Question

A firm uses a single input to produce a good according to the production function q = f(x) = 4x(1/2), where x is the input. The good sells for $4 per unit, and the cost of input x is w.

a. Create a function showing the firm’s profit as a function of x and w.
b. Find the profit maximizing amount of x as a function of w. What is the profit maximizing amount of output?
c. Will this firm always make a positive economic profit?

Answer 1

a)

Total revenue is given as

TR=P*f(x)

Total Cost is given as

TC=wx

Profit is given as

b)

Differentiate profit with respect to x

Set to find the input quantity where profit is maximized

(Profit maximizing value of x in terms of w)

Profit maximizing output is given as

c)

Set <0 for find that value of x where profit is non positive

We can say that firm will not make a positive profit if