1) (9 pt) Capital accumulation and wealth accumulation a) Suppose that the inflation rate for consumption is 3 percent per year, and the inflation rate for investment is 1 percent per year. Assume that the base year is t = 0. Write down the expressions for the consumption price index, Pc,t and the investment price index P1,4 (Hint: What is the value of a price index in the base year? Use the fact that inflation rate is the growth rate of the price index) b) Write down the expression for the price of capital, PK,t. What is the growth rate of the price of capital? Over time, is capital becoming cheaper or more expensive relative to consumption? How is the growth rate of the price of capital related to the capital gains rate? (Hint: How is the price of capital related to investment price index and consumption price index?) c) Suppose that the rate of wear-and-tear depreciation is d 0.07 and that the household saving decision rule is St = 0.12V+ (that is, households save 12 percent of their total wealth in every period). Calculate the growth rate of household wealth, Vt, and the growth rate of capital stock, Kt. (Hint: use the goods market clearing condition to figure out how investment is related to wealth. Use the fact that wealth equals the market value of capital, V+ = pktKt. Use the laws of motion for capital and wealth, respectively, to relate their rates of change to initial levels. Use the definition of the growth rate of wealth, 9v,t+1 (Vt+1 V+)/V+, and a similar definition for 9K,t+1). 1) (9 pt) Capital accumulation and wealth accumulation a) Suppose that the inflation rate for consumption is 3 percent per year, and the inflation rate for investment is 1 percent per year. Assume that the base year is t = 0. Write down the expressions for the consumption price index, Pc,t and the investment price index P1,4 (Hint: What is the value of a price index in the base year? Use the fact that inflation rate is the growth rate of the price index) b) Write down the expression for the price of capital, PK,t. What is the growth rate of the price of capital? Over time, is capital becoming cheaper or more expensive relative to consumption? How is the growth rate of the price of capital related to the capital gains rate? (Hint: How is the price of capital related to investment price index and consumption price index?) c) Suppose that the rate of wear-and-tear depreciation is d 0.07 and that the household saving decision rule is St = 0.12V+ (that is, households save 12 percent of their total wealth in every period). Calculate the growth rate of household wealth, Vt, and the growth rate of capital stock, Kt. (Hint: use the goods market clearing condition to figure out how investment is related to wealth. Use the fact that wealth equals the market value of capital, V+ = pktKt. Use the laws of motion for capital and wealth, respectively, to relate their rates of change to initial levels. Use the definition of the growth rate of wealth, 9v,t+1 (Vt+1 V+)/V+, and a similar definition for 9K,t+1)