Economics 331
Fall 2007
Name: _________________________________
EXAM #3
Make sure you justify all calculations, and that any diagrams you draw are clear and properly labeled.
Please write neatly.
I.
Short Answer (42 points)
1. True or False. If the demand curve facing a monopolist is linear and downward sloping, then the imposition of
a per unit production tax will increase the price by the amount of the tax. Illustrate your answer with a diagram.
FALSE. THE IMPOSITION OF THE TAX WILL INCREASE PRICE BY LESS THAN THE AMOUNT
OF THE TAX. IF YOU ASSUMED THAT THE MARGINAL COST WAS CONSTANT THEN THE
PRICE WOULD INCREASE BY ½ THE TAX.
2. True or False. Since firms in a monopolistically competitive industry produce at an output level where price is
greater than marginal cost and average total costs are not minimized, total welfare is less than under perfect
competition. Provide an explanation with your answer.
FALSE. ALTHOUGH A MONOPOLISTICALLY COMPETITIVE INDUSTRY IS INEFFICIENT IN THE
SENSE THAT P>MC AND AC NOT MINIMIZED, WELFARE IS NOT NECESSARILY LOWER THAN
UNDER PERFECT COMPETITION. SINCE FIRMS PRODUCE DIFFERENTIATED PRODUCTS THAT
BETTER MATCH CONSUMER TASTES, CONSUMERS ARE WILLING TO PAY MORE FOR THE
PRODUCTS THEY BUY.
NOTE: I’M NOT SURE WHAT HAPPENED ON THIS PROBLEM SINCE ONLY 2 OF YOU REALIZED
THAT I WAS ASKING ABOUT AN MC MARKET, AND NOT JUST A PLAIN MONOPOLY.
3. Consider two firms that compete in output. Firm 1’s marginal cost is lower than Firm 2’s marginal cost.
However, Firm 1’s fixed cost is greater than Firm 2’s fixed cost. Assume that both firms produce a positive amount
of output (neither firm needs to shut down). True or False. Firm 1 will always produce more output than Firm 2.
Provide an explanation with your answer.
TRUE. A FIRM’S OUTPUT DECISION IS INDEPENDENT OF THE LEVEL OF FIXED COSTS. EACH
FIRM MAXIMIZES PROFIT WHERE MR = MC, SO THE FIRM WITH LOWER MARGINAL COSTS
WILL PRODUCE A HIGHER LEVEL OF OUTPUT.
COULD ALSO HAVE SHOWN THAT UNDER COURNOT COMPETITION: qi* = (a-ci)/3b.
THEREFORE, IF ci < cj, FIRM i WILL ALWAYS PRODUCE MORE.
4. Consider two firms that produce differentiated products and compete in prices. Suppose one of those firms is
able to reduce its marginal cost. On a best response function diagram show what happens to the price equilibrium.
Provide a brief explanation.
YOU GUYS HAVE TO READ THE QUESTION PROPERLY. HALF OF YOU DREW THE REACTION
FUNCTION DIAGRAM FOR COURNOT COMPETITION. IN THIS CASE, THE BEST RESPONSE
FUNCTIONS HAVE POSITIVE SLOPES AND THE REACTION FUNCTION FOR THE FIRM WHOSE
MARGINAL COST FALLS WILL SHIFT TO THE LEFT, RESULTING IN A LOWER PRICE
EQUILIBRIUM.
5. Monopolists are said to operate with X-inefficiency. What does this mean and state two reasons why a profit
maximizing monopolist would operate with X-inefficiency.
X-INEFFICIENCY OCCURS WHEN THE FIRM PRODUCES A LEVEL OF OUTPUT AT A PER UNIT
COST GREATER. TWO REASONS: 1. NO COMPETITORS TO COMPARE ITSELF TO. 2.
SEPARATION OF OWNERSHIP AND MANAGEMENT LEADS TO ACTIONS THAT ARE NOT
PROFIT MAXIMIZING.
6. Although supermarkets are not monopolies, they do have the ability to markup prices above marginal cost. For
example, the markup of price above marginal cost as a percentage of price is 35% for candy but less than 10% for
baby food. What can you infer about the elasticity of demand for candy and baby food? Explain how you know.
USING THE LERNER INDEX: (P-C)/P = -1/e: CANDY: e = -2.86
BABY FOOD: e = -10
THEREFORE, THE DEMAND FOR CANDY IS LESS ELASTIC THAN FOR BABY FOOD.
II. Calculation Problem (58 points): Make sure you solve each part completely and make sure show your work.
1.
Suppose the demand for steel is given by:
P = 1,000 – 2Q.
Steel is produced with a constant marginal cost of $100 per unit and no fixed cost.
a. Suppose there are three firms in the industry. Therefore, Q = q 1 + q2 + q3. If the firms are Cournot competitors,
how much steel does each firm produce? How much profit does each firm earn?
Profit for Firm i: Πi(qi q-i) = (1000 – 2qi – 2q-i) x qi – 100qi
dΠ/dqi = 1000 – 4qi – 2q-i – 100 = 0
w/ q-i = (n-1)qi = 2qi since n = 3
1000 – 4qi – 4qi – 100 = 0
→ 8qi = 900
→
P = 1000 – 2 x 337.50
qi = 112.5
and Q = 337.5
→ P = $325
Πi = (325 – 100) x 112.5 → Πi = $25,312.50
b. Suppose two of the three firms merge and form a single firm. How much steel does the new merged firm make
and how much does the other firm make? How much profit does each firm earn?
We can use dΠ/dqi = 1000 – 4qi – 2q-i – 100 = 0 from before. Now q-i = (n-1)qi = qi since n = 2. Therefore:
1000 – 4qi – 2qi – 100 = 0
6qi = 900
→
P = 1000 – 2 x 300
Πi = (400 – 100) x 150
qi = 150
→ P = $400
→ Πi = $45,000
→
Q = 300
c. Compare your answers to (a) and (b). What seems odd about the outcome after the merger compared to before
the merger.
Two things you should have mentioned: i) the total output of the merged firm (150) is less than the combined
output of the two firms prior to the merger (112.5 + 112.5) (you could also have discussed this in terms of
market share) and ii) the total profit of the merged firm (45,000) is less than the combined profit of the two
firms prior to the merger (25,312.50 + 25,312.50). Therefore, the merger makes them worse off than they
were before the merger, and that is odd.
d.
From part (b): Suppose the two firms decide to collude. How much profit will each firm earn now?
The firms will now act like a monopoly:
Π(Q) = (1000 – 2Q) x Q – 100Q
dΠ/dQ = 1000 – 4Q – 100 = 0
Q = 225 or qi = 112.5
P = 1000 – 2 x 225 = $550
Π = (550 – 100) x 225 = $101,250 or $50,625 per firm.
e. Why is this outcome not sustainable in a one-period setting? Explain and illustrate your answer on a best
response function diagram. Make sure all the points are clearly labeled.
See your notes for the diagram.
Suppose that firm 1 believes the other firm will abide by the agreement. Therefore, the best response for firm
1, is to increase their production to 168.75 (qi* = 225 – ½ x 112.5). They would want to move from the
cooperative point to the point on their best response function when the other firm produces 112.5. But both
firms have the same incentive to renege on the agreement. Therefore, the cooperative agreement is not
sustainable.