Question

Consider two countries, A and B, that have the same technology given by Y=L^1/2N^1/2. The two countries have the same land area.

The population growth function in countries A and B are given by g(c)=5c and g(c)=4c, respectively.

For the periods from 0 to T-1 the economies were separated and at their steady states. However, at the beginning of time T, the wall between the two countries collapsed and the two countires were merged.

Making certain assumptions, plot the time path for c and N for the new economy.

Make sure that you state the assumptions.

Answer 1

Solution:--

The assumptions are as follows:

1. There is only one composite commodity which can be consumed or used as an input in the production or can be accumulated as a capital stock.

2. Labour force grows at a constant proportional rate c.

3. Full employment prevails at all times.

4. Capital-output ratio (v) is also given.

5. Saving-income ratio (s) is constant.

6. There are fixed coefficients of production. Thus, there is no possibility of the substitution of capital and labour.

7. There is no Technical change.

Plotting the time path for the new economy:

In the steady state, the output per worker Y, and the capital labour ratio, k remains constant, while total output and capital increase proportionately to the labour supply growth rate, N represents proportion of Capital.

The following figure shows steady state when population and labour growth are present . At the steady state, output and economic growth will equal the rate of increase in the population.

The following figure shows a steady state when net investment is zero and capital stock remains constant at K*.