Question 1 (16 points) Carmaker produces small cars in a perfectly competitive market. As production emits pollution, Carmaker must buy pollution permits. It also needs to hire labour. Therefore, Carmaker's production function is given by: f(L, K) = min{0.05L, E: }, where L denotes labour and E denotes the number of pollution permits. (a) (3 points) Draw the isoquant corresponding to q = 10 in a clearly labelled diagram where L is the horizontal axis and E is the vertical axis. Label two pairs (E, L) in the diagram which give q = 10. (b) (4 points) Suppose, for this part only, that L = 40 and E = 100. Calculate the marginal product of each input. Does Carmaker's production function exhibit constant returns to scale for all L > 0 and E > 07 (c) (2 points) Suppose that Carmaker wants to produce q cars when the price of labour (wage) is w = 200 and the price of emission permits is m = 20. Find an expression in terms of q for the minimum cost of such an undertaking. (d) (2 points) Suppose that the market price is p, and Carmaker will produce q units of cars. Using the cost function you found in the previous part, find Shoemaker's supply function. Express it as a function of price. (e) (2 points) At what price will Shoemaker shut down in the short run? (f) (3 points) Suppose that there are 40 identical firms like Carmaker who act as price-takers and the market demand for small cars is given by QD = 26000 - p. 0 S p S 26000. i. What is the equilibrium price in the small car industry? ii. How many cars are sold by Carmaker in market equilibrium? iii. What is the emission intensity for each individual firm