Assignment - Please use graph paper for all graphs, and clearly type all written answers.
Q1. Market Demand and Elasticities: Consider the demand for a Tesla Model S. Suppose that the demand for a Tesla Model S is Qd = 500,000 - 4P + 2PMaserati + 25,000Pgas, where P is the price of big SUVs (in thousands of dollars), PMaserati is the price of a Maserati Ghibli, and Pgas is the price for a gallon of gasoline. Assume that supply is given by Qs = -10,000 + 5P - 0.2PBattery. P is the price of a lithium battery for the Tesla Model S. Assume: PMaserati = $100,000; Pgas = $4/gallon; and PBattery = $20,000.
a) What is the equilibrium price and quantity for a Tesla Model S? Graph your supply and demand equations in inverse form (i.e. price on left side of equation and Q on the right) and show the equilibrium P*, Q*.
b) At market equilibrium, what are the coefficients for the price elasticity of demand and supply for the Tesla Model S?
c) What is the cross-price elasticity of demand for the Tesla Model S with gasoline? How would you describe the relationship between the Tesla and gas?
d) Ceteris paribus, what is the market equilibrium P* and Q* when the price of a Maserati Ghibli falls by $9,000?
e) Ceteris paribus, what is the market equilibrium P* and Q* when the price of lithium batteries increases by $10,000.
f) Now suppose the government wants to impose a tax on Tesla's because it wants to tax the rich and believes that people who buy Teslas tend to be wealthy. The government sets the tax equal to $10,000 per car. Model the tax placed on consumers as a shift in the demand curve. Show the change in your graph and the new equilibrium P* and Q*. (Fully label) Does it matter if the tax is placed on consumers rather than the producer of Tesla? Prove your answer by algebra and in a graph.
g) How much does the price increase in (f) resulting from the tax of $10,000 per car? Use the formula ΔP = η/(η-ε) Δt to verify your answer. What percentage of the tax is paid for by consumers in the form of a price increase? Does the burden of the tax change if the tax is placed on the consumer or the producer? Explain your answer.
Q2. Price Elasticity of Demand: Suppose Qd = 160-2P.
a) At what price and quantity will the price elasticity of demand be unit elastic?
b) At what price and quantity will the price elasticity of demand be equal to -2.0?
c) At what price and quantity will the price elasticity of demand be equal to -0.5?
Q3. Market interventions: SF Rent Control
a) The demand for housing in San Francisco for apartments is given by Qd = 340,000 - 40R + 0.1PH +2Y, where PH is the median price for homes, which is $1,000,000, and Y is average yearly SF household income, which is $100,000. The supply is Qs = -8,000 + 160R, where R is monthly rent. Find and graph the inverse demand functions. What is the equilibrium rent, R*, and quantity of housing on the market, Q*?
b) What happens in (b) when we institute rent control: rents are capped at R- = $2500 per month. What is QS? How much is the resulting shortage? Where will these people live?
c) Using your answers in (a) and (b) draw a graph showing the welfare effects of rent control. Calculate the deadweight loss.
Q4. Market interventions: tariffs and quotas. Consider the domestic market for silver scooters (such as Razors) with inverse domestic demand equal to P = 200 - 2Qd, and inverse domestic supply equal to P = 20 + Qs.
a) If the U.S. did not import these scooters, and instead relied completely on domestic supply, what would be the domestic U.S. equilibrium price of scooters, P*, and the domestic quantity purchased of scooters, Q*? Graph your answer on a large half-page graph, and calculate consumer surplus, producer surplus, and total social welfare in the market for scooters. (Find actual numbers using the ½*b*h formula for triangles.)
b) Now assume that the world price for scooters is $50 because they can be made more cheaply in Asia than in the U.S., and that the U.S. is free to import scooters with no tariff or quota barriers. What is the quantity demanded in the U.S. of scooters at the world price? What is the domestic quantity supplied? What is the level of imports? Calculate the new consumer surplus, producer surplus, and total social welfare in the market for scooters, and illustrate these on your graph (or on a new one). Has the level of social welfare increased with trade? Why? Explain carefully.
c) Let's pretend now that U.S. producers of scooters lobby Congress to impose a $10 tariff on imported scooters, increasing the price that domestic consumers must pay for scooters to $60. How does this $10 tariff affect consumer surplus, producer surplus, and social welfare? Illustrate on your graph and show your calculations using the triangle formula. (Remember to include tariff revenue when calculating social welfare!)
d) Finally, consider the difference in social welfare if Congress had imposed a quota on scooters instead of the $10 tariff. Specifically, what if Congress had imposed an import quota equal to 30 imported scooters? By how much would this have reduced the level of social welfare in the U.S. relative to your answer in (c)?
Q5. Market for Blood: The law in California does not allow you to sell your blood to blood banks. However, blood banks may sell the blood they receive to hospitals. Before the law, a healthy person could sell a pint for $25 per pint. Assume that people who give blood receive the equivalent of $2 in compensation because when they give they get donuts and orange juice. Use a supply and demand diagram to show what the effect of this law is on the market for blood. Based upon your conclusions and avoiding any moral considerations, is the law banning the sale of blood welfare enhancing? Specifically describe the welfare impacts.