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, K^1/2},

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 (c), we can show that Carmaker's supply function is of the following form:

where AVC stands for average variable cost. Find a, b, and AVC_min

d [3 marks] A new technology of producing cars has come to the market which only uses capital

g(K) = 0.5K^1/2

As in part (c), continue to assume w = 400 and r = 10.

Carmaker maximizes profits. It uses both technologies and sells Q^* cars in a perfectly competitive market where the price of small cars is p*. If 1/3 of cars are produced using new technology and 2/3 of the cars with old technology, then

p* = ___________________; Q* = _______________

How many cars do Carmaker produce in total? What must be the price of cars (assuming that the market for cars is perfectly competitive)?