This problem set is due Thursday, November 7, at the beginning of the class period. Problem sets done on notebook paper or unstapled will not be accepted. Late problem sets are unacceptable also.

1. The President of the Armani clothes factory in Milan calls and asks for your help. She tells you that her company faces a perfectly competitive market in its sales of Men's suits. She also gives you the following equation which represents the total cost function of Armani's suits :

where: TC = Total costs

Q = Number of suits produced

a) Derive the FC, VC, TC, AVC, ATC, and MC schedules (You should compute these costs for Q = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40).

b) Graph the AVC, ATC, and MC curves.

c) How many suits should the Armani factory produce if the market price for comparable suits is $1,300? How much would Armani's profits be when it produces this number of suits?

d) How many suits should the Armani factory produce if the market price for comparable suits is $700? How much would Armani's profits be when it produces this number of suits?

e) How many suits should the Armani factory produce if the market price for comparable suits is $80? How much would Armani's profits be when it produces this number of suits?

f) How much is the minimum price necessary for the Armani factory to operate in the short run?

g) Draw a diagram showing Armani's supply curve of men's suits.

2. The following table gives Ives' total utility for the consumption of three goods: burritos, sodas, and compact discs.

a) Burritos cost $2 per unit, sodas cost $1 per unit, and compact discs cost $15 per unit. Ives has $36 of disposable income. How many burritos, sodas, and compact discs should Ives buy if he wants to maximize his utility?

b) How does your answer to part a) change if the price of sodas rises to $2 per unit?

c) How does your answer to part a) change if the price of compact discs declines to $6 per unit, Ives' income rises to $42, and the prices of burritos and sodas stay at $2 and $1 respectively?

3. A 1996 Trinity graduate inherited her mother's printing company. The capital stock of the firm consists of three machines of various vintages, all in excellent condition. All machines can be running at the same time:

Assume that "cost of printing and binding per book" includes all labor and materials, including the owner's own wages. Assume further that Mom signed a long-term contract (50 years) with a service company to keep the machines in good repair for a fixed fee of $100 per month (for the three machines).

a) Derive the marginal cost curve of the firm.

b) Derive the total cost curve of the firm.

c) At P = 2.50, how many books would the company produce? What would total revenues be? Total costs? Total profits?

4. The Wall Street Journal recently published an article about the Texas Lottery System (Note: You might want to read it to learn more about it). This article described a new payout system that will let contestants choose whether they would like to receive their prizes in a lump sum payment (equal to half of the prize) or in 20 equal payments to be received over a 20 year period. Suppose that you win $20 million. According to the new scheme, you could either receive $10 million now, or $1 million per year (with the first $1 million being received now).

a) If the interest rate that you could receive on your money is 10%, how much is the present value of your prize under the 20-year payout scheme? Which payout scheme is better, the lump-sum payment or the 20-year program?

b) If the interest rate that you could receive on your money is 5%, how much is the present value of your prize under the 20-year payout scheme? Which payout scheme is better, the lump-sum payment or the 20-year program?