Does this production function have constant returns to scale? explain. b) what is the per-worker production function, y = f(k) c) assume that neither country experiences population growth or technological progress and that 20-percent of capital depreciates each year. assume further that country a saves 10% of output each year and country b saves 30% of output each year. using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. then find the stead-state levels of income per worker and consumption per worker. d) suppose that both countries start off with a capital stock

In the steady state level of Country A, the capital per worker is 0.354

In th steady state level of country B, the capital per worker is 1.387.

Now we can find the steady level income per worker like this:

Country A

Country B:

And if we want to find the consumption per worker we can apply this formula:

Country A

Country B

Explanation:

We assume that we have a common production function for country A and B given by:

And we can find the per worker production function like this:

And we can express the function just in terms of a constant like this:

From the info given by the problem we have:

Depressciation

Savings for A

Savings for B

And we assume that

Let's begin finding the steady state level of capital per worker, we need to satisfy the following condition:

The reason is because. The growth of capital per worker is given by investment per worker minus the depreciation per worker , and we have then and if is steady then k=0.

In the steady state level of Country A, the capital per worker is 0.354. For country B we can do a similar procedure like this:

In the steady state level of country B, the capital per worker is 1.387.

Now we can find the steady level income per worker like this:

Country A

Country B:

And if we want to find the consumption per worker we can apply this formula:

Country A

Country B