Gains from Trade: A Numerical Example

1. A closed Economy's problem

PPF y12 + 4 y22 = KL, MRT = y1/4y2.
Utility and MRS

U = x1x2, MRS = x2/x1

 
Constraints

Constraint: x1 = y1, x2 = y2.

 
How to solve

 

2. An Open Economy's Problem

Given data

K = 80, L = 100,

p*1 = p*2 = 1.
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. Homework 2

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 (export) and z2 (import).
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.