Assume that consumers at Home have the following demand function for car varieties: xi = 500 [(1/N) - (1 / 10,000)(p; - Pbar)] which leads to the following marginal revenue for each firm: MR; = pi - 20 yi Every firm has the following total cost function: TC; = 50,000 + 15,000 yi a) Assuming a closed economy (autarky), calculate the number of firms/varieties in equilibrium, the quantity produced by each firm, and the price they each charge. b) If there was free trade with a country with identical preferences but a market that is three times bigger (so S' = 1,500) how many varieties would consumers be able to consume and what price will they pay in the integrated equilibrium? Will consumers be better off? Why or why not? (Note that in the integrated equilibrium, the increase in the market size will change the MR equation provided above to: MR; = pi - 5y;)