College

Holding the human capital per worker and technology unchanged, the estimated aggregate production function in Jamaica is:

\[
\frac{Y}{L} = 50 \times \frac{K}{L}
\]

where:
- \( Y \) = real output
- \( L \) = number of workers
- \( K \) = quantity of physical capital

If real GDP per worker equals $3,200, calculate the physical capital per worker.

Answer :

Answer:

64.

Explanation:

We identify in the original equation what data we have and what we lack:

[tex]\frac{Y}{L} =50*\frac{K}{L}[/tex]

The problem statement gives us Y / L, which is the real GDP per worker = 3200, so we would lack K / L, which is the physical capital per worker, precisely, the data requested by the exercise. Therefore:

[tex]3200=50*\frac{K}{L}[/tex]

To find K / L we make a simple clearance:

[tex]\frac{K}{L} =\frac{3200}{50}[/tex]

[tex]\frac{K}{L} =64[/tex]

The physical capital equals 64.

Final answer:

The physical capital per worker (K / L) in Jamaica, given the real GDP per worker of $3,200 and the aggregate production function Y / L = 50 * K / L, is calculated to be $64.

Explanation:

The student is working with an aggregate production function, which in this scenario is defined as Y / L = 50 * K / L. Here, Y = real GDP, L = number of workers (labor), and K = physical capital. To find the physical capital per worker, we will rearrange the given equation to solve for K / L.

Given that the real GDP per worker (Y / L) equals $3,200, we can substitute this value into the equation:

3,200 = 50 * (K / L)

To find the physical capital per worker (K / L), we divide both sides of the equation by 50:

(K / L) = 3,200 / 50
(K / L) = 64

Therefore, the physical capital per worker equals $64.