Question

xm m A consumer chooses miles traveled m to maximize the difference between benefits and costs: Po +t max: 1000 In(m) - MPG utility of driving cost per mile where MPG is the miles-per-gallon (the energy efficiency) of a car, P, is the market price per gallon, and t is any tax per gallon. 5. Solve for m*, the consumer's utility maximizing amount of driving by taking a derivative and rearranging the first order condition. Your result will be a function of the other parameters, Pa, t and MPG. Write out the equation m* = ....* (2 points) 6. You can look at this equation to understand how changing different parameters will change the consumer's choice of how much to drive these relationships are called comparative statics). If MPG rises for some reason, holding the other parameters constant, will mileage go up or down? (1 point) 7. Now, suppose that there is no public policy, t = 0, and the price of gasoline p, is $3 per gallon. The price of gasoline will determine what MPG the consumer might have chosen. We aren't going to explicitly model that step here, but suppose that the consumer choses MPG = 30, which is privately optimal for them under these conditions. How many miles will they drive? (1 point) 8. Now, suppose that there is a negative externality equal to $1 per gallon. As a result, the policy maker applies the Pigouvian prescription and sets t= $1. Suppose that the consumer initially does not change what car they are driving, so MPG = 30. With the higher price due to the tax and same MPG, how many miles does the consumer drive? (1 point) 9. The tax increases the cost of driving per mile. This changes the optimal number of miles driven. This reduces the externality. But, the tax also increases the value of energy efficiency, so we might expect the consumer to invest more in efficiency and increase MPG. Suppose that the socially optimal response to a $1 tax is to increase MPG to 33. Calculate consumer welfare (benefits minus costs of driving if the consumer continues to drive the number of miles that you calculated in the prior step, but MPG is 33 and t = $1. (1 point)

Answer 1