Question

Consider the market for ice cream. Suppose that this market is perfectly competitive. The cost structure of the typical ice cream producer is as follows. Average total cost is equal to ???(?)=50?+12?, average variable cost is equal to ???(?)=12?, and marginal cost is equal to ??(?)=?.

a.) Give a formula for the typical ice cream producer’s average fixed cost ???(?). What is the typical ice cream producer’s total fixed cost?

b.) How many ice cream cones will each producer sell in a long-run equilibrium in the market for ice cream?

c.) What is the long-run market equilibrium price for ice cream?

Suppose that demand for ice cream cones is given by ??=403−1300×??.

d.) How many firms will operate in the market for ice cream in a long run equilibrium?

Now, suppose that a new scientific study comes out that shows that soil pollution from rock salt (a key input for making ice cream) is extremely hazardous to human health. In response, the government decides to impose harsh re-zoning restrictions on any land once used for making ice cream. This reduces the market rent for land used to make ice cream, which in turn lowers the opportunity cost of operating an ice cream factory. This reduction in the opportunity cost of capital causes the total fixed cost of ice cream production to fall to 32, but there is no change to variable cost.

e.) Give formulas for the typical ice cream producer’s new average total cost curve ???(?) and marginal cost curve ??(?).

f.) If the market for ice cream cones starts in its initial long run equilibrium, with the number of firms computed in d.), how much profit will ice cream firms make in the short run?

g.) How many firms will operate in the market for ice cream in the new long-run equilibrium?

Answer 1

a) Since some of the values of the functions are missing, I am writing the formulae down. In case of queries, please comment with the correct functions

Average fixed cost = Average Total cost - Average variable cost

Total fixed cost = Average fixed cost * Total quantity

b) In the long run equilibrium, the firm will produce at the point where Average total cost is minimised. Hence, take the derivative of ATC with respect to q and equate it to 0 and the calculated q value will be the long run supply of the producer

c) Once you calculate the q from part b, long run price will be equal to marginal cost and q would be put equal to the one calculated in part b

d) By substituting the price in the market demand function, one can calculate the total market quantity. Divide this total market quantity by quantity produced by each firm( calculated in part b), that will be the total number of firms that will exist in the market