3. In our third setup, there are four firms. Two firms who are identical with each other produce type 0 cars. Two other firms that are identical with each other (but not with the first two) produce type 1 cars. Each firm maximises profits given the output levels of the other three firms. The originally specified demand functions, (1), still apply to each type of car, and the originally specified cost functions, (2), still apply to individual firms. For example, if firms A and B produce type 0 cars, and firms C and D provide type 1, then Q0 =qA +qB andQ1 =qC +qD andthecostfunctionsare: CA(qA) = 50qA, CB(qB) = 50qB, CC(qC) = 20qC, CD(qD) = 20qD. (a) Write down a profit expression for a representative firm providing type 0 cars, and the profit expression for a representative firm providng type 1. (b) Take first-order conditions (c) What would the tax rates 0,1 have to equal, in order for the equi- librium quantities Q0,Q1 to be the same as the values you found in question 1(d)? Feel free to assume that two identical firms 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