The production function for a firm is Q = min(K, 4L), and the price per unit of
ID: 442546 • Letter: T
Question
The production function for a firm is Q = min(K, 4L), and the price per unit of capital is $40 and the price per unit of labor is $60.
a. What is the minimum cost of producing 20 units of output?
b. Using an isoquant and isocost line, illustrate the cost-minimizing input choice of the firm producing 20 units of output.
c. How would your answer to (a) change if the firm’s production function were instead given by Q= K + 4L?
d. Explain how the two production functions (initial and part c) differ conceptually? What do they imply about the way in which L and K are used?
Explanation / Answer
1.
Q = min(K, 4L)
It means that to produce 1 unit of output 1 unit of capital and ¼ unit of labor is reuired
Thus to produce 20 units of output minimum 20 units of capital and 20/4 =5 units of labor is required
Thus total minimum cost for 20 units of output =40*20+60*5=$1100
2.
Isocost line
TC=40K+60L
Isoquant line
Q=K+L/4
3.
Firm production function=K+4L
That is to produce1 unit of output, 1 unit of capital and 4 unit of labor is required
Thus to produce 20 units of output minimum 20 units of capital and 20*4=80 units of labor is required
Thus total minimum cost for 20 units of output =40*20+60*80=$5600
4.
The first production function says that to produce 1 unit of output, 1 unit of capital and ¼ unit of labor is required and the production function defined in 3 says that to produce 1 unit of output 1 unit of capital and 4 unit of labor is required
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