Question

20. Output for a simple production process is given by Q = K2L, where K denotes capital, and L denotes labor. The price of capital is $30 per unit and capital is fixed at 5 units in the short run. The price of labor is $20 per unit.

a. The total cost of producing 100 units of output is _____.b. The variable cost of producing 100 units of output is ____.

21.Determine whether the production function Q = K3/2L2 exhibits decreasing returns to scale, increasing returns to scale, or constant returns to scale.

SHOW WORK

Answer 1

Question 20

(a)

Production function is as follows -

Q = K2L

Output produced, Q = 100 units

Capital, K = 5 units

Q = K2L

100 = 5 * 2L

10L = 100

L = 100/10 = 10 units

Calculate the total cost of producing 100 units -

Total cost = [Units of capital * Price of capital] + [Units of labor * Price of labor]

Total cost = [5 * $30] + [10 * $20] = $150 + $200 = $350

Thus,

The total cost of producing 100 units of output is $350.

(b)

Quantity of capital is said to be fixed. So, capital is a fixed factor while the labor is the variable factor.

Total units of labor used to produce 100 units = 10 units

Price of labor = $20 per unit

Calculate the variable cost of producing 100 units -

Variable cost = Units of labor * Price of labor = 10 * $20 = $200

Thus,

The variable cost of producing 100 units of output is $200.