Please see attached.
2. (A Change in Autonomous Spending) Suppose that when aggregate output equals zero, consumption equals $100 billion, autonomous investment equals $200 billion, government purchases equal $50 billion, and net exports equal $50 billion. Suppose also that MPC is 0.9 and MPM is 0.1.
a) Construct a table showing the level of aggregate spending, net exports, and saving plus net taxes for aggregate output levels of zero, $500 billion, and $1,000 billion.
b) Use autonomous spending and the multiplier to calculate the equilibrium level of real GDP demanded.
c) What would be the new level of real GDP demanded if an increase in the U.S. interest rate caused net exports to change by $50 billion? Explain.
Different books sometimes choose to model the variables in this question in slightly different ways. I'll use the most common one here and explain it as clearly as possible so that you will be able to adjust the calculations if in your class you use different models/formulae.
I'll assume here that the consumption function has the form:
C = Co + MPC*Y
where Y is aggregate output and Ca is autonomous spending.
I will assume the investment and government purchases to be fixed for any value of aggregate output:
I = Io
G = Go
(notice that they are fixed in that neither of them depends on Y)
Finally, I'll assume that the net exports follow this formula:
NX = X - M = Xo - MPM*Y
where Xo is the exports level (which is fixed; i.e. doesn't depend on Y).
Now, in order to answer question 1 we must find all the formulae. Let's start ...
Please calculate the equilibrium level of real GDP demanded.
Simple spending multiplier
9. (Simple Spending Multiplier) For each of the following values for the MPC, determine the size of the simple spending multiplier and the total change in real GDP
demanded following a $10 billion decrease in autonomous spending:
a. MPC = 0.9
b. MPC = 0.75
c. MPC = 0.6