Please answer the following numerical problem. Please provide formulas and explanations.

5. An economy has full-employment output of 9000, and government purchases are 2000. Desired consumption and desired investment are as follows: Real Interest Desired Desired Rate (%) Consumption Investment 6100 1500 6000 1400 5900 1300 5800 1200 5700 1100 a. Why do desired consumption and desired invest- ment fall as the real interest rate rises? b. Find desired national saving for each value of the real interest rate. C. If the goods market is in equilibrium, what are the values of the real interest rate, desired national saving, and desired investment? Show that both forms of the goods market equilibrium condition, Eqs. (4.7) and (4.8), are satisfied at the equilibrium. Assume that output is fixed at its full-employment level. d. Repeat Part (c) for the case in which government purchases fall to 1600. Assume that the amountpeople desire to consume at each real interest rate is unchanged