Economics 207
Intermediate Microeconomics
Spring 2007
Dr. Léonie L. Stone
Homework 8
1. Consider an industry with two identical firms selling a homogeneous product. They cannot collude; that is, this
is a competitive oligopoly. The firms have identical and constant marginal (=average) costs of $50.
Demand in the industry is given by: Q = 500 – P
a. Assume that these firms are Bertrand competitors. Find the price, industry output, output of each firm, and profit
of each firm.
P=MC=50. At a price of 50, market demand is 450, so each firm produces 225 and earns a profit of zero.
b. Assume that these firms are Cournot competitors. Find the price, industry output, output of each firm, and profit
of each firm.
Find MR for the first firm: P = 500 – Q1 – Q2, so MR = (500 – Q2) – 2Q1. Set this equal to MC and solve for Q1 to
get the reaction function. Q1 = 225 – 1/2 Q2. Thus (solving the same way), Q2 = 225 – 1/2 Q1. Inserting one
reaction function into the other lets you solve for Q1=Q2= 150, and at a market quantity of 300, P= $200. Profit of
each firm = $22,500.
c. Compare the efficiency of the Bertrand and Cournot models with monopoly (or cartel) and perfectly competitive
market outcomes.
The Bertrand outcome is the same as perfect competition, since P=MC, and so it is equally efficient. If this industry
was a monopoly, output would be 225 and P would be $275, so the Cournot outcome is more efficient than
monopoly (output is greater and thus there is less of a deadweight loss) but less efficient than perfect competition or
the Bertrand outcome.
d. Use your results to show the interaction of the oligopolists as a Prisoner’s Dilemma game. Explain the dominant
strategy and Nash equilibrium.
You can answer this in a number of ways. One is to do it as a Stackelburg leader/follower problem, but if you do,
you have to change the payoffs because there’s not a negative-profit outcome, and so there’s no dominant strategy.
The other way to do it is to think of this as something like Bertrand vs. Cournot; price high vs. price low strategies,
similar to what we did in class.
Any answer that shows a traditional Prisoner’s Dilemma structure and explains how the dilemma relates to
oligopolists is ok.
e. Will oligopolistic industries tend to be relatively efficient (have prices that are close to competitive outcomes) or
relatively inefficient? Explain.
It depends on HOW firms compete.
 Since there a few firms, there is the potential for collusion. In this case, output and price will be close to
the monopoly price, as in the collusive case.
 However, firms may be very competitive, even though there are few. In this case, results will be close to
the competitive outcome, as in the Bertrand case above.
 Intermediate outcomes are also possible, as in the Cournot case.
2. Consider a monopolistically competitive industry, and assume that all firms are absolutely identical.
a. Draw a graph of a firm in short-run equilibrium (making a profit).
Your graph should show a firm making a profit, and should include D, MR, MC, ATC, as well as the current profit-
maximizing price and quantity.
b. Carefully explain and show graphically what will happen to this industry in the long run
The firm is making a positive profit. Thus more firms will enter. This will reduce demand and raise ATC (as
advertising costs rise). This continues until the firm makes a profit of zero. Graph should show this.
c. Show graphically and explain why we know that monopolistically competitive industries are not efficient in
production (P>min ATC) or consumption (P>MC).
This firm/industry is not efficient because:
1. P>MC, so there are more beneficial transactions that could take place (social welfare is not maximized), and
2. P > min ATC, so the firm is not operating at the efficient scale and we are wasting resources (per unit costs are
higher than they need to be).
d. Show graphically and explain why it is unlikely that monopolistically competitive industries will produce the
optimal amount of variety.
You need to draw graphs as we did in class for this. Consumer surplus increases with the number of varieties, but
at a decreasing rate. Firm profits decrease with number of firms. Total profits may increase as firms begin to
enter, but will eventually decrease with number of firms. Thus social welfare (=CS + profit in this case) increases
at a decreasing rate, and will eventually decrease. The optimal point for society is maximum social welfare, but
firms will enter until profits equal zero. It is unlikely (or merely coincidental) if this is the optimal number of firms
(since firms care only about profit and not CS or SW).
3. Advertising is a prisoner’s dilemma-type game. Suppose that Coke and Pepsi are trying to decide whether to
advertise during the Superbowl. If both advertise, they maintain the same market shares, but the advertising costs
money, so the payoff for each is $1 million. If neither advertises, they still maintain the same market share, but
don’t have to pay for advertising, so each gains $10 million. However, if one advertises and the other does not, that
firm gains $20 million and the other loses $5 million.
a. Draw this game in a payoff matrix, and explain the dominant strategy for each firm and the Nash equilibrium of
the game.
Coke
Advertise
Don’t
Pepsi
Advertise
(1, 1)
(-5, 20)
Don’t
(20, -5)
(10, 10)
The dominant strategy for each firm is to advertise (because that is better no matter what the other firm
does, you are better off advertising). Thus the outcome is (1, 1), or both firms advertise; it is a Nash
equilibrium because, given what the other player did, neither firm would want to change strategies.
b. Carefully explain why games of this type are called “prisoner’s dilemmas.” That is, what is the dilemma?
It’s a dilemma because you’d be best off, in this case, if neither firm advertises. But there’s a temptation to cheat, and
because of that, if you’re sure that the other firm won’t advertise, that’s exactly what you should do. And if you think
that the other firm WILL advertise, you should still do that… it’s a dominant strategy. So firms wish to be where they are
collectively best off, but the only equilibrium is where they are collectively worst off.