Question

2) Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.4; d = 0.05; A = 1; s = 0.75; n = 0.4 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher savings rate have on this model?

Answer 1

Capital accumulation equation is given by

kt + 1 = kt + It - (d + n)kt

Change in k = sy - (d + n)k

In the steady state, we have change in k = 0

sy = (d + n)k

k / y = s / (d + n)

k / 1*k^0.4 = 0.75/(0.05 + 0.4)

This gives k* = 2.34

Hence steady state capital per worker = 2.34

Steady state level of real output/income per worker = 1*2.34^0.4 = 1.4

Steady state level of investment per worker = sy = 1.055

Steady state level of consumption = 0.25*1.4 = 0.35

A higher saving rate would raise the capital accumulation and capital stock per worker in the short run. This would increase economic growth rate in short run. An increase in the saving rate causes immediate fall in consumption but increases investment.

With time, the capital stock rises which increases real income, and thus raising the level of consumption and investment. This happens until the economy reaches a new steady state. But a higher saving rate would not bring sustained economic growth.