Question

(5)

Suppose two countries, A and B, currently have the same level of output per worker. Further assume they have the same depreciation rate and same level of productivity. However, output per worker is growing in country A and falling in country B. What can you say about each country’s rate of investment? Support your conclusion with an appropriate graph

Answer 1

As per the question, Country A and B has the same level of output per worker, same depreciation rates and same productivity.

Thus, the steady state ratio of the output per worker in country A to the output per worker in country B is given by:

When Country A and Country B has same depreciation rates and same productivity, this implies:

But, the question states that the output per worker is growing in country A and falling in country B

This implies that both countries are not given in their respective steady states, rather they are converging to their respective steady states.

Under the condition of same level of output per worker, same depreciation rates and same productivity, by the process of elimination, the only difference between the countries can and must be with respect to the level of capital stocks.

Capital stock levels follow the process:

Thus, one can conclude that the differences in investment rates are responsible for the divergence in output per worker.

Specifically, a rise in output per worker for Country A and a fall in output per worker for Country B imply that the ratio of steady-state output per worker is:

Thus, it can be said that with same depreciation rates and same productivity such that the output per worker is growing in country A and falling in country B, the investment rate in Country A is higher than that in Country B.

Thus, it can be observed that the conclusion as stated can be draw using steady state equation forms. The graphs are not required.