Please see below for question thank you

3. In our third setup, there are four rms. Two rms who are identical with each other produce type 0 cars. Two other rms that are identical with each other (but not with the rst two) produce type 1 cars. Each rm maximises prot-s given the output levels of the other three rms. The originally specied demand functions, {1), still apply to each type of car, and the originally specied cost functions, [2), still apply to individual rms. For example, if rms A and B produce type 0 cars, and rms C and D provide type 1, then Q0 = 1354 + qB and Q1 2 19 + :99 and the cost functions are: GAGA) = 50%, 03(qu = 50913, Ochre) = 20th:, 09011)) = 20(19- (a) Write down a prot expression for a representative rm providing type 0 cars, and the prot expression for a representative rm providng type 1. (b) Take rst-order conditions (c) What would the tax rates 79,11 have to equal, in order for the equi- librium quantities (2'le to be the same as the values you found in question 1(d)? Feel free to assume that two identical rms producing a type of car, will provide the same amount as each other. (d) How does your answer to 3(c) compare with your answer to 1(d)? What is the intuition for this? There are two types of car, distinguished by how fuel efficient they are. Type 0 is the less fuel efficient type, and type 1 is the more fuel efficient. The inverse demand curves for the two types of car are: Po = 250 - Q0 - Q1/2, P1 = 120 - Q1 - Qo/2. (1) Cost functions are Co(Qo) = 50Qo, C1(Q1) = 20Q1 (2) respectively