Choose the correct answer and provide a brief justification:

Consider a competitive industry with several firms all of which have the same cost function, c(y) = y2 + 4 for y > 0 and c(0) = 0. The demand curve for this industry isD(p) = 50 - p, where p is the price. The long-run equilibrium number of firms in this industry is

a.4.

b.23.

c.25.

d.46.

e.2.

Brand X is one of many firms in a competitive industry where each firm has a constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase?

a.2 dollars

b.1 dollar

c.0 dollar

d.where n is the number of firms in the industry

e.None of the above.

A firm uses a single input to produce its output, which is sold in a competitive market. It gets quantity discounts on purchases of its input. If it buys x units of the input, the price it must pay per unit of input is+ 3. If it buys no inputs, it doesn't have to pay anything. The firm's produc-tion function is f(x) = 45x - x2. If the price of the firm's output is 1, the profit-maximizing amount of input to buy is

a.21.

b.0.

c.42.

d.31.50.

e.None of the above.