Reference no: EM132560181

People frequently talk about the impact of population change. In this question, we will expand our simple Solow model to reflect how labor influences the production process. Now:

Y = A√(KL)

Where A is a country's level of technology/innovation, K is the amount of capital a country has, and L is the working age population of the country. As with capital, labor has diminishing marginal returns. For the purposes of this question, assume depreciation (D) and investment (I) are unchanging. Since the economic recession of 2008, the US birth rate has declined. By 2025, the number of college-aged students is predicted to fall by more than 15% due to decreased fertility among the US population. By 2070, L, the working age population of the country, will be much smaller than it was in the year 2000.

1) Using our simple version of the Solow model, how will decreases in L, resulting from decreased birth rates in the United States, impact output in the US in the short run? How will decreases in L impact the new steady state level of output?

2) What happens to output per worker (Y/L) in the new steady state?

3) What happens if innovation & technology (A) continues to increase even as the US population shrinks? If A increases while L decreases, will the US get poorer, richer, or stay the same (will Y increase, decrease or stay constant)? Does the increase in A relative to the decrease in L matter to answer that question?

Answer the question here verbally, and/or attach a visual answer to the question below. I recommend drawing a Solow model illustrating the impact of a population shock.

If you would like, you can illustrate the change on a Solow model. Here are some easy example numbers.

In the year 2000, the US is in steady state (ss) where

Yss = A√(Kss*L)

where A = 1, Kss = 100 and L2000 = 100, D = .5 and I = .5

In the year 2070, the US population is L2070 = 81. Change Kss and Yss to find the new steady state.