The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2.
a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium.
b). Is a government policy that raises the saving rate to 40% socially desirable? Explain your answer with reference to a comparison of this new steady state equilibrium and the initial steady state equilibrium in a) above.
c). If the initial capital-labour ratio is 30, is the economy operating efficiently in the sense that welfare cannot be improved? Explain concisely. What if the initial capital-labour ratio is 15? Again explain concisely.