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Econ 100A - Oligopoly in the smartphone market

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Subject: Economics
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Econ 100A Fall 2016
Problem Set 5
2=HJ 

1 Oligopoly in the smartphone market
Two rms are operating on the market for smartphones, Apple and Samsung. Despite all their marketing
eorts, consumers consider their products perfect substitutes. The market demand for these homogenous
1
cellphones is Q = 1000
3 P. They are producing cell phones with a unit cost of 60 dollars.
1. How much would be the production, market price, and the prot of Apple if it was a monopolist
producer of smartphones?
2. What would be the market equilibrium if the two rms collude?
3. If the rms are competing in a Cournot fashion:
(a) What are the best response functions of the two companies?
(b) What is the equilibrium output, price, and prot levels for each rm?
4. Now imagine the rms compete according to the Stackelberg model. Samsung is the leader.
(a) What is the best response functions for Apple?
(b) What is the equilibrium output, price, and prot levels for each rm?
(c) The Federal Trade Commission (FTC) imposes a ne on Samsung of $5 per unit for violating
Apple's patent rights. What is the equilibrium output, price, and prot for each rm?
(d) The FTC now wants to adjust the ne so that the quantities produced by each rm will be equal.
What is the right amount to ne Samsung per unit? Calculate the new equilibrium output, prots,
and equilibrium price. 2=HJ 11 Rock, Paper, Scissors Thanks to Jerey Kang of UC Berkeley.
Consider the following game, which is just like a standard rock-paper-scissors game except that choosing
to play rock bears some small cost, c, whereas there is no cost to play the other options: Rock Paper Scissors Rock 0-c, 0-c -5-c, 5 5-c, -5 Paper 5, -5-c 0, 0 -5, 5 Scissors -5, 5-c 5, -5 0, 0 Note that this game is symmetric. 1 1. Consider the Nash Equilibrium strategy of players playing the normal, unmodied game: each player
employs a mixed strategy of 1/3(Rock), 1/3(Paper), 1/3(Scissors). Show that this mixed strategy is not
a Nash Equilibrium for the new game (is it protable for one player to deviate from this strategy, if
the other player retains it?)
2. How should you adjust your strategy now that the game has changed? Find your best responses (both
pure and mixed, if both are applicable) to your opponent's strategy.
3. Suppose each player decides to never play Rock and randomize 50/50 over Paper and Scissors. That
is, each plays 0(Rock), 1/2(Paper), 1/2(Scissors). Is this an NE of the game if c = 1? Explain why or
why not.
4. In a symmetric, mixed-strategy NE of the game with c = 1, each player plays Rock 1/3 of the time.
Find the mixed-strategy equilibrium.
5. What is each player's expected outcome in the above equilibrium? 2=HJ 111 Classifying the personal computer market
1. Find and list the top ve producers of PCs sold in the U.S, along with their respective market shares.
Make sure to cite your data source, including the year.
2. Use the internet or other research tools to learn about the following measures of market power. Calculate them for the PC market.
(a) Four-Firm Concentration Ratio
(b) Herndahl Index
3. What do each of these measures imply about the concentration of the laptop industry? 2=HJ 18 Externalities
Woodonia, the world's leading exporter of bespoke wooden furniture, produces the furniture at a per-unit cost
of Q = P + 60 and the market demand is Q = 120 - P. However, the production of bespoke furniture comes
with a signicant negative externality deforestation! The externality cost is $40 per piece of furniture. In
addition, the country is opened up to free trade at a world price of $100.
1. Find and draw the domestic equilibrium
2. Find and draw the free trade equilibrium
3. Find and draw the socially optimal equilibrium
4. A policy maker is proposing to use an export tax to achieve the socially optimal level of production.
What would be the impact of an export tax on your graphs? Will this policy be eective? 2
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