Question

14. In the Solow growth model, output ? is produced using capital ? and labour ?.
There are constant returns to scale, and diminishing returns to capital and labour
individually. The production function is ? = ?(?, ?), capital depreciates at rate ?,
the population grows at rate ?, and the saving rate is ?.
(a) Sketch graphs of saving per worker, and the amount of investment
per worker needed to maintain a constant level of capital per worker, both
plotted against capital per worker on the horizontal axis. Explain the shapes
of these graphs.
(b) Explain why there exists a steady state for capital per worker and
output per worker.
(c) Suppose the countries of the world were to share the same
parameters (saving rate, population growth rate, etc.). Explain why the Solow
model predicts convergence over time in living standards across countries.
(d) Consider a country that is relatively poor compared to the richest
countries of the world. How will its growth rate compare to richer countries
according to the Solow model? What will happen to its growth rate over
time? Explain.
(e) Is it possible to change the long-run predictions in parts (c) and (d)
if a country increases its saving rate? Explain your answer.

Answer 1

1. The Y-axis represents per capita saving and capital per worker is plotted on the horizontal axis. The 45 degree straight line represents break-even investment, which depicts the exact amount of gross savings needed to offset the depreciation in capital to keep capital per worker constant. The sy curve depicts per capita savings as the share of per capita income for people and the intersection of the two curves gives us the steady state level of capital per worker k*. The sy curve derives its shape from the production function itself because the difference between y curve and sy curve is investments.

2. The model predicts a convergence to a stable equilibrium, or the steady state where capital per worker and
output per worker are constant. The Solow model assumes CRS and is diminishing in capital itself therefore, it cannot sustain perpetual growth. When the system reaches the steady-state, the economy stops growing, and the economy only invests to keep up with effective depreciation.This is why there exists a stable equilibrium for output per worker and capital per worker.

3. If countries of the world were to share the same parameters (saving rate, population growth rate, etc.) they ultimately exhibit similar levels of per capita income and share similar standards of living. It states that the initial conditions do not matter and as long as parameters are same and there are diminishing returns, countries are bound to converge in their standards of living.

4. If countries have the same underlying characteristics that determine their steady state levels, then the solow model predicts that  a country that is relatively poor compared to the richest countries of the world would grow faster. In essence, it means that poor countries will grow relatively fast (since their initial stock of capital is low), while richer nations will grow quite slowly and over time the Solow model predicts that both the poor and rich countries will approach the same k*.