Gains from Trade: A Numerical Example

  1. A Closed Economy's Problem
elliptic production function

y12 + 4 y22 = KL, MRT = y1/4y2.


(Stars race around a supermassive blackhole of the Milky Way in an elliptic orbit.)

Utility and MRS

U = x1x2, MRS = x2/x1



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. 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