Assignment

Question 1)

You are making an investment of 10 dollars. You have two options:

1) A security that will return you either 8 (-20% return) or 14 (+40% return) with equal 50% probabilities.
2) A security that will return you 10.8 (8% return).

Your utility of the receipt of money you receive back is equal to the square root of the total money returned. Once again, to be clear, Utility (Total Money received back) = Utility (Principal + Interest/loss)
=sqrt(Principle+interest/loss)

a) What is the risk premium necessary to make 1) and 2) equal? Please make clear what the sign is.

b) Please clearly interpret what the risk premium implies in this situation? What does it say about the relative riskiness of the situations?

Question 2)

As is typical in this game, in every one of these infinite rounds, player one goes first and player two can accept or make a counter offer.

In this game, Player 1 and Player 2 have different levels of impatience. Player 1's discount function is δ1 and Player 2's discount function is δ2.

Let's consider what would happen in the final round of offer by 1 ... and potential counter-offer by 2

a) Find the offer that Player 1 should make Player 2 so that Player 2 will be indifferent between accepting or making a counter in this round.

b) In other words, calculate (A, B) where A is the amount Player 1 would get and B is the amount Player 2 would get.

(Hint: Use the concept of sub-game perfect equilibrium).

Accept
Accept
Reject
Reject
(ε,1- ε)
(0,0)
Player 2 makes offer
Player 1 accepts or rejects
Player 2 accepts or rejects
Player 1 makes offer
(A,B)

c) For part (b) assume δ1=δ2. In this situation, for the solution to the Rubinstein bargaining game model does it matter who goes first? Or, if they are equally inpatient, it doesn't matter who makes the first offer at the start of the game? Support your answer using the generalized Rubenstein result. But also, and (most important), explain in an intuitive way why we should have expected that result.

Question 3)

Suppose that there are two types of used cars: Peaches and Lemons. Note that:

• A Peach is worth 10,000 to the buyer and 7,000 to the seller.
• A Lemon is worth 3,000 to the buyer and 1,500 to the seller.
• If a sale is going to occur, it will occur at the highest price the buyer is willing to pay.
• Assume that both parties are risk neutral.
• Initially, let's assume that 50% of the market is Peaches and 50% is lemons.

a) If everyone had perfect information, what would the prices be for Peaches and Lemons?

b) What would the price of cars be if neither buyers nor sellers had information about the quality of Peaches and Lemons?

c) Now assume asymmetric information; sellers know if their car is a Peach or Lemon. However, buyers do not know. What will the market price be for used cars be in this market? Explain.

d) Assume that the Car Institute was going to offer a service: they are going to test cars and certify they are Peaches or Lemons for a price of P*.

For what prices of P* would sellers of Peaches use the Car Institute's service?

Something has changed in the market. Cars have improved in quality this year. Now 70% of the cars are Peaches.

e) Answer question "c" again, but under the assumption that 70% of the cars are Peaches.

Problem 4)

Consider the market for printers.

• A firm is introducing an innovative new product which comes with a lifetime ink supply. Based on market research, a firm knows that:

o Some consumers don't print much, but there seem to be a lot of them. There are 8,000 "low valuation" consumers willing to pay $500 for a certain printer that comes with lifetime ink.

o There is another segment of 2,000 "high valuation" consumers willing to pay $2,000 for the printer with lifetime ink.

• It costs the company $300 to manufacture the print and lifetime ink supply.

a) Describe the two pricing strategies the firm might have at this point? How much profit might the firm have with the different strategies? Based on this, how should they price the product?

(Hint: Consider two pricing strategies).

b) The firm wants to get another pricing option in order to segment the market.

• For a one time (fixed) development cost of $500,000, they can offer a second version of the product.
• Consumers can purchase the original "Unlimited" version for $2,000.
• Alternatively, the "low valuation" segment can purchase a "Limited" printer with sufficient ink for their needs $500.
• This Limited version has enough ink for the low valuation segment, but isn't satisfactory for the high valuation segment.
• The Limited version can not be refilled.

How profitable would it be for the company to offer both versions? What should it do?