Midterm #3 (100pts)
Name:
Monopolistic competition (#1 - 20pts)
1. (original) Cournot model with free entry can be thought of as a model of monopolistic competition with
representative consumer. Inverse demand is given by P  24  2Q , n firms compete by producing
undifferentiated products. Each firm’s cost function is given by C  Q   8  2Q . There is free entry.
a. Find the number of rims in the long run free entry equilibrium. Show your calculations (hint: it is
either 4, 5, or 6)
Competitive quantity from the inverse demand is 2=24-2Q -> Q=11.
n
4
q (firm) Q (market)
2.2
8.8
P
AC
Variable Profit
profit
6.4
5.636364
9.68
1.68
Q(n-1)
X in (P=X-2q)
6.6
10.8
5
1.833333 9.166667
5.666667 6.363636 6.722222222
-1.27778 7.333333 9.333333333
6
1.571429 9.428571
5.142857 7.090909
-3.06122 7.857143 8.285714286
4.93877551
1. (corrected) Cournot model with free entry can be thought of as a model of monopolistic competition
with representative consumer. Inverse demand is given by Q  24  2 P , n firms compete by producing
undifferentiated products. Each firm’s cost function is given by C  Q   8  2Q . There is free entry.
a. Find the number of rims in the long run free entry equilibrium. Show your calculations (hint: it is
either 4, 5, or 6)
Competitive quantity from the demand is Q=24-2x2=20. For n=4, q=20/(4+1)=4, Total quantity Q=4x4=16,
market price is then 16=24-2P -> P=4. Firm profit is then 4x4-4x2-8=0. Therefore n=4 is the long run equilibrium.
Residual demand of one firm is q+3x4=24-2P, q=12-2P.
b. Draw each firm’s demand and AC curve, make sure that the numbers are to scale
It is important that in the original setup the AC curve dips below the demand since when n=4 the firms make
positive profits.
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Monopolistic competition, continued (15pts this page)
2. What can firms do to differentiate their product? (list at least two methods)
- Quality
- Location
- Advertising
3. If two firms compete by selling a product to consumers who have circular preferences, do they have
incentive to locate as close to each other or as far from each other on the circle? Explain briefly
As far from each other as possible because when firms are close they may compete for a part of the
consumers (the competitive region). When the firms are as different as possible (that is as far as
possible from each other in the product space) they
4. How will your answer to the above question change if the consumers instead have Hotelling’s
preferences where firms choose to locate along a line?
As close to each other as possible
5. In general, what is the effect of fixed cost on the following values in a long run equilibrium
a. Number of firms
Is lower when FC is high
b. Market price
Is higher when FC is high
c. Output per firm
Is higher when FC is high
6. (+ )Under monopolistic competition the price is always above the marginal cost and thus is higher than
the competitive price. In what sense such outcome is referred to as the second best?
First best would be achieved at the point where AC crosses the demand. This requires government intervention
to ensure that the price is not bid down to the marginal cost and equibrium exists. When the equilibrium does
not exist the consumers lose all surprlus. In the second best the equilibrium exists, it is not as good as when
AC=Demand but it is better than no production at all.
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Auctions (15 pts)
7. What is a double auction (used for example at New York Stock Exchange)
8. In which type of auction there it is always optimal to shade bids?
First price sealed bid
9. (+ ) Dutch auction and the second price sealed bid auction are two different ways to allocate an item to
a set of competing bidders. Every auction leads to certain outcomes: revenues (price of the item),
allocation (who gets the item), exchange of information (who knows what).
a. Which outcome(s) are the same for both auctions? Explain
Allocation: the bidder with the highest valuation always wins
b. Which outcome(s) are different for both auctions? Explain
Revenue: Dutch – items sells at the highest value
Information: the auctioneer knows values of ALL bidders in the second price sealed bid
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
Price discrimination (#10 - 10 pts, #11 - 10 pts, #12 - 20 pts)
10. A price discriminating monopolist is facing the following demand: Q  12  P . Show calculations.
a. What is the optimal two part tariff if marginal cost is 4?
P1=
32
, P2= 4
b. How much would the monopolist charge for a block of 6 units of the product?
P6=54
11. There are three consumers. Two of them are accountants and one of them is a writer with the following
reservations prices for Word and Excel. Assume that the marginal cost is zero and the fixed cost is sunk.
Word
Excel
Bundle (office)
Accountant (2)
60
120
180
Writer (1)
110
30
140
Price
60
120
140
Profit
60x3=180
2x120=240
420
a) Fill out the above table
b) Determine whether bundling is optimal
The revenue is the same either way
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
12. Monopoly can sell in two markets with the following inverse demands:
P  4  0.5Q1 and P  8  Q2 .
Assume that monopoly’s marginal cost is 0 and the fixed cost is sunk. Find the monopoly profit if the
monopoly cannot prevent resale:
a. At what price does the total demand kink?
P=4
b. What is the inverse demand and the marginal revenue before the kink?
P=8-Q
, MR=8-2Q
c. What is the inverse demand and the marginal revenue after the kink? Show necessary
derivations.
P= 16/3-1/3xQ
, MR=16/3-2/3xQ
d. Find monopoly quantity, price, and profit if it cannot prevent resale. Show necessary
Q=8
calculations
, P= 2.667
, Profit=21.36
e. Please demonstrate the answer to this problem on the following graph by showing only the
combined demand, marginal revenue, and kinks.
P
Q__
Information (20 pts)
13. There are 200 used cars for sale. Half of them are good and the other half are bad. The owners of the
good cars would sell their cars for $500 and the owners of the bad cars would sell them for $360. A good
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.
car is worth $560 to the buyer while a bad one is worth only $400. Assume that the sellers are able to
capture all consumer surplus.
a. How many cars will be sold and at what price if the buyers are not able to differentiate between the
Q=100
good and the bad cars? Show calculations
, P= 400
EV=480, the owners of good cars do not sell , so only the 100 bad cars sold. Since the sellers capture the whole
surplus the price reaches the consumer valuation.
b. If reservations values were such that both types of cars were sold, owners of which cars make higher
profit?
bad
2. What is the effect of reduction in search cost on the single-price equilibrium in a tourist trap model with
fixed number of firms? Would your answer change if the search cost is zero?
Reduction in transaction cost does not change the nature of single price equilibrium. The sellers still have
incentive to increase the price until it reaches the monopoly price. When there is no transaction cost the
equilibrium price is the competitive price.
14. (+) Two firms produce 50 laptops each. They value their laptops at $100 per unit (this is their constant
marginal cost of production). Consumers are willing to pay $150 per laptop. An equilibrium arises where
all laptops are sold at $150 and the surplus is fully captured by the sellers. If one firm improves quality of
its laptops its cost would increase to $150 per unit? What should be the consumers’ reservation value
for a high quality laptop for one firm to increase quality if the quality is not observable?
The producers of bad laptops make $50 profit on each unit. When the cost increases to $150 the price would
have to be $200 to justify investment in quality. If the consumers are willing to pay 250 per laptop the expected
valuation is 0.5x150+0.5x250=200.
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Notes: 1. (+) denotes scrumptious questions; 2. questions requiring an explanation will not be credited without one.