Microeconomics Homework #3
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Microeconomics
Homework #3, due Dec. 23
Monopolistic Competition
Q1: For each of the following characteristics, say whether it describes a perfectly competitive firm, a monopolistically competitive firm, both, or neither.
(a) sells a product differentiated from that of its competitors
(b) has marginal revenue less than price
(c) earns economic profit in the long run
(d) produces at the minimum of average total cost in the long run (e) equates marginal revenue and marginal cost
(f) charges a price above marginal cost
Q2: For each of the following characteristics, say whether it describes a monopoly firm, a monopolistically competitive firm, both, or neither.
(a) faces a downward-sloping demand curve
(b) has marginal revenue less than price
(c) faces the entry of new firms selling similar products
(d) earns economic profit in the long run
(e) equates marginal revenue and marginal cost
(f) produces the socially efficient quantity of output
Perfect Competition
Q3: Consider a firm in a perfectly competitive industry with total cost function TC(q) = 50 + 
q2 , where q is the individual firm’s quantity produced. The market demand curve for this product is given by QD = 120 − P , where Q is the total quantity of the product, summed over all firms. Currently, there are 9 firms in the market.
(a) Find the individual firm’s fixed cost, variable cost, and average total cost as a function of
.
(b) What quantity minimizes average total cost?
(c) Give the equation for the invidividual firm’s supply curve.
(d) Give the equation for the market supply curve in the short run, when the number of firms is fixed.
(e) What is the equilibrium price and quantity for this market in the short run? (f) In this equilibrium, find each firm’s quantity produced and profit or loss.
(g) In the long run with free entry and exit, what is the equilibrium price and quantity in this market?
(h) In the long run, how many firms are there in the market?
Monopoly
Q4: Suppose a monopolist owns the only well in a town, with the following demand and cost curves:
❼ Demand: P = 70 − Q
❼ Marginal Revenue: MR = 70 − 2Q
❼ Marginal Cost: MC = 10 + Q
(a) What is the profit-maximizing quantity and price?
(b) The town government is considering imposing a price ceiling that is 10% lower than the monopoly price in part (a). What quantity would be demanded at that price? What quantity would a profit-maximizing monopolist choose to produce under this condition? (Hint: graph the marginal revenue and marginal cost curves under the price ceiling). How large is the shortage?
(c) Now suppose that the government reduces the price ceiling to 50% of the monopoly price in part (a). What is the quantity demanded and the quantity produced? How large is the shortage?
Consumer Choice
Q5: Jacob consumes two goods: milk and cookies.
(a) In year 1, Jacob earns 100, milk costs 2 per unit, and cookies cost 4 per unit. Draw Jacob’s budget constraint.
(b) Now suppose that all prices increase by 10 percent in year 2 and that Jacob’s salary increases by 10 percent as well. Draw Jacob’s new budget constraint. How would Jacob’s optimal combination of milk and cookies in year 2 compare to his optimal combination in year 1?
2023-01-05