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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. E19}, 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 5 b and min {a,b} = b if a a b. (a) [1 mark] Draw the isoquant corresponding to q = 10 in a clearly labelled diagram where L is in the x-axis and E is in the y-axis. Label two pairs of E and L in the diagram which give q = 10. (b) [2 marks] What is the marginal product of L and the marginal product of E when L = 40 and E = 100? Does the production function (1) exhibit constant returns to scale for all L > 0 and E > 0. (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 q cars when w = 200 and m = 20. [Hint: the answer would involve q.] (d) [2 marks] Using the answer to part (c), we can show that Carmaker's supply function is of the following form: _ a + bp for p > AVCmI-n '3 '{ 0 for p s Avcmm where AVC stands for average variable cost. Find a. b, and AVCmin. (e) [3 marks] Suppose there are 40 identical rms like Carmaker who act as price takers and the market demand for small cars is given by Q = 26000 p if p 5 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 rm (i.e., emission per unit of output, g)