One aspect of the policy that is also heavily debated is the fact that not every household can afford to upgrade their car in order to avoid paying the ULEZ fees. We now want to understand how best to design the scrappage scheme, which subsidises changing cars for those who need it the most. In particular, we want to know whether the scrappage scheme can create a moral hazard problem. To guide our analysis, consider the following simple model. The government would like to introduce a subsidy to help citizens who need their car for work and cannot afford to buy a ULEZ-compliant car. It also wants to ensure that only citizens who need to drive their car regularly use the subsidy. Instead of the two groups of citizens discussed above, we focus on one particular citizen who does not drive very often, only once a year. As a result, this citizen does not emit excessive pollution even with a car that is not ULEZ-compliant. The government would therefore prefer citizens like her not to buy a new car to avoid having to pay the subsidy unnecessarily. Once a year, the citizen derives a benefit of driving through the ULEZ area of B = 20. She can choose to either buy a new ULEZ-compliant car at a cost of C = 10, 000, denoted x = new, or stick with her old car at no cost, denoted x = old. If she sticks with her old car, she has to pay a ULEZ fee of τ = 12.50 on the day that she drives. Her net benefit of driving on that day is therefore B(old) = 20 −12.50 = 7.50. If she buys a new ULEZ-compliant car, she doesn’t have to pay the fee. Her net benefit of driving on that day is therefore B(new) = 20. However, if she buys a new car she also has to pay the cost of the car, C, but can deduct the government subsidy, S from that price. The citizen decides whether to buy the new car by comparing her net utility of having a ULEZ-compliant car, U(x = new) = B(new) − (C − S), to her net utility of keeping her old car, U(x = old) = B(old). A) Suppose first that there is no scrappage scheme, so the subsidy is equal to S = 0. If the citizen buys the new ULEZ-compliant car, she has to pay the full cost: C = 10, 000. What is her utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car? B)Suppose now that there is a scrappage scheme which fully reimburses the citizen if she buys the new ULEZ-compliant car. That is, the subsidy is equal to S = 10, 000. What is her utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car? C)Finally, suppose that there is a scrappage scheme which only provides a partial subsidy: if the citizen buys the new car, she receives a subsidy of 2, 000. What is the citizen’s utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car?
One aspect of the policy that is also heavily debated is the fact that not every household can afford to upgrade their car in order to avoid paying the ULEZ fees. We now want to understand how best to design the scrappage scheme, which subsidises changing cars for those who need it the most. In particular, we want to know whether the scrappage scheme can create a moral hazard problem. To guide our analysis, consider the following simple model.
The government would like to introduce a subsidy to help citizens who need their car for work and cannot afford to buy a ULEZ-compliant car. It also wants to ensure that only citizens who need to drive their car regularly use the subsidy. Instead of the two groups of citizens discussed above, we focus on one particular citizen who does not drive very often, only once a year. As a result, this citizen does not emit excessive pollution even with a car that is not ULEZ-compliant. The government would therefore prefer citizens like her not to buy a new car to avoid having to pay the subsidy unnecessarily.
Once a year, the citizen derives a benefit of driving through the ULEZ area of B = 20. She can choose to either buy a new ULEZ-compliant car at a cost of C = 10, 000, denoted x = new, or stick with her old car at no cost, denoted x = old.
If she sticks with her old car, she has to pay a ULEZ fee of τ = 12.50 on the day that she drives. Her net benefit of driving on that day is therefore B(old) = 20 −12.50 = 7.50. If she buys a new ULEZ-compliant car, she doesn’t have to pay the fee. Her net benefit of driving on that day is therefore B(new) = 20. However, if she buys a new car she also has to pay the cost of the car, C, but can deduct the government subsidy, S from that price.
The citizen decides whether to buy the new car by comparing her net utility of having a ULEZ-compliant car, U(x = new) = B(new) − (C − S), to her net utility of keeping her old car, U(x = old) = B(old).
A) Suppose first that there is no scrappage scheme, so the subsidy is equal to S = 0. If the citizen buys the new ULEZ-compliant car, she has to pay the full cost: C = 10, 000. What is her utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car?
B)Suppose now that there is a scrappage scheme which fully reimburses the citizen if she buys the new ULEZ-compliant car. That is, the subsidy is equal to S = 10, 000. What is her utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car?
C)Finally, suppose that there is a scrappage scheme which only provides a partial subsidy: if the citizen buys the new car, she receives a subsidy of 2, 000. What is the citizen’s utility of buying the new car? What is her utility of keeping the old car? Does the citizen prefer to buy the new car?
2)Using the model proposed, explain in what sense the scrappage scheme can create a moral hazard problem. To answer that question, you should first define what a moral hazard problem is, then explain what action the citizens might take in this example which the government cannot control. Finally, you should explain which of the two possible subsidies (full vs. partial subsidy) can reduce the moral hazard problem.
3)Compare and contrast the moral hazard problem that arises here with the one we studied in the lecture. What policy did we study in the context of moral hazard? In what ways was the moral hazard problem in that policy similar to this one? In what ways was it different?
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