1. Sushico imports fresh fish from the Orient for usage in the firm's Japanese restaurant and for packaging

into prepared dinners that are sold to customers. Because of limitations on the availability of fish, Sushico

can buy only 20 pounds of fish per month. The price of the fish is $5 per pound. Recent production data

for the restaurant indicates that output can be described as:

QR = 25FR - .5(FR)2

where QR= units of output, and FR= quantity of fresh fish used in the restaurant. Similarly, production for

the packaging division shows that production takes place according to:

QP = 35FP - (FP)2

where QP = units of outputs, and FP = quantity of fish used in the packaging division. Fish dinners sold in

the restaurant or sold packaged bring the same price to the firm. For each unit of output:

PR = PF = $1.

a. How should Sushico allocate the fresh fish between the two uses?

b. What is Sushico's profit?

c. Suppose that Sushico is able to buy an extra pound of raw fish at $11 per pound. Should Sushico

buy this additional pound of fish? (Hint: Find an imputed value for this marginal pound of fish.)

d. Suppose that an extra 12 pounds of fish became available also at $5 per 1 pound. Should Sushico

buy all of the additional fish? How much of the additional fish should Sushico purchase. How should

Sushico allocate their additional fish between the two divisions? What is their profit now?

e. Now Sushico has 32 pounds of fish. Suppose that in addition to the original 20 pounds of fish and

the additional fish purchased in part (d) Sushico is again able to buy an extra pound of raw fish at $11 per

pound. Should Sushico buy this additional pound of fish?

2. A private-garage owner has identified two distinct market segments: short-term parkers (S) and allday

parkers (A) with respective demand curves of

PS = 3 (QS/200) and PA = 2 (QA/200).

Here P is the average hourly rate and Q is the number of cars parked at this price. The garage owner is

considering charging different prices (on a per-hour basis) for short-term parking and all-day parking. The

capacity of the garage is 600 cars, and the cost associated with adding extra cars in the garage (up to this

limit) is negligible.

a. Given these facts, what is the owner's appropriate objective? How can he ensure that members of

each market segment effectively pay a different hourly price?

b. What price should he charge for each type of parker? How many of each type of parker will use

the garage at these prices? Will the garage be full?

c. Answer the questions in part b assuming the garage capacity is 400 cars.

4. Avinash has preferences over the 2 consumption goods {a, b} that can be represented by the following

utility function:

U(Ca, Cb) = (!

" + #

")

!

" r = 1 - 1/s (0, 1)

He purchases these goods from his income.

a. Solve for the Marshallian (also known as Walrasian) demands for these preferences.

b. Show that the relative demand function (for good a in terms of good b) can be written as a declining

function of the relative prices alone and is not a function of income.

c. Solve for the expenditure function for these preferences.

d. Find the Hicksian demand function for both goods.

e. Solve for the indirect utility function.

f. Use Roy's identity to solve for the Marshallian demand functions.