Question

6. A purely competitive firm has a single variable input L (labor), with the wage rate Wo per period. Its fixed inputs cost the firm a total of Fdollars per period. The price of the product is Po. (a) Write the production function, revenue function, cost function, and profit function of the firm,

Answer 1

(a) Production function:Q=f(L)

Revenue function=R=P₀Q=P₀f(L)

Cost function:C=W₀L+F

Profit function:π=R-C=P₀f(L)-W₀L-F

(b) The first order condition for maximization of profit is:

The first order condition of maximization of profit involves that the first derivative of profit function must be equal to zero.

dπ/dL=P₀f'(L)-W₀=0, or P₀f'(L)=W₀

The value of the marginal product must be equated with the wage rate.

(c) The economic circumstance that ensures profit is maximized rather minimized is:

d²π/dL²=P₀f''(L)

If f''(L)<0 (diminishing MPPL) then we would be sure that profit must be maximized by L*.