## Eco380: Problem Set 2

Eco380: Problem Set 2

Required Questions (due Nov 12, 2015)

1. Please brie y evaluate the following arguments: true or false? Please explain why?

(a) A foreign rm that competes in prices with a domestic rm in the domestic market su ers

from facing a quota.

(b) Suppose that two rms, producing substitute but di erentiated products, compete in

prices. A government-imposed oor on rm 1’s price may increase rm 1’s pro t.

(c) Suppose a domestic rm and a foreign rm compete in quantities in the foreign market.

The domestic rm bene ts from an export subsidy that induces it to expand its output.

2. A seller uses a second-price sealed-bid auction to sell a painting to two bidders. The seller

claims that the painting was drawn by a famous painter, say Monet. Both bidders are not sure

about the seller’s claim, and think that the probability of the painting being drawn by Monet

is 1=2. Both bidders can examine the painting before bidding. After examination, bidder 1

gets signal x1 and bidder 2 gets signal x2. Both x1 and x2 are independently drawn from a

uniform distribution on [0; 1]. Let us assume that if a bidder is an expert on Monet’s painting,

then after examination he or she can immediately know whether the painting is authentic.

Otherwise, he or she still thinks that the probability of the painting being authentic is 1=2.

If the painting is authentic, it will worth 10+x1 to bidder 1, and will worth 10+x2 to bidder

2. If the painting is fake, it will worth x1 to bidder 1, and will worth x2 to bidder 2. Suppose

you are bidder 1 and x1 = 0:6.

(a) First suppose both you and bidder 2 know that neither you nor bidder 2 is an expert

of Monet’s painting. How much will you bid? Brie y explain your answer. [hint: bid your

expected value of the object which is 5 + x1 = 5:6]

(b) Next suppose both you and bidder 2 know that bidder 2 is an expert while you are not.

How much will you bid? Brie y explain your answer. [hint: bid your expected value of the

object conditional on winning which is x1 = 0:6]

(c) Finally suppose you know that neither you nor bidder 2 is an expert. But bidder 2 is

not sure whether you are an expert or not. Suppose you could pretend to be an expert and

convince him that you are an expert. Will you choose to do so? Why? [hint: use (a) and (b)]

Practice Questions

1. Consider the Hotelling model with location choice we discussed in class. Two rms, A and

B, are located along a line [0; 1] and choose prices simultaneously.

(a) Suppose A moves towards the center (i.e. towards B). What’s the direct e ect? What’s

the strategic e ect? What happens to rm A’s pro ts? In equilibrium, where do you think

the rms will locate? [Mathematical calculation is not necessary]

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(b) Now suppose both prices are identical and exogenously xed by a regulator. What happens

to A’s pro ts when A moves towards the center? In equilibrium, where do you think the rms

will locate? [Mathematical calculation is not necessary]

2. Chapter 5, Q4-5, Q9. Q12-13. [5th edition: Chapter 8, Q9-11, page 235-236.]

3. Chapter 6, Q1, Q4, Q8-10. [5th edition: Chapter 11, Q1, Q3-7, page 324.]

4. Chapter 7, Q1-7, Q9-14. [5th edition: Chapter 9, Q1-3, Q5-11, page 261, Chapter 10, Q4-11,

page 296.]

5. Explain how the following factors may increase the di culty of sustaining cooperative pricing:

(a) reaction time and detection lag

(b) small or failing rms

(c) competition in both quality and price

(d) asymmetry between rms

6. In a model of entry, an entrant can enter with a very small scale so as not to trigger an

agressive response by a large-capacity incumbent (here the entrant is the strategic player).

Consider the following example. There is an large incumbent hotel in a resort location and

a new entrant considers to enter. It might be a good strategy for an entrant to build a

comparable but small hotel with lower rates. Why? What type of strategy does the entrant

adopt?

7. Please explain why predatory pricing (and limit pricing) can be rationalized by

(1) undertainty about the toughness” of the incumbent

(2) asymmetric information about the market demand and the production cost of incumbent

8. Which auction format, rst price auction or English auction, is easier for bidders to collude?

Why?

9. Consider two risk neutral bidders i = 1; 2 competing for a single object. Each bidder receives

a private signal si independently drawn from the uniform distribution on [0; 1] : Bidder i’s

value for the object is vi = 2si + sj ; i; j = 1; 2; i 6= j: If the object is sold by an English

(ascending) auction (start price at p = 0 and then increase continuously), when shall bidder

i quit the auction?

[answer: when p = 3si; that is when it is clear that your opponent valuation is higher than

you]

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