question

C/q

answer

how do you find average cost?

question

write out the long run production function

substitute 5 for K and simplify

substitute 5 for K and simplify

answer

you're given the long run production function

K = 5

how do you solve for the short run production function

K = 5

how do you solve for the short run production function

question

write out the short run production function

find the derivative

find the derivative

answer

how do you find the marginal product of labor?

question

q/L (q = the short run production function)

answer

how do you find the average product of labor

question

write out the short run production function

substitute 4 for L and solve for q

substitute 4 for L and solve for q

answer

if asked to find a quantity given a certain number of workers how do you solve?

example:

how many oil changes would a firm sell if they have 4 workers?

example:

how many oil changes would a firm sell if they have 4 workers?

question

2 ways to solve:

1) find the average product of labor for the current amount of workers given

find the average product of labor for one less than that number of workers

2) take the derivative of the average product of labor

next using the derivative equation plug in the original number of workers

next using the derivative equation, plug in one less number of workers

if this number is higher than the original number of workers this means the APL goes up when number of workers goes down

1) find the average product of labor for the current amount of workers given

find the average product of labor for one less than that number of workers

2) take the derivative of the average product of labor

next using the derivative equation plug in the original number of workers

next using the derivative equation, plug in one less number of workers

if this number is higher than the original number of workers this means the APL goes up when number of workers goes down

answer

if a company had to lay off one worker what happens to the average productivity of the remaining workers?

question

substitute (5) for L

substitute (10) for K

solve for the quantity = 6.60

substitute (10) for K

solve for the quantity = 6.60

answer

L .6 K .4 (K = 10) (L = 5)

short run prod. function = 2.51L .6

how many products can a firm provide with the given inputs?

short run prod. function = 2.51L .6

how many products can a firm provide with the given inputs?

question

C = wL + rK

the cost equals the wage x labor + price of capital x capital

the cost equals the wage x labor + price of capital x capital

answer

how do you find the total cost or production?

question

r x K (rK)

the price of capital x the number of capital given

if K = 10 and r = 20

fixed cost = rK = (20)10 = 200

the price of capital x the number of capital given

if K = 10 and r = 20

fixed cost = rK = (20)10 = 200

answer

how do you calculate the fixed cost?

remember that in the short run production function capital (K) is fixed because you're given a number for K

Labor (L) could be any number

remember that in the short run production function capital (K) is fixed because you're given a number for K

Labor (L) could be any number

question

L is variable

wages x labor (wL)

wages x the number of workers

if w = 5 and L = 10

variable cost = 5 x 10 - 50

wages x labor (wL)

wages x the number of workers

if w = 5 and L = 10

variable cost = 5 x 10 - 50

answer

how do you calculate the variable cost?

which is variable L or K?

which is variable L or K?

question

fixed cost/quantity = FC/q

fixed cost = rK

fixed cost = rK

answer

how do calculate AVERAGE fixed cost?

question

variable cost/quantity = VC/q

VC = wL

VC = wL

answer

how do you calculate AVERAGE variable cost

question

C/q = total cost/q

to calculate total cost = FC + VC = rK + wL

to calculate total cost = FC + VC = rK + wL

answer

how do you calculate average cost?

question

given: K.4 L.7

add the exponents

if > 1 means increasing returns to scale

if < 1 means decreasing returns to scale

if = 1 means a constant returns to scale

add the exponents

if > 1 means increasing returns to scale

if < 1 means decreasing returns to scale

if = 1 means a constant returns to scale

answer

how would you determine the returns to scale (RTS) given a production function?

question

take the derivative for L

answer

how do you solve for the marginal product of labor?

question

given K.4 L.7

the exponent for L is always "a"

the exponent for K is always "b"

regardless of the order they appear

shortcut = a (q/L) = .7 (q/L)

the exponent for L is always "a"

the exponent for K is always "b"

regardless of the order they appear

shortcut = a (q/L) = .7 (q/L)

answer

what is the shortcut method to solve for the marginal product of labor?

question

take the derivative for K

answer

how do you solve for the marginal product of capital?

question

b(q/L)

remember "b" is always the exponent for K

regardless of the order they appear

for K.4 L.7 = .4 (q/L)

remember "b" is always the exponent for K

regardless of the order they appear

for K.4 L.7 = .4 (q/L)

answer

what is the shortcut method to solve for the marginal product of capital?

question

-MPL (marginal product of labor)/MPK (marginal product of capital)

OR

- a/b (K/L)

OR

- a/b (K/L)

answer

how do you solve for the MRTS (marginal rate of technical substitution)?

question

wL + rK = C

answer

what is the cost equation?

question

take the derivative of cost

= wL + rK

= wL + rK

answer

how do you find marginal cost?

question

revenue - cost

= (price x quantity) - cost

if given a cost function use that for cost

= (price x quantity) - cost

if given a cost function use that for cost

answer

what is the profit equation?

question

K ^L^ = q (quantity)

^ = a for L and b for K

^ = a for L and b for K

answer

what is a production function?

question

example:

cost = 10L + 40K

constraint = 10 = k5L5

(for lagrangian set this to zero = 10 - K5L5)

set up lagrangian:

cursive L (L, K, cursive L) = 10L + 40K +

cursive L(10 - K5L5)

cost = 10L + 40K

constraint = 10 = k5L5

(for lagrangian set this to zero = 10 - K5L5)

set up lagrangian:

cursive L (L, K, cursive L) = 10L + 40K +

cursive L(10 - K5L5)

answer

how do you set up lagrangian equation

question

remember that the production function =

K (b exponent) and L (a exponent)

shortcut = aK/bL = w/r

K (b exponent) and L (a exponent)

shortcut = aK/bL = w/r

answer

how do you use the shortcut method to solve for L and K?

question

take the profit equation = revenue - cost

and take the derivative and set equal to zero

example:

p x q - (800 + 4q +0.25q2) For price = 34

= 34q -800 -4q - 0.25q2

= 30q -800 - 0.25q2

and take the derivative and set equal to zero

example:

p x q - (800 + 4q +0.25q2) For price = 34

= 34q -800 -4q - 0.25q2

= 30q -800 - 0.25q2

answer

how do you find the profit maximizing output (quantity)?

question

profit = revenue - cost

= (price x quantity) - (wL + rK)

= (price x quantity) - (wL + rK)

answer

how do you find profit?

question

...

answer

how do you find consumer surplus

question

revenue - variable costs

answer

how do you find producer surplus?