Question

1. Suppose that a firm’s short-run total cost function is STC= 0.1q² + 4q +100. Will the producer surplus at P=$15 be $302.5?
2. Suppose that a firm is price taker. If the price is equal to marginal cost, then the profit is being maximized.
3. If a firm wished to maximize profit, it will always reduce output if wage rates rise.
4. If a competitive firm's price is below its marginal cost, an increase in production will usually decrease profits.
5. A profit‑maximizing firm will never hire that quantity of a factor of production for which that factor has an increasing marginal productivity because it would not be maximizing profits.

Answer 1

a.

TC = 0.1q^2 + 4q +100

TVC = 0.1q^2 + 4q

TFC = 100

MC = 0.2q +4

P = $15

At equilibrium P = MC

15 = 0.2q + 4

q = 55

When q=0, MC = $4

When q = 55, MC = $15

Hence, producer surplus is: 0.5*(15-4)*(55-0) = 302.5

Thus, producer surplus is $302.5

b.

Yes, if the firm is price taker, the equilibrium is given by P = MC and the profit is considered maximized.

c.

If wage rate rate rises, the MC increases and hence, there is a leftward shift of the supply curve.

So, given the price, for the profit maximization, the firm will reduce output when wage rate increases.

d.

When competitive firm's price is lower to marginal cost, it costs more to the firm to increase the production by 1 unit, than the amount earned from this 1 unit of additional production.Hence, the firm is said to be not profit-maximizing. An increase in production will usually decrease profits

e.

A profit-maximizing firm would hire that quantity of factor of production for which the ruling wage rate is equal to the marginal physical productivity.

The factor of production need to have downward sloping marginal productivity as per the law of diminshing marginal productivity in the short-run, for the firm to maximize its profit.

But, when factor of production has an increasing marginal productivity, it means, the firm hiring would never be maximizing its profit.

So, it will not hire that quantity of a factor of production for which that factor has an increasing marginal productivity