Countries 1 and 2 have the production function: Yt = AiKαt L1−α t , where country 1 has Total Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35 for both. In the two countries population is constant and there is no technological progress. Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, and country 2 saves 20%. a) Write down the function of production per unit of labor. Suppose the two countries start with an initial capital stock (per unit of labor) of 500, what are the initial income and consumption per unit of labor in both countries? b) Determine their steady state levels of capital, income and consumption per unit of labor. c) Determine the difference in their steady state level of income per unit of labor, and how much of that difference is due to differences in TFP and how much is due to differences in capital per unit of labor.
Exercise 2: Growth and development
Countries 1 and 2 have the production function: Yt = AiKαt L1−α
t , where country 1 has
Total Factor Productivity (TFP) of A1 = 25, country 2 has TFP A2 = 100, and α = 0.35
for both. In the two countries population is constant and there is no technological progress.
Every year capital depreciates by 6% in both countries. Country 1 saves 40% of output, and
country 2 saves 20%.
a) Write down the function of production per unit of labor. Suppose the two countries
start with an initial capital stock (per unit of labor) of 500, what are the initial income and
consumption per unit of labor in both countries?
b) Determine their steady state levels of capital, income and consumption per unit of
labor.
c) Determine the difference in their steady state level of income per unit of labor, and
how much of that difference is due to differences in TFP and how much is due to differences
in capital per unit of labor.
d) Suppose now that country 2 suddenly has access to the country 1 level of technology.
What would you expect to happen both in the short run and in the long run?
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