12.6 In the country of Rotorooa 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

;

here lx and ly are the quantities of labour devoted to x and y production, respectively. Total labour 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 labour available in region B:

lx + ly = 100.

a.

Calculate the production possibility curves for regions A and B.

b.

c.

What condition must hold if production in Rotorooa is to be allocated eficiently between regions A and B (assuming labour cannot move from one region to the other)?

Calculate the production possibility curve for Rotorooa (again assuming labour is immobile between regions). How much total y can Rotorooa produce if total x output is 12? Hint:
A graphical analysis may be of some help here.