Answer to Question #58859 in Macroeconomics for Frances Fitzgerald

Question

A. Suppose that the demand and supply curves for coffee in the United States are given by P = 200 - QD and P = 50 + 0.5QS respectively.

i. What are the equilibrium price and quantities if there is no international trade?
ii. What are the equilibrium quantities (supply, demand) for the US if the nation can trade freely with the rest of the world at a price of 50? In other words, what is the quantity demanded and supplied in the US at this new price? What trade occurs as a result of this change? Show this diagrammatically.
iii. What is the effect of the shift from autarky to free trade on US consumer surplus (CS), on US producer surplus (PS) and on overall US welfare (CS + PS)? Discuss these changes and illustrate them diagrammatically.

Answer 1

P = 200 - QD and P = 50 + 0.5QS, Qd = 200 - P, Qs = 2P - 100.
i. The equilibrium price and quantity are in the point, where Qd = Qs and Pd = Ps, if there is no international trade. So:
200 - Q = 50 + 0.5Q
Qe = 100 units.
Pe = 200 - 100 = $100.
ii. If the nation can trade freely with the rest of the world at a price of 50, then Qd = 200 - 50 = 150 units, Qs = 2*50 - 100 = 0. So, there will be no national production at world price.
iii. The shift from autarky to free trade will increase consumer surplus (CS), decrease US producer surplus (PS) and will decrease overall US welfare (CS + PS).