Question

Define and draw the firm’s production function. 6b. What determinants allow a firm to expand. 6c. Explain why a profit maximizing competitive firm would produce up to the point where price equals marginal costs.

Answer 1

A production function represents a technological relation between a physical input such as a labor and output of the goods. Below is the production function diagram -

b. Below are the determinants that allow a firm to expand -
1. Productivity of labor: As productivity of labor improves, then firms are able to produce more output with same amount of labor.
2. Resources: As resource size - capital stock or labor stock increases the overall production possibilities also increase for the firm.

c.

Profit, π = TR - TC where TR is total revenue and TC is total cost.

TR = p*Q where p is competitive firm's price that is taken as given.

TC is total cost of the firm which is a function of the output level (Q).

π = p*Q - C(Q)
The profit maximizing output level will be determined by the first order condition:
dπ/dQ = 0
p - C'(Q) = 0
p = C'(Q), where C'(Q) is marginal cost of production (MC).
That is, profit maximizing output level is the one where p = C'(Q).

If P> MC, then firm can increase its overall profit by producing more output.
If P<MC, then also firm can increase its overall profit by reducing its output.

Hence, the firm maximizes its profit where p = MC.