Homework #2
1. State whether the following statements are true or false, and explain your answer.
a. If good A is relatively more expensive than good B, then good A must have a lower opportunity cost than good B.
b. A supply curve shows the maximum price required in order for the last unit of a good to be produced.
c. Once a market reaches equilibrium, its price will not change.
2. What will happen to the equilibrium price and quantity in these markets if the following changes occur?
a. The cost of wheat, which is used to produce bread, rises. What will happen to the equilibrium price and quantity in the bread market?
b. New technology for manufacturing computers lowers the cost of producing a computer. What will happen to the equilibrium price and quantity in the computer market?
c. The fall this year has been unusually mild. What will happen to the equilibrium price and quantity in the market for sweatshirts?
3. Consider the market for chocolate. The demand curve and supply curves are given by
Demand: P = 10 - (1/3)Q
Supply: P = Q + 2
a. Find the equilibrium price and quantity in the market for chocolate.
b. Assume the supply curve for chocolate shifts to the left by 2 units at every price. Write the equation for the new supply curve for chocolate and then find the new equilibrium price and quantity in the market for chocolate. How much did the price change relative to its initial level?
Now consider the oil market. Suppose that the supply function is the same as above, but the demand function is different:
Demand: P = 44 - 6Q
Supply: P = Q + 2
c. What do the differences in slope for the demand functions for chocolate and oil imply? (Hint: for chocolate, if the price increases by one, then the quantity demanded decreases by 3 units. For oil, if the price increases by one, then the quantity demanded decreases by only 1/6 of a unit.)
d. Find the equilibrium price and quantity in the oil market.
e. Now assume there is also a supply shock in the oil market and the supply curve for oil shifts to the left by 2 units for any price. Write an equation for the new supply curve for oil and then find the new equilibrium price and quantity in the oil market. By how much did the price change?
f. Compare the changes in price in parts (b) and (d). Where is the change in price larger? Explain your answer.
4. Consider the market for taxi rides. In this market, the taxi drivers are producers and the taxi riders are consumers. The demand curve and supply curves in the market for taxi rides are given by
Demand: P = 10 - (1/2)Q
Supply: P = (1/2)Q
(where quantity if measured in millions of rides per year and price is measured in US dollars)
a. Find the equilibrium price and quantity in the market for taxi rides.
b. Calculate the consumer's surplus and producer's surplus in the market for taxi rides. Sum consumer and producer surplus to get the total surplus in the market for taxi rides.
Assume now that the city government imposes a quota of 8 million rides per year. To implement this quota, the government requires that drivers purchase an operating license that allows them to drive a taxicab.
c. Calculate the price that consumers will be charged per ride if they purchase only 8 million rides per year (hint: what is the maximum price that will allow 8 million rides to be sold?). Calculate the price producers must received in order to be willing to sell 8 million rides? Use this information to calculate how much the government can charge drivers (per ride) for the right to operate a taxicab (this is called a quota rent).
d. Calculate the consumer's surplus, producer's surplus, and the total quota rent. Compare the sum with the total surplus of the market you obtained in part (2). Is this policy desirable from an efficiency standpoint? Explain your answer.