Market Demand and Elasticities: 

Consider the demand for very large, gas hogging SUVs like Cadillac EscaladesÒ and Toyota Land CruisersÒ. Suppose that the demand for big SUVs is Q_d = 500 - 3P + 3P_SF - 2P_RW , where P is the price of big SUVs (in thousands of dollars), P_SF is the price of small SUVs like Subaru ForestersÒ (in thousands of dollars), and P_RW is the price of the platinum-plated wheel rims cool people put on big SUVs like Escalades that keep rotating even when you come to a stop. Assume that supply is given by Q_s = 100 + 7P. Assume P_SF = 40 and P_RW = 10.

1. What if the government wants to impose a tax on big SUVs because they get low miles per gallon, hog the road and are dangerous to other vehicles. Suppose the tax is equal to 10 (in thousands) per car. Model the tax as on producers, as a shift in the supply curve. Show the change in your graph and the new equilibrium P* and Q*. Does it matter if the tax is placed on consumers rather than producers of big SUVs? Prove your answer by algebra and in a graph.

2. How much does the price increase in (f) resulting from the tax of 10? Use the formula to verify your answer. What percentage of the tax is paid for by consumers in the form of a price increase?