# The countries of Aloha and Biki both have the production function Y = K^{1/3} L^{2/3} (a) Does...

## Question:

The countries of Aloha and Biki both have the production function

{eq}Y = K^{1/3}L^{2/3} {/eq}

(a) Does this production function have constant returns to scale? Show why or why not.

(b) Derive the per-worker production function (i.e. y = f(k))

(c) Draw a Solow diagram for Aloha and show their steady state. Now, suppose that the depreciation rate of capital, {eq}\delta {/eq} increases due to inadequate maintenance of their roads. Show the new steady state.

(d) Suppose that the country of Aloha has a higher savings rate than Bikini. Draw a Solow diagram and show the steady state of both countries on the same diagram. Which country will be richer in terms of income per capita?

## Production:

The term production in economics can be defined as a process by which the raw materials and other valuable inputs are utilized to manufacture a final product for the market by using production factors like labor, capital and entrepreneurship.