1. A closed Economy's problem

PPF: y₁² + 4 y₂² = KL, MRT = y₁/4y₂.

Utility: U = x₁x₂, MRS = x₂/x₁

Constraint: x₁ = y₁, x₂ = y₂.

2. An Open Economy's Problem

K = 80, L = 10,

p*₁ = p*₂ = 1.

Step 1: Choose y₁ and y₂ to Maximize GDP

Step 2

Choose x₁ and x₂ to maximize U(x₁,x₂)

 

Prices: p*₁ = p*₂ = 1.

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

Homework 2

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

K = 18, L = 100,

Prices: p*₁ = p*₂ = 2. 

A. The autarky problem:
Find y₁, y₂, U^A, (p₁/p₂)^A in autarky.

B. Optimal production under free trade:
Given international prices, p*1, p*2, find optimal output, y1, y2, and I^o (maximized income) evaluated at world prices.

F. Optimal consumption under free trade:
Find, x₁, x₂, U^F, z₁ (export) and z₂ (import).

G. Evaluate the gains from trade, G = U^F - U^A.

S. Sketch the solutions and carefully label points A, B, and F.

This concludes the math portion of the course.