The market for widget in Home is given as follows:

(Domestic) Supply: Q^S = 6P - 200 (Domestic) Demand: Q^D = 600 - 2P

a) Find the autarky equilibrium price and quantity. (4 points)

b) If the world price of widget is $80 per widget, find the quantity traded (i.e., the quantity of exports or quantity of imports). Compare to the autarky equilibrium, find the change in consumer surplus, change in producer surplus, and change in total surplus. (9 points)

c) Suppose Home is a large open economy in the world market for widgets, and studies show any trade policy by Home will change the world price by $2 per widget. If the government of Home wants to lower the level of imports in part (b) by 32 units via an imposition of a specific tariff. Find the per-unit tariff that will achieve the goal. Compared to the free-trade equilibrium, calculate the change in consumer surplus, the change in producer surplus, and the change in total surplus. (12 points)