Question

The country of Gondor is prosperous, but with a somewhat different produc- tion model than most industrial countries. It depends significantly more on agricultural output and stone masonry, especially outside of its political capital of Minas Tirith. For purposes of the applying the Solow growth model, we can understand these inputs as “land.” To a first approximation, this land cannot be exhausted (it does not depreciate) but its share of production is 20%. The other factors, labor and capital have shares of 50% and 30%, respectively. Capital depreciates at a rate of 10%, the population is not growing and they save 25% of their income. For quantitative purposes, suppose there is one unit of land for every worker and the production scale, what we’ve called Ā, is 1.

1. What is the steady state capital per worker?

2. At what rate is total capital (not capital per worker) growing in steady state?

3. Suppose A were growing by 1% per year, so A_t+1 = (1.01)A_t, at what rate is capital per worker growing in steady state?

4. With everything else equal, suppose the land share fell from 20% to 10% and this was replaced with physical capital. So now the shares for land, labor and capital are 10%, 50%, 40%. Is steady-state consumption per worker higher or lower?

Answer 1

The new production function is given as

Assuming A=1, and Land=L

In per capita term

Therefore, the steady-state capital per worker is

As steady state capital per worker is higher than before, the steady-state consumption is also higher than before.