

Economists reserve the label normal, for the demand of a commodity whose consumption increases when income increases.

Jane has preferences that satisfy *more is better*. Jane’s demand of good x as a function of prices px and py and income W is given by W/(px+5py). What is Jane’s consumption of y when px=1, py=3, and W=32.

Let x

**and y**be Jane's consumption when px=1, py=3, and W=32. Observe that x

**=W/(px+5py)=32/(1+5**3)=2. Since (x

**,y**) is on the budget line, then pxx

**+pyy**=W. Then, y

**=W/py-(px/py)x**=32/3-(1/3)2=30/3=10.

W/(px+5py)=32/(1+5*3)=2.

What is the value of py for which the curve shown in the figure was drawn?

Let Qx(px,py,W) and Qy(px,py,W) be the agent's consumption of x and y when prices are px and py and income is W, respectively. Since the preferences satisfy more is better, consumption is always in the budget line. Thus, px Qx(px,py,W)+py Qy(px,py,W)=W. This means Qx(px,py,W)=W/px- py Qy(px,py,W)/px. This means Qx(px,py,W)=W/px- (py /px) [3W/(px+3py)]=W/(px+3py). From the information in the demand curve we know that 70=W/(1+3py) and 56=W/(2+3py). Thus, 70+210 py=W and 112+168py=W. Then, 70+210 py=112+168py. Then, py=1 and W=70+210=280.

Then the value of W for which the demand curve shown is drawn is?

Since 10= W/(3x4), then W=120.

The income effect of a change in price of x from px to px' is?

Positive and reinforces the substitution effect. The total effect is positive and the substitution effect is always positive. Income effect reinforces substitution effect.

Juan consumes 10 units of each good in the initial market situation, because since his preferences satisfy more is better, he spends all his income in goods. When price drops to $4, Juan consumes 14 units of x, because the total effect, which is the summation of substitution effect and income effects, is 4. This means that Juan spends $56 in good x. Since his income is $100, he spends $44 in good y. Since the price of y is $5, Juan consumes 8.8 units of good y after the change. His consumption of y decreases 2.2 units, which is 22%.

The income effect of a price reduction is always positive: an income increase implies a consumption increase.

The income effect of a price reduction may be negative for some price changes. It is not always negative because the Engel curve cannot be always decreasing.

-4.17%=1%/(-.24).

The demand of good x increases when its price increases. Then x is a Giffen good. Giffen goods are always inferior at some market situations. If this happens the demand for the good has a negative income elasticity. It can be different from -1.

Price elasticity measures the relative change in consumption in proportion to the relative change in price. Thus, demand will fall approximately by 3% if price increases by1%.

for each 1% in price increase of whole milk, demand decreases by 0.803 %; for each 1% in price increase of 2% milk, demand decreases by 0.512%. Demand for whole milk is more sensitive to price changes than the demand of 2% milk.

Which demand is more elastic at px=3 (that is, the one with greater price elasticity at px=3)?

The flatter demand at px=3 is more elastic: a proportional change in price of x causes a bigger proportional change in consumption.

Since the derivative is measured in different units of consumption in both countries, then the derivative is not conclusive. Since 1 kg is approximately 2 pounds, then the growth in demand in country A must be at least twice the growth in country B in order to justify the investment in country A. A greater elasticity in A would have picked up this effect.

-0.10274%=1%/(-9.733).

-50%=1%/(-0.02).

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A+B+E+C+F+K.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A-D.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A+B+C.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A-D-G-H.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A.

Depending on Jonny's preferences, he may substitute pizza for tacos, now that tacos are more expensive.

Demand for home improvements is decreasing with income. This means the Engel curve bends backward.

y^2

The income effect of a change in price of x from px to px' is?

Negative and dominates the substitution effect. The total effect is negative and the substitution effect is always positive.

Coffee is a Giffen good for John. An increase of price will always cause a negative substitution effect. Then the income effect of the decrease in income is positive.

By inspection of its Engel curve: demand is normal when the corresponding Engel curves is non-decreasing.

Jane's utility function is of the Cobb-Douglass form. Using the formula for this case x*=4W/(5+4)px.

Jane's utility function is of the Cobb-Douglass form. Using the formula for this case x*=5W/(5+4)px.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A+B+C+E+F.

The CS is the net size of the area determined by a horizontal line at the level of the price and the demand function up to the consumption of the agent: A+B+E.

Price elasticity measures the relative change in consumption in proportion to the relative change in price. Thus, demand will fall approximately by 2.3% if price increases by1%.

Tall Rectangle, not y^2

The income effect of a change in price of x from px to px' is?

Here, Firm A and B are two airlines. If the two airlines must decide simultaneously, which of the following statements is true?

Firm A and B are two airlines. If the two airlines must decide simultaneously, what is the Nash equilibrium prediction for this game if the government offers a $30 subsidy to airlines that serve this route?<