Exciting Insights into Production Functions and Output per Capita!

What is output per capita and how is it calculated in a production function?

In a production function Y = K^0.3 * N^0.7, what is the correct expression for output per capita Y/N?

Correct Expression for Output per Capita Y/N:

The correct expression for output per capita Y/N is Y/N = K^0.3 * N^(-0.3).

Output per capita, represented by Y/N, is a crucial economic indicator that measures the average output produced per person in a population. It gives insights into the efficiency of resource utilization and the productivity of a society. In the context of a production function like Y = K^0.3 * N^0.7, where Y represents total output, K is capital input, and N is labor input, output per capita Y/N can be calculated by dividing the total output by the total population.

To find the expression for output per capita Y/N in the given production function Y = K^0.3 * N^0.7, we first need to understand that output per capita is calculated by dividing the total output (Y) by the total population (N). Thus, the formula for output per capita Y/N can be derived by dividing the production function by the total population.

Dividing both sides of the production function Y = K^0.3 * N^0.7 by N, we get:

Y/N = (K^0.3 * N^0.7) / N

Simplifying the expression by canceling out N in the numerator and denominator, we get:

Y/N = K^0.3 * N^(0.7-1)

Y/N = K^0.3 * N^(-0.3)

Therefore, the correct expression for output per capita Y/N in the production function Y = K^0.3 * N^0.7 is Y/N = K^0.3 * N^(-0.3). This formula provides valuable information on the average output per person and is essential for analyzing economic growth and productivity.