Question

a. Compare and contrast the assumptions of the Malthus and Solow models of growth and their conclusions about the determinants of growth. How do the models’ predictions relate to the empirical evidence on growth?

b. Consider the Solow model. Consider an economy with capital per worker below the steady state level. Show in a graph and explain in words what will happen to the economy over time.

Answer 1

a)

Assumptions of Malthus model :

i) Population growth creates pressure on the land and depresses the living standards in agricultural economies, i.e, Real wage depends on population growth.

ii) Lower living standards raises mortality rates

iii) P(t) = P0ert

Where P(0) is initial population size.

Assumptions of Solow model:.

i) Population grows at constant rate G, Hence, N1 = N(1+g)

Where, N1 is the future population and N is the current population.

ii) All consumers in the economy save a constant proportion of their income.

iii) All firms in the economy produce output using the same production technology that takes in capital and labor as inputs.

iv) Production function assumed to exhibit constant returns to scale.

In both models, the behavior describing aggregate consumption is the same. Population growth rate is an important component to influence economic growth in both the model.

Empirical evidence of Malthus model:

During 14th century, 40% of European population were killed in Plague. As death rates increased, there were decrease in population and hence followed by a significant increase in real wage in these regions.

Empirical evidence of Solow model:

During 1950-73 period, rate of technological progress in US was 2.6 whereas, growth in output per capita was 4.3%. During 1973-87 rate of technological progress in this country was 1.6% and corresponding per capita output growth was 2.1%.

b)

In Solow model steady state depends on

k*: sf(k*) = (δ + n+ g)k*

s= saving rate, δ= rate of depreciation; n= population growth rate and g= rate of technological progress

Change in capital stock => Δk = sf(k) - δk

If an economy starts with capital per worker below the steady state level, k1 <k*, the investment level exceeds depreciation amount. Therefore, capital per worker (k) will rise overtime. It will continue until the steady state k* is reached. Once k* is reached, it will not change,

i.e, Δk =0

f(k) function in the diagram show the corresponding output per worker in the long run.