Question

Consider the version of the Solow growth model without technological change covered in lecture. Assume that one country has been at the BGP for many years and suddenly at time there is a permanent decrease in the savings rate. Show how the economy will adjust to a new BGP by working with the modified system (per capita/worker variables). Show how capital per worker adjusts to the new Steady State level and how its growth rate changes over time

Answer 1

In the Solow growth model without technological change, a decrease in the savings rate leads to a new lower steady-state level of capital per worker and lower economic growth over time. The growth rate of capital per worker declines during the transition and returns to zero once the new steady state is achieved.

Step-by-step explanation:

When considering the Solow growth model without technological change, a permanent decrease in the savings rate in a country that has been at a Balanced Growth Path (BGP) leads to a new steady-state adjustment. At the initial steady state, capital per worker and output per capita are at equilibrium levels, with no capital per worker growth. After the savings rate drops, the new steady-state level of capital per worker will be lower because the economy will be saving and investing less in capital deepening.

In the transition to the new steady state, the economy will see the growth rate of capital per worker decline as it adjusts to a lower level of steady-state capital per worker. However, once the new steady state is reached, the growth rate of capital per worker will return to zero, as it is in any steady state in the Solow model without technological progress. Economic growth over time will also be lower in the new steady state due to the lower level of savings and investment.