Image transcription text Question 1: Supply [9 Marks; 2, 2, 2, 3] Carrnaker produces small cars in a perfectly competitive market using labour (L) and

Image transcription text Question 1: Supply [9 Marks; 2, 2, 2, 3] Carrnaker produces small cars in a perfectly competitive market using labour (L) and capital
(K). Carmaker’s production function is given by f(l=§) = min {0.05L, Km}, 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 Mwhere 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 (c), we can show that Carmaker’s supply function is
of the following form: _ {a + by for p > gill/Cm;n
‘3 ‘ o for p 5 Mem-n where AVG stands for average variable cost. Find a, b, and mm (d) [3 marks] A new technology of producing cars has come to the market which only uses
capital 900 = 0.5K”2
As in part (c), continue to assume w = 400 and r = 10. Carmaker maximizes profits. It uses both technologies and sells 0’ cars in a perfectly competitive market where the price of small cars is p". If 113 of cars are produced using
new technology and 213 of the cars with old technology, then p*= :Q": How many cars do Carrnaker produce in total? What must be the price of cars (assuming
that the market for cars is perfectly competitive)?