Econ 302
Homework 4 B
1. (20 total points) Suppose the demand for a product is given by QD = 50 - (1/2)P.
a) (10 points) Calculate the Price Elasticity of Demand when the price is $60.
b) (5 points) What price should the firm charge if it wants to maximize its revenue?
c) (5 points) Over what price range is demand elastic?
2. (30 points) Complete the following table:
|
Quantity
|
FC
|
VC
|
TC
|
AFC
|
AVC
|
ATC
|
MC
|
|
0
|
30
|
0
|
30
|
------
|
------
|
------
|
------
|
|
1
|
30
|
20
|
50
|
30
|
20
|
50
|
20
|
|
2
|
30
|
35
|
65
|
15
|
17.5
|
32.5
|
15
|
|
3
|
30
|
45
|
75
|
10
|
15
|
25
|
10
|
|
4
|
30
|
75
|
105
|
7.5
|
18.75
|
26.25
|
30
|
|
5
|
30
|
120
|
150
|
6
|
24
|
30
|
45
|
3. (30 total points) Suppose a firm’s production function is given by Q = L1/2 *K1/2 . The Marginal Product of Labor and the Marginal Product of Capital are given by:
MPL = 2L1/2/K1/2, and MPK = 2K1/2/L1/2.
a) (12 points) If the price of labor is w = 36, and the price of capital is r = 64, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q = 36?
Q=L^1/2*K^1/2
replace K with 9L/16
Q=L1/2*(9L/16)^1/2
Q=9L/4
4Q/9=L
b) (12 points) What is the firm’s Total Cost function TC(Q)?
replace L with 16K/9
Q=(16k/9)^1/2*K^1/2
Q=16K/3
3Q/16=K
Total cost(TC) = price of labor (w) x units of labor(L) + price of capital (r) x units of capital(K)
TC for producing Q level of output
TC= 36x(4Q/9)+64x(3Q/16)
TC= 16Q+12Q
TC=28Q
c) (6 points) What is the firm’s marginal cost of production?
Marginal Cost= delta TC/ delta Q
TC=28Q
delta TC= change in total price
delta Q=change in Quantity
TC=28Q Marginal cost=28
4. (20 total points) Suppose in the short run a perfectly competitive firm has variable cost = 3q2, and MC = 6q where q is the quantity of output produced. Also, the firm has fixed cost F = 3200.
a) (8 points) If the market price of the product is 198, how much output should the firm produce in order to maximize profit?
b) (6 points) How much profit will this firm make?
c) (6 points) Given your answer to b), what will happen to the market price as we move from the short run to the long run?