Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 23

In the country of Ruritania there are two regions, A and B. Two goods (X and Y) are produced in both regions. Production functions for region A are given by
LX and LY are the quantity of labor devoted to X and Y production, respectively. Total labor available in region A is 100 units. That is,
Lx + Ly = 100
Using a similar notation for region B, production functions are given by
There are also 100 units of labor available in region B: Lx + Ly = 100
a. Calculate the production possibility curves for regions A and B.
b. What condition must hold if production in Ruritania is to be allocated efficiently between regions A and B (assuming that labor cannot move from one region to the other)?
c. Calculate the production possibility curve for Ruritania (again assuming that labor is immobile between regions). How much total Y can Ruritania produce if total X output is 12? (Hint: A graphic analysis may be of some help here.)d. Without making any explicit calculations, explain how you might develop a production possibility frontier for this whole country.