Econ 302 Homework 4 BC/C++

Java Python 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