2. Refer to the following figure. The price of capital is $70 per unit 200 1so 1

Question

2. Refer to the following figure. The price of capital is $70 per unit 200 1so 130 Q 1.200 100 Q-800 60 Q-,400 250 Units of labor 0 1 20 375 500 a. What is the price per unit of labor? How many units of labor should the firm use in order to produce 400 units of output at the least cost? b. c. The minimum cost of producing 800 units is d. How many units of capital should the firm use to produce 800 units of output at the least cost? What is the minimum cost of producing 400 units of output? What is the minimum cost of producing 1,200 units of output? How many units of labor should the firm use to produce 1,200 units of e. f. g. output at the least cost? h. What is the MRTS at each cost minimizing point?

Explanation / Answer

Given price of capital is $70 per unit

a) As the budget contraint on axis gives the total expenditure of producer, we will have 70*100 = $7000 total expenditure therefore price per unit of labor will be 7000/250 = 28

b) It is given that firm is optimizing at 60 units of capital therefore in order to produce 400 units at least combination the firm should do 60*70 + 28*100 as total expenditure is 7000 and expenditure on capital is 60*70 thus 4200 therefore we have 7000-4200 = 2800 as price of labor is $28 per unit we will have 2800/28 = 100 units of labor in order to producer 400 units of output at the least cost.

c) The minimum cost of producing 800 units will be found using the x-axis therefore, we will have 375*28 where we have 375 units of labor and $28 as price of labor.

d) To producer 800 units the firm should have 70 units capital as we have 120*28 + 70*x = 10500 solving for x

10500 - 120*28 = x*70
10500 - 7140 = x*70
3360 = x*70
3360/70 = x
48 = x

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