Q1 Factor prices and income

Suppose that the production function of the economy is:

Y=AK^(0.5)L^(0.5)

Consider the following hypothetical scenario regarding a decline in a country's capital stock. An economy is initially in equilibrium with a capital stock K1 and an initial labor supply L. Suppose that a natural disaster destroys half of the country's capital stock so that K2=0.5K1. Thankfully none of the population was hurt so the labor supply is unchanged.

Q1.1

Find the ratio of output after the capital destruction to output before the capital destruction Y2/Y1.

Report your answers as decimals rounded to at least three decimal places.

Q1.2

Find the ratio of the new real wage to the initial real wage:

[(W/P)2] / [(W/P)1]

Report your answers as decimals rounded to at least three decimal places.

Q1.3

Find the ratio of the new real rental rate to the initial real rental rate:

[(R/P)2] / [(R/P)1]

Report your answers as decimals rounded to at least three decimal places.

Q1.4

Suppose that people in the economy don't equally share ownership of the capital and that individual capital owners either lost all of their capital or none.

As a result of the capital destruction, does the rental income for people who still own capital increase, decrease, or stay the same?

a. Increase

b. Decrease

c. Stay the same

Q1.5

As a result of the capital destruction, does the labor income for workers increase, decrease, or stay the same?

a. Increase

b. Decrease

c. Stay the same

Q1.6

As a result of the capital destruction, does share of national income paid to labor increase, decrease, or stay the same?

a. Increase

b. Decrease

c. Stay the same