Question

Consider the Basic growth model from your text and lecture as defined below: Production function: GDP = f(At, Kt, Lt); where capital (K) and labor (L) are substitutes and technology (A) aids production

Demographic Behavior: Lt+1= Lt(1+n) = Nt+1; where n is the population growth rate, N is the total population and there is no unemployment

Capital and Savings/Investment Dynamics: Kt+1 = It + Kt(1-δ); It = St = s*Y; where δ is the depreciation rate of capital, s is the savings rate and investment is I.

Technology Change: At+1= At(1+λ); where λ is the constant growth rate of technology Suppose output would be Y*1 in the next period if nothing changed.

Part 2: Consider the savings/investment functions

c) What is the effect of an increase in the savings rate s on GDP growth?

d) How does the savings rate affect growth (what is the mechanism, 1-2 sentences)?

Now suppose that a country has a very low GDP, such that GDP per capita can purchase exactly enough food to exactly satisfy a minimum consumption constraint (meaning all households must consume at least that much).

e) What is the savings rate of this country?

f) What level of capital will this country achieve in the long run?

Answer 1

c) there will be no effect on GDP in period t because increase in savings would increase GDP of period t+1.

d) now, we think about the mechanism of growth by savings then first consider St which increases due to increase in s . Higher St means higher It. Higher It implies higher capital in t+1 period and higher output.

e) If GDP of a country is low then it's saving rate would be less than s^*.

d) In future country would try to increase it's saving and hence capital that much where it achieves the optimal output y^*.