Problem Set # 1

This problem set is due Thursday, September 26, 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. In a simplified economy, imagine that there is only one scarce input, labor, and only two outputs, guns and roses. The following tables show how many guns and how many roses can be produced daily with different quantities of labor.

a) If there were only 2,500 workers available in the economy, derive a table showing the maximum amount of guns that can be produced for different levels of rose production.

b) Compute the opportunity costs of a gun for each level of production.

c) Use the data in part a) to draw a production possibilities frontier (PPF).

d) Suppose that this nation is ruled by a dictator that puts a lot of emphasis on national defense, and therefore on gun production. Show a point on the PPF where this country is likely to be producing (Call it point X).

e) Suppose that this dictator changes his mind and puts having many roses as the most important national goal. Where will this economy be producing on the PPF (Call it point Z) ?

2. The Government of Nirvana is currently discussing the possibility of imposing a price floor on silk.

a) Draw a diagram showing Nirvana's demand and supply of silk before the price floor is imposed.

b) Draw a diagram showing Nirvana's demand and supply of silk ties before the price floor on silk is imposed.

c) Draw a diagram showing Nirvana's demand and supply of polyester ties before the price floor on silk is imposed.

d) How do your diagrams in parts a), b), and c) change when the government of Nirvana imposes a price floor on silk at a level above the equilibrium price. Explain and illustrate graphically.

3. The following equation represents the demand for tickets for the Pearl Jam concert in Austin:

QD = 5,000 - 40P

where: QD = Quantity of tickets demanded

P = Price per ticket ($/ticket)

a) Make a demand schedule showing the quantities demanded corresponding to prices from $20 to $100 (using $20 intervals).

b) Graph the demand curve.

c) Calculate the price elasticity of demand if price increases from $20 to $40.

d) Calculate the price elasticity of demand if price falls from $80 to $100.

e) Suppose that the supply of tickets is fixed at 4,000 tickets. What will the equilibrium market price be?

f) Assume that the demand for Pearl Jam tickets is now given by:

QD = 5,000 - 40P ? 4Y

where: Y = Income

? = Unknown sign (you have to determine it)

If supply is still fixed at 4,000 tickets and income is equal to $500, what would the equilibrium market price be? (Assume that Pearl Jam tickets are normal goods).

g) What would the equilibrium market price be if income declined to $300?

4. You have been hired as an economist by Warner Bros. Records and your boss tells you that you are responsible for setting the price of two of the Compact Discs produced by the company. These two compact discs are: "New Adventures in Hi-Fi" by R.E.M. and "A Boy Named Goo" by The Goo Goo Dolls. She gives you the following demand and supply curves for these two CDs (As you can tell by the equations (how?), these two compact discs are substitutes both on the consumption and the production sides):

Q_DREM = 20 - 2 P_REM + 3 P_GOO

Q_SREM = 5 + 3 P_REM - 2 P_GOO

Q_DGOO = 40 - 2 P_GOO + 1 P_REM

Q_SGOO = 10 + 4 P_GOO - 2 P_REM

Where: Q_DREM and Q_SREM represent the quantity demanded and supplied of R.E.M.'s CD (in thousands of CDs per week), Q_DGOO and Q_SGOO are the quantity demanded and supplied of The Goo Goo Dolls' CD (in thousands of CDs per week), P_REM is the price of the R.E.M.'s CD, and P_GOO is the price of The Goo Goo Dolls' CD.

a) How much would the quantity demanded and supplied for each CD be if you set the price of both CDs at $14 each? Would you have equilibrium in both markets at these prices? If your answer to the previous question is no, compute the surplus or shortage that occurs in each.

b) How much would the quantity demanded and supplied for each CD be if you set the price of R.E.M. CD at $10, while you set the price of the Goo Goo Dolls' CD at $15? Would you have equilibrium in both markets at these prices? If your answer to the previous question is no, compute the surplus or shortage that occurs in each.

c) How much would the price of each CD have to be in order for both markets to achieve equilibrium simultaneously?

d) How many units of each CD would be sold if you set the prices at levels that you selected on question c)?

5. The owner of the Houston Astros is trying to set the price at which the tickets to the Astros games will be sold. He calls and asks for your help. He provides you with the following information. The demand for Astros tickets is given by the following schedule:

a) If the capacity of the Astrodome (the Astros' 1996 home) is 40,000 and the number of tickets is limited to the number of seats, what price maximizes total receipts from ticket sales?

b) Starting in the 1998 season the Astros will be moving their home games from the Astrodome to the Houstondome (a new baseball stadium to be built in downtown Houston). If the capacity of the Houstondome is 60,000 and the number of tickets is limited to the number of seats, what price maximizes total receipts from ticket sales in the new stadium?

c) Use the elasticity of demand concept to explain your answers to parts a) and b).

You receive another call from the Astros's owner telling you that he made a mistake in the computation of the demand schedule for Astros tickets, the correct schedule is as follows:

d) Given the new information, what price maximizes total receipts from ticket sales in the Astrodome?

e) Given the new information, what price maximizes total receipts from ticket sales in the Houstondome?

f) Use the elasticity of demand concept to explain your answers to parts d) and e).