Question

Consider the production function faced by an economy in a particular year, Y=square root of K. N. Where K is the capital stock and its value is 8 million naira, N is the number of workers amounting 9 million naira and s = 40%(saving rate). Given this in formation, complete the following
1. Output per worker
2. Output
3. Consumption
4. Consumption per worker
5. If both capital and labour double, what happens to output
6. If the production function characterised by constant return to scale?

Answer 1

1.

$Y=\sqrt{K.N}=\sqrt{8\times9}=8.48528$

output per worker$=\frac{8.48528}{9}=0.942809041\space million\space naira$

2.

output $=Y=\sqrt{K.N}=\sqrt{8\times9}=8.48528$

3.

consumption$=0.6\times8.48528=5.091168$

4.

$consumption\space per\space worker=\frac{5.091168}{9}=0.565685333$

5.

The output will double if both labor and capital doubles

6.

The prodction function is charecterized with constant returns to scale