Question

A certain planet is inhabited solely by two races-the Aliens and the predators, who acquire food according to the following,, production" possibilities: 2xa^2 +2ya^2=8 and 3xp^2+3yp^2=27. provide the algerbraic form for the production possibility curve on this planet.

a. x^2 + y^2=13

b.5x^2 +5y^2=100

c.x^2+y^2=25

d.none of right

e.5x^2+5y^2=35

Answer 1

We have the single production possibilities as

Aliens: 2xa^2 +2ya^2=8

Predators: 3xp^2+3yp^2=27

Take the case of Aliens:

2xa^2 + 2*(0)^2 = 8 or xa = 2 while 2*(0)^2 + 2ya^2 = 8 or ya = 2.

This indicates that Aliens can either produce a maximum of 2 units of x or 2 units of y so they face an opportunity cost of 1 unit of x equal to 1 unit of y.

Now take the case of Predators

3(0)^2 + 3yp^2 = 27 or yp = 3 and 3xp^2 + 3*(0)^2 = 27 or xp = 3.

This indicates that Predators can either produce a maximum of 3 units of x or 3 units of y so they face an opportunity cost of 1 unit of x equal to 1 unit of y.

Hence total production of x is 5 units and that of y is also 5 units when they produce collectively. This shows

that the combined production possibilities should satisfy x = 5 or y = 5

Option C is correct because x^2 + 0^2 = 25 gives x = 5 and 0^2 + y^2 = 25 gives y = 5.