question
How do we derive Demand Curves?
answer
-Need a utility function
-Need a BC
1. Find MRS
2. Find MRT
3. Set MRS = MRT
4. Solve q1 or q2 (Establish Relationship)
5. Substitute into budget constraint
6. Solve for q2 or q1 (opposite q from step 4) to establish one demand function
7. use answer from step 6, substitute into step 4, to establish the other demand function
-Need a BC
1. Find MRS
2. Find MRT
3. Set MRS = MRT
4. Solve q1 or q2 (Establish Relationship)
5. Substitute into budget constraint
6. Solve for q2 or q1 (opposite q from step 4) to establish one demand function
7. use answer from step 6, substitute into step 4, to establish the other demand function
question
Cobb Douglas Utility Function
answer
U(q1,q2) = q1^aq2^1-a
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Budget Constraint
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Y = p1q1 + p2q2
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cobb douglas demand curve
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q1 = a(Y/p1)
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Effects of an increase in Income
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an increase in an individual's income, holding tastes and prices constant, causes a shift of the demand curve.
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Normal Good
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an increase in income causes an increase in demand (a parallel shift away from the origin). vice versa
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Inferior Good
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An increase in income causes a decrease in demand (parallel shift toward the origin). vice versa
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The result of the change in INCOME and the new utility maximizing choice can be depicted three different ways:
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1. income-consumption curve
2. shifts in demand curve
3. engel curve
2. shifts in demand curve
3. engel curve
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Income Consumption Curve (ICC)
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traces out a line connecting optimal consumption bundles, P is constant. Graph is Q1 vs. Q2.
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Engel Curve
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curve relating the quantity of a good consumed to income
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interior solution
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a utility-maximizing bundle that contains positive quantities of both goods
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corner solution
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A utility-maximizing bundle located at the "corner" of the budget constraint where the consumer purchases only one of two goods.
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How do we derive an Engel Curve for good 1?
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For any utility function and if using the optimization method...
1. Find a relationship b/w q1 and q2
-to find an engel curve for good 1: solve for q2
-to find an engel curve for good 2: solve for q1
2. Substitute into the budget constraint and solve for the appropriate q
3. Find the D curve for good 1
4. Solve for Y to determine the Engel curve for good 1
1. Find a relationship b/w q1 and q2
-to find an engel curve for good 1: solve for q2
-to find an engel curve for good 2: solve for q1
2. Substitute into the budget constraint and solve for the appropriate q
3. Find the D curve for good 1
4. Solve for Y to determine the Engel curve for good 1
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How do we derive an Engel curve for good 1? (ALTERNATE METHOD)
answer
1. Derive the demand curve for good 1
2. Solve for Y to find the Engel Curve
2. Solve for Y to find the Engel Curve
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Price Consumption Curve (PCC)
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holding income and the price of Y constant, the PCC for a good X is the set of optimal bundles traced on an indifference map as the price of X varies
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upward sloping Engel Curve (positive)
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normal good
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downward sloping Engel Curve (negative)
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inferior good
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back-ward bending Engel Curve
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when income reaches a certain level the curve will "bend-backward," begin to slope negatively. Demand for that good begins to fall when you reach a certain income level.
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Holding tastes, other prices, and income constant, an increase in the price of a good has two effects on an individual's demand:
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1. Substitution Effect
2. Income Effect
2. Income Effect
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Substitution Effect
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the change in quantity demanded when the good's price increases, holding other prices and consumer utility constant.
e1--->e* movement along the same indifference curve
e1--->e* movement along the same indifference curve
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Income Effect
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the change in quantity demanded when income changes, holding prices constant.
e*--->e2 movement to different indifference curve
e*--->e2 movement to different indifference curve
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When the price of a good increases, the total change in Qd is the sum of...
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the substitution and income effects
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Income Effect with a Normal Good
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Price Increase and Normal Good leads to an income effect of <0
decrease in Qd
decrease in Qd
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Price increases (purchasing power decreases) and the good is normal...
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income effect is neg.
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Price increases and the good is inferior...
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the income effect is positive
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For a price increase...
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the direction of the substitution effect is neg.
when price increase, individuals consume less of it because they are substituting away from the now more expensive good
when price increase, individuals consume less of it because they are substituting away from the now more expensive good
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For a price decrease...
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the direction of the substitution effect is positive.
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Giffen Good
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a good where higher price causes an increase in demand. the increase in demand is due to the income effect of the higher price outweighing the substitution effect.
A giffen good is an inferior good
A giffen good is an inferior good
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income effect <0
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decrease in Qd
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The case of perfect complements has...
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NO SUBSTITUTION EFFECT
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Marshallian (Uncompensated) Demand Curve
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consumer utility is allowed to vary with the price of the good
Ex. utility falls when the price of a good rises
(flatter because the income effect reinforces the substitution effect)
Ex. utility falls when the price of a good rises
(flatter because the income effect reinforces the substitution effect)
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Hicksian (Compensated) Demand Curve
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shows how quantity demanded changes when price increases, holds utility constant.
Curve is steeper because it reflects ONLY the substitution effect (already compensated for the income effect)
Curve is steeper because it reflects ONLY the substitution effect (already compensated for the income effect)
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Deriving Compensated Demand Curve
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...
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Slutsky Equation
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Total Effect = income effect + substitution effect
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Consumer Surplus
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monetary difference b/w the max amount a consumer is willing to pay for the quantity purchased and what the good actually costs
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Demand Function
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Q=a-bP
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Inverse Demand (Willingness to Pay Function)
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P=a/b-(1/b)Q
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Consumer surplus is...
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the area under the inverse demand curve and above the market price up to the quantity purchased by the consumer
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Effect of a Price Change on Consumer Surplus
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if the price of a good rises, purchasers of that good lose consumer surplus
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Compensated Consumer Welfare
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one measure of the harm to a consumer of a price increase is an increase in the consumer's income needed to maintain the consumer's utility.
use compensated demand curve and the expenditure function because both hold utility constant
use compensated demand curve and the expenditure function because both hold utility constant
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Welfare change
answer
...
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Compensating Variation
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amount of money we would have to give a consumer after a price increase to keep the consumer on their original indifference curve
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equivalent variation
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amount of money we would have to take away from a consumer to harm the consumer as much as the price increase did
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Three Measures: CS, CV, and EV
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Relationship b/w these measures for normal goods:
CV>change in CS>EV
CV>change in CS>EV
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Effects of Gov't. Policies on Consumer Welfare
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government programs can alter consumers' budget constraints and thereby affect consumer welfare
-Quota: reduces the number of units that a consumer buys
-Welfare Programs: may produce kinks in budget constraint
-Subsidy: causes a rotation or parallel shift of the budget constraint. either lower prices or provide lump-sum payments to low-income individuals
-Quota: reduces the number of units that a consumer buys
-Welfare Programs: may produce kinks in budget constraint
-Subsidy: causes a rotation or parallel shift of the budget constraint. either lower prices or provide lump-sum payments to low-income individuals
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Private (for-profit) firms
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owned by individuals or other non-governmental entities trying to earn a profit (ex. Toyota, Amazon, Walmart)
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Public Firms
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owned by governments or government agencies (Amtrak, public schools, post office)
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Not-for-profit firms
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owned by organizations that are neither governments nor intended to earn a profit, but rather pursue social or public interest objectives (Salvation Army, Rutgers)
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Legal forms of organization
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-Sole Proprietorship
-General Partnership
-Corporation
-General Partnership
-Corporation
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Sole Proprietorship
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firms owned by a single individual who is personally liable for the firm's debts
-72% of firms, but responsible for 4% of sales
-72% of firms, but responsible for 4% of sales
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General Partnership
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businesses jointly owned and controlled by two or more people who are personally liable for the firm's debts
-10% of firms, but responsible for 15% of sales
-10% of firms, but responsible for 15% of sales
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Corporation
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firms owned by shareholders in proportion to the number of shares or amount of stock they hold
-18% of firms, but responsible for 81% of sales
-Corporation owners have limited liability; they are not personally liable for the firm's debts even if the firm goes into bankruptcy
-18% of firms, but responsible for 81% of sales
-Corporation owners have limited liability; they are not personally liable for the firm's debts even if the firm goes into bankruptcy
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Profit
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difference between revenue (what a firm earns from selling its product) and cost (what it pays for labor, materials, and other inputs)
pi= r-c r=pq
pi= r-c r=pq
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Efficient Production
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to maximize profits, a firm must produce as efficiently as possible.
efficient production means it cannot produce its current level of output with fewer inputs (use an optimal amount of inputs)
efficient production means it cannot produce its current level of output with fewer inputs (use an optimal amount of inputs)
question
The various ways that a firm can transform inputs into the maximum amount of output are summarized in the ...
answer
production function
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Production Function
answer
q = f(L,K)
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Short Run Production (Total Product of Labor)
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period of time so brief that at least one factor of production cannot be varied
capital is fixed
capital is fixed
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Long Run Production
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long enough period of time that all inputs can be varied (NO fixed inputs in LR)
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Marginal Product of Labor
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the additional output produced by an additional unit of labor, holding all other factors constant.
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Average Product of Labor
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ratio of output to the amount of labor employed
= q/L
= q/L
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Marginal Product of Labor Curve intersects Average Product of Labor at...
answer
Average Product of Labor's maximum
MPL > APL before the intersection
APL > MPL after the intersection
MPL > APL before the intersection
APL > MPL after the intersection
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Law of Diminishing Marginal Returns (LDMR)
answer
the law holds that, if a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will eventually become smaller
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Production Isoquant
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graphically summarizes the efficient combos of inputs (labor and capital) that will produce a specific level of ouput
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properties of isoquants
answer
1. the farther an isoquant is from the origin, the greater the level of output
2. they do not cross
3. slope downward
4. must be thin
the shape of isoquants (curvature) indicates how readily a firm can substitute between capital and labor in the production process
2. they do not cross
3. slope downward
4. must be thin
the shape of isoquants (curvature) indicates how readily a firm can substitute between capital and labor in the production process
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Perfect Substitutes Production Function
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A production function where the MRTS is constant at all points. Isoquants are straight lines.
q = x + y
q = x + y
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Fixed-proportions production function
answer
q = min{cereal, box}
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Imperfect Substitutes
answer
...
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Convex Isoquant
answer
Within some range, a declining number of units of one input can be substituted for a unit of the other input, and output can be maintained at the same level. In this case, the MRTS is diminishing as we move down along the isoquant.
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Slope of an isoquant
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shows the ability of a firm to replace one input with another (holding output constant)
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Marginal Rate of Technical Substitution
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slope of an isoquant at a single point.
-tells us how many units of K the firm can replace with an extra unit of L
=change in capital/change in labor
negative ratio of marginal products
-tells us how many units of K the firm can replace with an extra unit of L
=change in capital/change in labor
negative ratio of marginal products
question
MRTS diminishes along...
answer
a convex isoquant.
-the more L the firm has, the harder it is to replace K with L.
slope decreases
-the more L the firm has, the harder it is to replace K with L.
slope decreases
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Returns to Scale
answer
how much does output changes if a firm increases all its inputs proportionately
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constant returns to scale
answer
exhibited in the production function when a percentage increase in inputs is followed by the same percentage increase in output
-doubling inputs, doubles output
f(2L,2K)=2f(L,K)
-doubling inputs, doubles output
f(2L,2K)=2f(L,K)
question
Increasing Returns to Scale
answer
when a percentage increase in inputs is followed by a larger percentage increase in output.
-double inputs, more than double output
f(2L,2K)>2f(L,K)
-double inputs, more than double output
f(2L,2K)>2f(L,K)
question
Decreasing Returns to Scale
answer
when a percentage increase in inputs is followed by a smaller percentage increase in output.
-double inputs, less than double output
f(2L,2K)<2f(L,K)
-double inputs, less than double output
f(2L,2K)<2f(L,K)
question
Varying Returns to Scale
answer
increasing returns to scale, generally for smaller amounts of output
constant returns to scale, generally for moderate output
decreasing returns to scale, generally for larger amounts of output
constant returns to scale, generally for moderate output
decreasing returns to scale, generally for larger amounts of output
question
Returns to Scale Example
answer
q = L^0.5K^0.5, RTS=1, thus it is CRTS
q = L^0.2K^0.9, RTS>1, thus it is IRTS
q = L^0.5K^0.2, RTS<1, thus it is DRTS
q = L^0.2K^0.9, RTS>1, thus it is IRTS
q = L^0.5K^0.2, RTS<1, thus it is DRTS
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