Answer all questions correctly.,,,

1.

Felix and Oscar are playing a simplified version of poker. Both make an initial bet of $1. Felix (and only Felix) draws one card, which is either a king or a queen with equal probability (there are four kings and four queens). Felix then chooses whether to Fold or to Bet. If Felix chooses to Fold, the game ends, and Oscar receives Felix's $1 in addition to his own. If Felix chooses to bet, he puts in an additional $1, and Oscar chooses whether to fold or to call. Is Oscar folds, Felix wins the pot (consisting of Oscar's initial bet of $1 and $2 from Felix). If Oscar calls, he puts in another $1 to match Felix's bet, and Felix's card is revealed. If the Card is a king, Felix wins the pot ($2 from each of them). If it is a queen, Oscar wins the pot.

But to make the game more interesting, they decide to add a third type of card: Jack. Four Jacks are added to the initial deck of four queens and four kings. All rules remain the same as before, except for what happens when Felix bets and Oscar calls. When Felix bets and Oscar calls, Felix wins the pot if he has a king, they tie and each gets his money back if Felix is holding a queen, and Oscar wins the pot if the card is a Jack.

(a) Show this game in extensive form (be careful to label information sets correctly)

(b) How many pure strategies does Felix have in this game? Explain your reasoning.

(c) How many pure strategies does Oscar have in this game? Explain your reasoning.

(d) Represent this game in strategic form. This should be a matrix of expected payoffs for each player, given a pair of strategies.

(e) Find the unique pure-strategy Nash equilibrium of this game.

(f) Would you call this equilibrium a pooling equilibrium, a separating equilibrium, or a semiseparating equilibrium?

(g) In equilibrium, what is the expected payoff to Felix of playing this game? Is it a fair game?

2.

You work in the treasury department of a global consulting company that typically invoices its customer bills in local currency. One of your company's consulting teams has been working on a project in Australia that you expect will be completed within six months, at which time you expect to bill your client A$2,400,000. You are concerned that the Australian dollar will depreciate over the next six months and have decided to consider using currency futures contracts as a hedge. You collect the following data: S[AUD/USD] = 1.3261 June '21 Sept. '21 AUD futures contract prices: 1.3352 1.3449 Open interest (# of contracts:) 103 ,000 8,200 Contract notional amount: USD 100,000 Minimum tick size: .0001 per U.S. dollar increment

Assume today is March 15, 2021, and the September '21 contract expires on September 15th. If 6-month U.S. Libor is .25% p.a., what is the approximate rate of Australian 6-month Libor expressed as an annual percentage rate [Note: assume both Libor rates are quoted on an actual days divided by 360 day basis]?

Using the September contract, calculate the amount of contracts you would use if you employed (i) a naive hedge and (ii) a delta hedge approach to minimize the difference in the change in the value of this hedge with the change in the value of the AUD2,400,000 receivable. Specify if you would buy or sell these contracts.

3.

9. Consider a second-hand car market with two kinds of cars:

Kind A cars work fine with probability 9/10 and break down with probability

1/10

Type B cars work fine with probability 1/2 and break down with probability

1/2.

Other than the difference in the probability of break down, kinds A and B cars

are identical. Each seller knows the type of their own car, but this information

is not available to the buyers. The buyers only know that 1/2 the cars are type

A and 1/2 are type B.

Sellers value a car that works fine at 800, while buyers value a car that works

fine at 1000. Both sellers and buyers have a zero value for a car that breaks

down. Both sellers and buyers are risk-neutral.

There are many sellers and even more buyers, and you can assume that in any

transaction the seller gets all the surplus.

(a) Given that quality is observable to sellers but not to buyers, which type(s)

of car(s) would be traded and at what price(s)? Is the market outcome

efficient?

[Hint: Note that the value of a kind A car to a buyer is (9/10)1000 = 900.

Similarly derive other values.]

(b) Suppose any seller can offer a guarantee, which is a contract that promises

to pay the buyer R if the car breaks down (no payment is made if the car

does not break down).

Find the range of values of R for which there is a separating equilibrium

in which kind A cars sell with a guarantee and type B cars sell without a

guarantee.

(c) Suppose the government forces all sellers to offer a guarantee that promises

a refund of 1100 if the car breaks down. Would such a policy promote

efficiency?