a) Set up Lagrangian to represent the situation faced by the firm, assuming that it wishes to comply with the standard (i.e., treat the regulation as a constraint). Remember to set both tax rates to zero.(b) Take first-order conditions.(c) Is there some value of the standard x ? that would induce the firm to choose the values of Q0, Q1 proposed in question 1(d) (i.e., Q0 = Q1 = 60)? If so, what is it?(d) What is the intuition for your answer to question 5(c)?

5. Fifth and nally, we return to the framework of question 2 (with a single rm providing both types of car) to consider Clean ear standards instead of a Clean car discount. Assume that To = 0,71 = 0. That is, a rm does not have to pay any taxes, but it must keep average CO: emissions per kilometre travelled of the cars it sells down to some required level, 5:. Let CO; per kilometre of the two types of car be xed (per vehicle) at 120 for type 0 cars and 80 for type 1 cars. This means that the only way a rm can reduce its average is to sell a higher proportion of the more fuel eicient type. The regulation requires a rm to choose Q0, 01 to satisfy the following constraint: 12000 + 3001