Question

A country has a labor endowmwnt of100 units of labor (L) and production functions x = (Lx)^0.5 and y = 4Ly. When the country divides its labor equally between producing x & y, what
is the rate of product transformation (slope) for the PPF?
a. 49.3
b. 56.7
c. 61.1
d. 71.0

Answer 1

Answer: We will derive the rate of transformation as follows:

Given the production functions, x = L_x^0.5 and y = 4L_y ;

The marginal product of labor for x is

and the marginal product of labor for y is

We know that the rate of product transformation is simply the slope of the PPF. So, if we measure the product y on the vertical axis and x on the horizontal axis, then the slope of the PPF will be given by

Now we can re-write   as follows

[since labor is equally distributed, so if we put L_x = L_y = 50, then they will be crossed out, leaving behind dy/dx ]

substituting the values of dy/dL and inverse value of dx/dL, dL/dx, we get

[as labor is equally distributed between x and y, so replacing L_x = 50]

Hence the rate of product transformation is 56.8 (approx), i.e option b.