Question

1. On an island economy, Juanita has 50 units of labor, and can produce x using x = 0.25L_x, and y using y = 10(L_y)^0.5, where L_x and L_y are labor for sectors x and y. The equation of the PPF is ____, and if Juanita only likes to consume y, she will produce y = ____.

1. 4x + y²/100 = 50; 104
2. 4x + y²/100; 70.7
3. 2y² + 4x = 120; 104
4. Y² + 12x = 50; 70.7

Answer 1

The correct answer is (b) 4x + y²/100 = 50; 70.7

PPF shows combination of goods(here x and y) that one can produce if it uses all of its resources efficiently.

Here Resources available is Labor endowment = 50 units. Thus L_x + Ly = 50 => L_x 50 - Ly

It is given that Juanita can produce x using x = 0.25L_x, and y using y = 10(L_y)^0.5

x = 0.25L_x = 0.25(50 - L_y) -----------------------------------(1).

As, y = 10(L_y)^0.5 => L_y = (y/10)² = y²/100

Putting this in (1) we get :

x = 0.25(50 - L_y) = 0.25(50 - y²/100)

=> x = 0.25(50 - y²/100)

=> 4x + y²/100 = 50

Thus, combination of x and y it can produce if it uses all its resources fully and efficiently is given by the following equation:

4x + y²/100 = 50

Hence equation of PPF = 4x + y²/100 = 50 ---------------------------(2).

If Juanita only likes to consume y then she will produce only y and will not produce any x => x = 0. Putting this in (2) we get :

4*0 + y²/100 = 50

=> y = 70.7

Hence, the correct answer is (b) 4x + y²/100 = 50; 70.7