4. (20 marks) Assume a monopolistically competitive car industry. The demand facing any firm / is given by: 9.=[(x)-(100,00 ) (P.-P) where q, is firm /'s sales, O signifies total industry sales (i.e. the size of the market), N is the number of firms in the industry, p, is the price charged by firm / itself and p is the average price charged by firm /'s competitors. Assume that the production function for cars is such that: (i) 5,000,000 hours of labour are required even if no cars are produced and (ii) 1000 hours of labour are required to produce each additional car. The wage rate is $20/hour. Now, suppose that there are two countries: Home and Foreign. Home has annual sales of 500,000 cars and Foreign has annual sales of 1,000,000. Both firms face the same production function. i. (4 marks) Assuming a symmetric autarky equilibrium, use the zero profit condition to derive the equation for the price of cars in Home as a function of N. Do the same for Foreign. ii. (4 marks) Assuming a symmetric autarky equilibrium, use the profit maximising profit condition to derive the equation for the price of cars in Home as a function of N. Do the same for Foreign. iii. (4 marks) Using your answers from (i) and (ii), solve for the autarky equilibrium number of firms, the price of cars and the output of each firm in Home and Foreign. (solve to 2 decimal places if required) iv. (4 marks) Assume no transportation cost and that Home and Foreign freely trade cars with one another. For this integrated market, solve for the equilibrium price, the number of firms in Home and Foreign, and the output per firm. (solve to 2 decimal places if required). v. (4 marks) Explain how and why the integrated equilibrium calculated in part (iv) differs to the autarky equilibria calculated in part (iii)