$3.$ Isla is a small exporting country with supply and demand given by the following equations:QD $=2004$PQS $=8$P $40$a$)$ Solve for the equilibrium price and the equilibrium quantity and calculate the consumer surplus, producer surplus and total surplus.b$)$ Suppose that Isla moves from autarky to open its economy to international free trade and the world price for this particular good is $$22.$ Solve for the new equilibrium. Specifically, what is the quantity bought by the domestic consumers and the quantity sold by the domestic producers? Is this country importing or exporting this good and how many units? Calculate the new consumer, producer and total surpluses and the gains from trade in this market due to free trade.c$)$ Suppose the Isla government offers the islader producers an export subsidy of $$2$ per unit. Determine the new equilibrium. Specifically, what are the new price paid and the quantity bought by the domestic consumers and the price received and the quantity sold by the domestic producers? Is this country importing or exporting this good and how many units? Calculate the new consumer surplus, producer surplus, the government cost of this subsidy program, the new total surplus and the deadweight loss.