Question 1: Supply [9 Marks; 2, 2, 2, 3] Carmaker produces small cars in a perfectly competitive market using labour (L) and capital (K). Carmaker's production function is given by f(L,K) = min {0.05L, K1/2), where q is the number of cars produced. (a) [2 marks] Starting from L > 0, K > 0, suppose you double the amount of L and K. Is it possible for output (q) to more than double (i.e., increase from q to Aq where A > 2)? (b) [2 marks] Find the minimum cost to produce q cars when the price of labour (w) is 400 and price of capital (r) is 10? [Hint: the answer would involve q.](c) [2 marks] Using the answer to part (b), we can show that Carmaker's supply function is of the following form: q = 1 ja + bp for p > AVCmin 0 for p s AVCmin where AVC stands for average variable cost. Find a, b, and AVCmin{d} [3 marks] A new technology of producing cars has come to the market which only uses capital gm = ssh?\" As in part to}, continue to assume w = 4m and r = 1t}. lCarrnaker maximizes prots. It uses both technologies and sells (1' cars in a perfectly competitive market where the price of small cars is p\". If \"3 of cars are produced using new technology and 233 of the cars with old technolug'f. then pl: :ql= How many cars do Cemaker produce in total? What must be the price of cars (assuming that the market for cars is perfectly competitive}