Suppose there is a country called Solowland whose output (Y) is produced using capital (K), labour (L) according to the following aggregate production function: 13 Y = AK^(1/4) L^(3/4) where A is Total Factor Productivity (TFP). The rate of population growth (n) is 2.5% per year (0.025). The rate of depreciation of capital is 15% per year (0.15). Total factor productivity equals 20 (A=20) and we assume there is no technical progress (growth rate of A is zero). a)Show, analytically, that the production function displays diminishing marginal product of capital and labour and constant returns to scale. Explain your answer. b)If Solowlands savings rate (s) is 20% (0.20), find its steady state capital stock per capita, income per capita, consumption per capita and investment per capita. c)Suppose there is another county, Swanland where output is also produced by a diminishing returns production function using capital, labour, and technology. In this country, population growth is just 0.5% (0.005) per year, but TFP grows at a rate of 3% per year. Show, in steady state, what will be the rate of growth of Y, K, Y/L, K/L, and Y/K for both Solowland and Swanland
Suppose there is a country called Solowland whose output (Y) is produced using capital (K), labour (L) according to the following aggregate production function:
13 Y = AK^(1/4) L^(3/4)
where A is Total Factor Productivity (TFP). The rate of population growth (n) is 2.5% per year (0.025). The rate of
a)Show, analytically, that the production function displays diminishing marginal product of capital and labour and constant returns to scale. Explain your answer.
b)If Solowlands savings rate (s) is 20% (0.20), find its steady state capital stock per capita, income per capita, consumption per capita and investment per capita.
c)Suppose there is another county, Swanland where output is also produced by a diminishing returns production function using capital, labour, and technology. In this country, population growth is just 0.5% (0.005) per year, but TFP grows at a rate of 3% per year. Show, in steady state, what will be the rate of growth of Y, K, Y/L, K/L, and Y/K for both Solowland and Swanland
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