Q. Assume the following information about an economy (in million of dollars):

GDP = $1000

C = $800

G = $120 I = $100

X - IM = - $20 T = $80

TR = $10

Where C is private consumption spending, G is public spending, I is investment spending, T represents taxes and TR represents transfers from government to households. Finally, X - IM represents net exports.

a. Given the above information, compute the level of private savings (Sp), public savings (Sg) and net capital inflows (KI). Is the sum of private savings, public savings and net capital inflows equal to the level of investment? What is the value of national savings (SN)?

b. Now, lets change the problem. First, assume that a net capital inflow is 0. Now, suppose that Consumption (C) is given by the following equation instead of being a provided value: C= 380 - 800i.

And, finally suppose that investment is given by the following equation instead of being a provided

value: I= 2500-200i, where i is the nominal interest rate.

Given this information and these equations, form a equation for national savings (SN). This equation will contain two variables: SN and i. You will need to use the identities (the underlying relationships) that you used in (a). Show your work and any equations or identities that you use.

c. The Savings Curve represents the supply of funds that are available in the loanable funds market while the Investment Curve represents the demand for funds from the loanable funds market. Given this information and the national savings equation you found in (b) as well as the investment equation you were provided in (b) to calculate the equilibrium interest rate and the equilibrium quantity of loanable funds. That is, find the interest rate and loanable funds that make the supply of loanable funds (i.e, national savings) equal to the demand for loanable funds (i.e., investment). Notice in this problem we are explicitly assuming that there are no capital inflows so the only source of savings is private savings and government savings.

d. Suppose that the government wants to reduce the deficit and in order to make it possible the government reduces its expenditures by $100 million. That is, now G=$20. Compute the new equilibrium rate of interest in the loanable funds market. Note: you will need to compute a new equation for SN based on this new government behavior. Assume that nothing has happened to the demand for loanable funds curve you were provided (the investment demand curve in (b)) and that everything else in (b) continues to be true except for the described change in government expenditures. Note this problem still assumes that capital inflows are equal to zero. Explain the result you calculate.

e. Suppose that the only thing that changes in the problem you were given in (b) is that taxes increase by $10 million to a total of $90 million. What happens to the equilibrium interest rate in the loanable funds market? Illustrate your answer by providing a proof of your results (this will require you to use the equations for private savings, government savings, and national savings!) as well as an explanation. Make sure you provide both proof AND explanation.