Gains from Trade: A Numerical Example

 1. A Closed Economy's Problem PPF elliptic production function y12 + 4 y22 = KL, MRT = y1/4y2. Graph (Stars race around a supermassive blackhole of the Milky Way in an elliptic orbit.) Utility and MRS U = x1x2, MRS = x2/x1 Constraints x1 = y1, x2 = y2. How to solve
2. An Open Economy's Problem
Given data

Step I

Choose y1 and y2 to Maximize GDP

Step 2 Choose x1 and x2 to maximize U(x1,x2)

world prices: p*1 = p*2 = 1.

Budget Constraint: p*1x1 + p*2x2 = Io(income from step 1).

 3. Excercise Given data Production possibility frontiers, MRT, utility function, MRS, resource supplies and international prices are as follows: PPF: y12 + 4 y22 = KL, MRT = y1/4y2. Utility: U = x1x2, MRS = x2/x1 Resources: K = 18, L = 100, Prices: p*1 = p*2 = 2. A. Autarky problem Find y1, y2, UA, (p1/p2)A in autarky. B. Optimal production under free trade Given international prices, p*1, p*2, find optimal output, y1, y2, and Io (maximized income) evaluated at world prices. F. Optimal consumption under free trade Find, x1, x2, UF, z1 (= x1 - y1 = export, if negative) and z2 (x2-y2= import, if positive). G. Gains from trade Evaluate the gains from trade, G = UF - UA. S. Sketch Sketch the solutions and carefully label points A, B, and F. This concludes the math portion of the course. No more math from now on.

Mauritz Escher, Amalfi coast