Corporate Economics

Corporate Economics

(True/False). For each statement, assert whether it is true of false
and explain your answer.
1. In a one shot sequential move pure Betrand game with two identical firms, there
can be more than one subgame perfect Nash equilibrium.
2. In a Cournot-Stackelberg game with identical firms, the equilibrium price is
invariant to which firms moves first.
3. In a Bertrand-Stackelberg game, the follower firm has a second mover advantage
because prices are strategic substitutes.
4. It is possible to support a collusive outcome in a finitely repeated simultaneous
Bertrand game.
Problem 2. Two Sandwich shops, Early Sandwich (ES) and Best Sandwich
(BS), sell identical sandwiches and are located side-by-side in State College. Every
morning, ES opens at 8am and advertises its sandwich price pES on a billboard outside
the store. BS opens at 9am, observes ES’s daily price, and advertises its daily prices
pBS on its store’s window. BS faces a unit cost of 4 while ES faces a unit cost of 3
for making a sandwich. The market (inverse) demand for sandwiches is P = 60-Q.
1. Suppose ES and BS operate for only one day. That is, they open, sell their
Sandwiches, collect profits, and never open again. Write down BS’s best response
function, the equilibrium strategy profile, and the equilibrium prices,
quantities, and profits in this market. Is this outcome (Pareto) efficient?
2. Suppose now ES and BS get one week (e.g. 7 days) to operate. After that
week they both must shut down and move on. Both firms care about the total
Econ 444: Problem Set #4 2
profits earned during the week. How would daily prices change? How much
more profit do they earn?
3. The owner of ES is tired of always having to post prices first. Would she do
better if she waited until 9am to post her price and open the store? Why or
why not? Explain.
4. At the end of the week, a new town ordinance lets ES and BS stay and sell
sandwiches forever, however they must now open at the same time (e.g. set
prices simultaneously each day). Moreove, BS has made a new contract with
ES’s supplier so that they now both face a unit cost of $3 for making a sandwich.
Lastly, unlike previously, both firms discount future profits at a rate
d. Under what conditions does there exist an equilibrium in which both firms
make positive profits. Derive one such equilibrium, noting both the strategies,
equilibrium prices, discounted profits, and quantities sold in each period.
Problem 3. Two independent ice cream vendors own stands at either end of a 2
mile long beach. Everyday there are 200 beach-goers who come to the beach and
distribute themselves uniformly along the water. Every beach-goer wants exactly one
ice cream during the day, and values the ice cream from both stands at $10. All of the
beach-goers would rather be sunbathing or in the water, so they have a disutility to
walking on the beach of $1 per mile. Early’s Ice Cream, the firm at location 0, is an
early riser and always posts his price first. Cali Creamery, at location 2, is more laid
back and posts her price just before the beach opens (the beach requires all prices be
posted by the time the beach opens). Both firms have a marginal cost of $1.
1. Each individual is also referenced by a location x on the beach between 0 and
2. What are the utilities of purchasing from Early’s and Cali for the person at
location 1.25, given that Early’s names price pe and Cali names price pc? What
are the utilities for each individual as a function of their location on the beach,
x?
2. What is the demand for Early’s Ice Cream and Cali Creamery given the firms
name prices pe and pc?
Econ 444: Problem Set #4 3
3. What is Cali Creamery’s best response function when Early’s posts a price of
pe?
4. What is the Sub-game Perfect Nash Equilibrium outcome for this market? Report
prices, quantities, and profits for each firm.
5. Early’s owner feels that his hard work is not paying off, he hires you as a
business consultant. He’s annoyed that Cali is always undercutting his price
and is considering waiting to post so that Cali will not learn his price before
naming her own. He wants you to predict how waiting to post his price will
affect his profits. What will Early’s profits be under this new regime? What
advice do you give him?
Problem 4. First Bank of SC (FBSC), Second Bank of SC (SBSC), and
Third Bank of SC (TBSC) open branches in State College. As their names
suggest, FBSC opens branches first, SBSC second after having observed FBSC’s
branches, and TBSC opens branches last. The cost of opening a branch is the same
for all three banks at c = $3 Million. The total revenue each bank can earn from each
of its branches, also in millions of dollars, is given by P = 43 – Q.
1. Write down SBSC’s and TBSC’s best response functions.
2. Given the above, how many branches does FBSC open in State College?
3. How many total branches would you expect to see in State College?
4. What are each of the three banks’ equilibrium branch revenues and profits?
5. Suppose all three banks were to open branches simultaneously. Would total
industry profits increase or decrease?
6. As FBSC is about to start breaking ground on its first branch, there is public
news that TBSC has lost its charter and will not be able to open any branches
at all. What is the effect of this news on consumer surplus? Explain.

 

 

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