Suppose we have a competitive industry with n number of firms. Each firm has an

Question

Suppose we have a competitive industry with n number of firms. Each firm has an identical cost function, c(y) = y^2 + 1 for y > 0 and c(0) = 0 for y = 0. Notice that for each firm fixed costs F = 0, because c(0) = 0, but the "+1" component of the cost function does not vary with y. What type of factor could cause this "+1" component of the cost function? Notice that since F = 0 for each firm, AVC(y) = AC(y). Thus the shutdown point will equal the break even point. Calculate the price and individual firm's output for this point. Write the individual supply as a function of output, p = ftn(y). (This is actually called the inverse supply function.) Do not worry about supply below the shutdown/break-even point; simply give me the equation for y > 0. Using your answer from part (c), rewrite the individual supply in the more standard form, as a function of price, y = ftn(p), (often denoted S_i(p)). What is the supply curve for the industry/market? Write this as S(p). Recall there are n firms, so this equation will be a function of n. Now suppose the demand for the industry (market demand) is given by D (p) = 52 - p. In the long run, how many firms will be in this industry? To calculate this, use our equilibrium condition (S=D) and the price that you know must be associated with the long run equilibrium, to solve for n.

Explanation / Answer

1.a

“+ 1” component of the cost function could be indirect cost. This type of cost doesn’t vary with the production unit “y”, but very important. Examples are salary of employees, machine lubricants, repairs and maintenance, etc.

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