Question

4. Short questions: A firm has production function f(K, L) = 2L + 3K. The price of L is w and the price of K is r. Derive the cost function of the firm. a. b. A firm in a competitive industry takes account of the fact that the demand curve it faces has a negative slope. True or false? C. A profit-maximizing firm continues to operate even though makes negative profits. It sells its product at a price of $100. Which of the following statements are certainly true? o Marginal cost is everywhere increasing. o Average fixed cost is less than $100. o Average total cost is more than $100. o Average variable cost is less than $100. O Marginal cost is decreasing.

Answer 1

a. given production function is q= 2L+3K and from the tangency condition

MPL/MPK =w/r

MPL=2, MPK=3

w/r=2/3

the total cost function is wL+rK

from tangency condition

TC= 2L+3K

b. A firm in a perfectly competitive industry would have a perfectly elastic demand curve which is a horizontal line along the price which is determined by the industry market forces of demand and supply curves. The firms are price takers and hence P=MR sis the constant demand in this case.

the correct option is False

c. A profit-maximizing firm operates even though the firm is earning negative profits till it can cover variable costs implies price is above average variable cost. The price given is 100 and the average variable cost is less than 100

the correct option is (d)