Answer to Question #94239 in Macroeconomics for monica torres

Question

5. Suppose there is an increase in the population growth rate.
a. Show graphically how this affects the growth rate of both output per capita and total output in the short and the long run. Briefly explain your answer (Hint: Use a diagram like Figure 3-5.)
b. Chart the time paths of per capita income and the per capita capital stock following this change. Briefly explain your answer (Hint: Use a diagram like Figure 3-6.)

Answer 1

Population growth, of course, affects accumulation of capital per worker. To see how, start with the approximation that the proportional change in a ratio is equal to the proportional change in the numerator minus the proportional change in the denominator yields. The approximation is good for modest-sized changes, such those for macroeconomic aggregates from year to year. 

Population growth, in itself, reduces the steady-state level of capital per worker. Via the production function, this translates directly to lower per capita output and income. Steady-state per capita income is constant; total output grows at the rate of population growth.

Solow’s model, even in a rudimentary version without technical change, explains

• positive correlation of investment rates and per capita income

• negative correlation of population growth and per capita income

see graphic here:

https://slideplayer.com/slide/4756224/

http://qed.econ.queensu.ca/pub/faculty/clintonk/econ223/3%20Solow%20growth%20model.pdf