The cost of automobile production in Mexico is given by TC = 0.5X2 where X is thequantity produced. Let there be a single domestic supplier of automobiles. Also, let the demand curve faced by this producer be given by: Q = 30 - 0.5 P where Q and P denoted the quantity demanded and the price respectively.

 a. Graph the demand curve, the marginal cost curve and the marginal revenue curves. 

b. Solve this producer's profit maximizing problem. How many autos does the producer supply to the home market? What is the socially optimal level of production? What are the producer's profits? 

c. Now assume automobiles are allowed to be imported into Mexico. Let the world price be 8. How many cars are now demanded in Mexico? How does this compare with the socially optimal level of output (and consumption)? How much profit does the producer now make? What can you conclude about the effect of opening up to trade on monopoly profits in the home country? d. Determine equilibrium quantities with the imposition of a tariff that raises the domestic price of the importable to 12.5 (the world price stays at 8). What is the level of imports in this case? Compare the tariff outcome to a quota set at the same level of imports. Which results in higher welfare? Why?