Assume that the production function is Cobb_Douglas(CD) in capital K and effective units of labor E*L:Y=F(K,EL)=(K)^a(EL)^(1-a).
Labor L is growing at rate n, productivity E increases at rate g, depreciation rate is & and savings rate is s. Marginal product of 1 unit capital goes to the capital owner and compensates him/her for depreciation & and opportunity cost r of this 1 unit: MPK=r+&. Thus, the real interest rate in Solow model is equal to r=MPK-&.
1. In his book " Capital in the Twenty_first Century" T. Piketty show that for many countries real interest rate r is greater than the growth rate of real GDP: r>n+g. What does this fact tell us about the level of capital per effective worker k=K/EL in these countries relative to the "Golden Rule"level?
2.Piketty argues that if all capital income is reinvested then the total amount of capital will grow at rate r>n+g-faster than GDP. Let's check if this is possible in the steady state in our model. Namely, assume that investments are equal to capital income, ie. i=MPK(k) * k rather than i=s*f(k)as in the standard Solow model. What will the steady state level of capital per effective worker (k*)be under this investment function? Would r>n+g still hold in that steady state?
3. When the conditions i=MPK * k and r>n+g hold simulataneously in Solow model with CD production function? Illustrate this situation with a graph.[Hint:remember that the economy may for some periods be ourside the steady state]
Assume that the production function is Cobb_Douglas(CD) in capital K and effective units of labor E*L:Y=F(K,EL)=(K)^a(EL)^(1-a).
Labor L is growing at rate n, productivity E increases at rate g, depreciation rate is & and savings rate is s. Marginal product of 1 unit capital goes to the capital owner and compensates him/her for depreciation & and opportunity cost r of this 1 unit: MPK=r+&. Thus, the real interest rate in Solow model is equal to r=MPK-&.
1. In his book " Capital in the Twenty_first Century" T. Piketty show that for many countries real interest rate r is greater than the growth rate of real GDP: r>n+g. What does this fact tell us about the level of capital per effective worker k=K/EL in these countries relative to the "Golden Rule"level?
2.Piketty argues that if all capital income is reinvested then the total amount of capital will grow at rate r>n+g-faster than GDP. Let's check if this is possible in the steady state in our model. Namely, assume that investments are equal to capital income, ie. i=MPK(k) * k rather than i=s*f(k)as in the standard Solow model. What will the steady state level of capital per effective worker (k*)be under this investment function? Would r>n+g still hold in that steady state?
3. When the conditions i=MPK * k and r>n+g hold simulataneously in Solow model with CD production function? Illustrate this situation with a graph.[Hint:remember that the economy may for some periods be ourside the steady state]
