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?
Our earlier model focused on the most basic trade-off introduced by the policy. 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.
5
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).
Question
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?
Step by step
Solved in 3 steps
