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

XA = √LX

YA = √LY

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

XB = 1/2 √LX

YB = 1/2 √LY

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?