Problem 1
Ethanol (i.e., ethyl alcohol) is a colorless, flammable liquid that, when blended with gasoline, creates a motor fuel that can serve as an alternative to gasoline. The quantity of ethanol motor fuel that is demanded depends on the price of ethanol and the price of gasoline. Because ethanol fuel is a substitute for gasoline, an increase in the price of gasoline shifts the demand curve for ethanol rightward. The quantity of ethanol supplied depends on the price of ethanol and the price of corn (since the primary input used to produce ethanol in the U.S. is corn). An increase in the price of corn shifts the supply curve of ethanol leftward. In the first half of 2008, the price of gasoline in the U.S. increased significantly as compared to 2007, and the price of corn increased as well. How would the equilibrium price of ethanol motor fuel in the first half of 2008 compare to the price in 2007?
Problem 2
An electricity producer has two power plants, each of which emits carbon dioxide (CO2), a greenhouse gas. Each plant is currently emitting 1,000,000 metric tons of CO2 per year. However, new emissions rules restrict the firm's emissions to 1,000,000 metric tons of CO2 per year from both plants combined. The cost of operating a power plant goes up as it curtails its emissions. The table below shows the cost of operating each plant for different emissions levels:
The firm's goal is to choose emissions levels at each plant that minimize its total cost of operating its plants, subject to meeting its emissions target of 1,000,000 metric tons of CO2 per year from both plants combined. Let X denote the quantity of emissions from plant 1 and Y denote the quantity of emissions from plant 2. Let TC(X,Y) denote the total operating cost of the firm when the quantity of emissions from plant 1 is X and the quantity of emissions from plant 2 is Y.
a. What is the objective function for this problem?
b. What is the constraint?
c. Write a statement of the constrained optimization problem.
d. In light of the information in the table, what emissions levels from each plant should the firm choose?
Problem 3
Explain which of the following statements suggest a positive analysis and which a normative analysis?
a) If the United States lifts the prohibition on imports of Cuban cigars, the price of cigars will fall.
b) A freeze in Florida will lead to an increase in the price of orange juice.
c) To provide revenues for public schools, taxes on alcohol, tobacco, and gambling casinos should be raised instead of increasing income taxes.
d) Telephone companies should be allowed to offer cable TV service as well as telephone service.
e) If telephone companies are allowed to offer cable TV service, the price of both types of service will fall.
f) Government subsidies to farmers are too high and should be phased out over the next decade.
g) If the tax on cigarettes is increased by 50 cents per pack, the equilibrium price of cigarettes will rise by 30 cents per pack.
Problem 4
The demand curve for ice cream in a small town has been stable for the past few years. In most months, when the equilibrium price is $3 per serving for the most popular ice cream, customers buy 300 servings per month. For one month the price of materials used to make ice cream increased, shifting the supply curve to the left. The equilibrium price in that month increased to $4, and customers bought only 200
portions in the month. With these data draw a graph of a linear demand curve for ice cream in the town.
Find price elasticity of demand for prices equal to $3 and $4. At what price would the demand be unitary elastic?
Problem 5
You are given the following information:
• Price elasticity of demand for cigarettes at current prices is -0.5.
• Current price of cigarettes is $0.05 per cigarette.
• Cigarettes are being purchased at a rate of 10 million per year.
Find a linear demand that fits this information, and graph that demand curve.
Problem 6
Consider the following sequence of events in the U.S. market for strawberries during the years 1998-2000:
• 1998: Uneventful. The market price was $5.00 per bushel, and 4 million bushels were sold.
• 1999: There was a scare over the possibility of contaminated strawberries from Michigan. The market price was $4.50 per bushel, and 2.5 million bushels were sold.
• 2000: By the beginning of the year, the scare over contaminated strawberries ended when the media reported that the initial reports about the contamination were a hoax. A series of floods in the Midwest, however, destroyed significant portions of the strawberry fields in Iowa, Illinois, and Missouri. The market price was $8.00 per bushel, and 3.5 million bushels were sold.
Find linear demand and supply curves that are consistent with this information.