Question

Consider two economies that are identical in all dimesions -- the same population, same saving rate, the same production function, etc, -- except for the fact that one has a level of productivity that is twice as high as the other, that is A^h = 2A^l . Assume both economies are in their steady states. what is the relationship between the levels of income per worker in these two economies?

Answer 1

There are 2 ecoonomies that are identical in population, saving rate and same production function. The level of productivity is different. In one economy the level of productivity is twice as hish as other Ah=2Al.

Both economies are in the steady state. The percapita income at steady state in 2 economies are

Economy 1:

y1*=ka(sAh/d+n)(a/1-a)

y1*=ka(2sAl/d+n)(a/1-a)

k is the per capita capital, s is the saving rate, Ah is the productivity of one country, d is the deprication rate and n is the population growth rate , a is the share of capital in the output.

Economy 2:

y2*=ka(sAl/d+n)(a/1-a)

k is the per capita capital, s is the saving rate, Ah is the productivity of one country, d is the deprication rate and n is the population growth rate , a is the share of capital in the output.

If all factors are same in 2 economies then comapring y1 and y2 we can say y1 is higher than y2 by a multiple of

2(a/1-a). The multiple value depends on the capital share of the output in the economy.