Question 1: Supply [9 Marks: 1.2.1.2,3] Carmaker produces small cars. As production emits pollution. Cannaker needs to buy:r pollution permits. It also needs to hire labour. Carmaker's production function is given by: (1) q = min {c.osL. Em}, where E denotes the number of pollution permits. L denotes the amount of labour and min{a,b} denotes the minimum function where min{a,b} = a if a s b and min {a,b} = b if a e b. (a) [1 mark] Draw the isoquant corresponding to q = '10 in a clearly:r labelled diagram where L is in the xaxis and E is in the yaxis. Label two pairs of E and L in the diagram which give (1 = H). (b) [2 marks] 1|.r'lfhat is the marginal product of L and the marginal product of E when L = 40 and E = 1GB? Does the production function {1) exhibit constant returns to scale for all L 2:- DandEa-U. (c) [1 mark] Let m denote the price of a pollution permit and w denote the price of labour. Find the minimum cost to produce {1 cars when w = 2m) and m = 2U. [Hint: the answer would involve c.] (d) [2 marks] Using the answer to part {c}, we can show that Cannalter's supply function is of the following form: _ [a + bp for p ;,-. AVle-n 9' ' c for p 5 AVCm-n where AVG stands for average variable cost. Find a, h. and AVCmin. (e) [3 marks] Suppose there are 40 identical firms like Carmaker who act as price takers and the market demand for small cars is given by Q = 26000 - p if p s 26000, and 0 otherwise. Complete the table. Equilibrium price in the small car industry Number of cars sold by Carmaker Emission intensity for each individual firm (i.e., emission per unit of output, =)Question 1: Supply [9 Marks: 1,2,1,2,3] Carmaker produces small cars. As production emits pollution, Carmaker needs to buy pollution permits. It also needs to hire labour. Carmaker's production function is given by: (1) q = min {0.05L, E1/2), where E denotes the number of pollution permits, L denotes the amount of labour and min{a,b} denotes the minimum function where min(a, b} = a if a s b and min {a,b} = b if a > b