Imagine a closed economy operating at its potential.

(a) Starting with the definition of national income (from the expenditure side) show that national saving (composed of private and government saving) must equal the level of investment. Briefly explain why the supply of loanable funds (national saving) is upward sloping in the interest rate and why the demand for loanable funds (investment) is downward sloping in the interest rate. In a diagram of the market for loanable funds, show the equilibrium interest rate and level of investment.

(b) Suppose the government institutes an "investment tax credit" to increase investment. This policy reduces the amount of taxes paid by firms based on the amount they invest. Explain (and show in your diagram) why this policy may lead to an increase in investment, but an increase that is less than what a simple analysis of the effect on investment demand might suggest.

(c) Suppose instead that the government institutes a "private saving tax credit". This policy reduces the amount of taxes paid by individuals based on the amount they save. Explain (and show in another diagram) why this policy may lead to an increase in investment, but an increase that is less than what a simple analysis of the effect on private saving might suggest.

(d) Now suppose that rather than either of the policies described above, the government reduces its deficit by decreasing its spending. In another diagram, show that this leads to an increase in investment spending. Explain why the composition of the spending cuts is important in determining whether "investment" more broadly defined will increase by as much as your diagram indicates.

(e) Each of the policies described above may lead to an increase in the long-run level of investment spending in the economy. Using a diagram of the aggregate production function, show that any such increase will lead to an increase in the future level of potential output and potential output per worker.