1) In real intertemporal model with investment, suppose the economy is in a competitive equilibrium initially. Suppose now all the consumers and firms anticipate a reduction in future total factor productivity.
(a) Draw a diagram to show how the reduction in future total factor productivity would affect individual firms' demand for future capital. Keep in mind that future capital is related to current capital and investment. Explain your diagram briefly.
(b) Suppose the economy is in a competitive equilibrium initially. Use the current-labormarket-equilibrium diagram and the current-goods-market-equilibrium diagram to show how the reduction in future total factor productivity would affect current output, real interest rate and current employment. Explain your diagram briefly.
2) A) In Solow growth model, we focus on the growth of per-worker capital. Please derive how the per-worker capital grows from time t to t+1, by starting with the law of motion of aggregate capital, which express how the aggregate capital accumulates over time. And please show by what conditions that the economy reaches the steady state.
(b) Draw a diagram to show how a decline in the growth rate of the work force would affect the steady-state level of per-worker capital in the Solow growth model. Explain your diagram briefly.