### What is the government spending multiplier in the economy

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Assignment: This assignment is due in hard copy at the beginning of class on Thursday February 14. Remember that the process of how you arrive at an answer is as important as the answer itself. Therefore, full credit will require you to show all steps and work, clearly label all graphs, and fully explain any answers that ask for an explanation.

Question 1: Fiscal policy in the Keynesian cross model

Recall the following hypothetical economy from problem set 1:

C = 140 + 0.6(Y  −  T)
I¯ = 200
G = 150
T = 150

(a) Use the Keynesian cross diagram and the specific equations here to show the effect of a 150 increase in government spending on equilibrium GDP. Label your graph completely (axes, each line, slopes and intercepts).

(b) What is the government spending multiplier in this economy?

(c) Say that government spending increases by 150. How much does GDP increase? Use the government spending multiplier to arrive at your answer. Now assume investment is described by I = 100 + 0.3Y. (Return government spending to its original level of 150).

(d) What is the equilibrium level of GDP (Y)?

(e) Say that government spending increases by 150. How much does GDP increase?

(f) Is fiscal policy more or less effective now that investment depends on income? (You don't need to do it here, but make sure that you can also explain why).

Question 2: Manipulating the graphical model

Consider an economy described by the following behavioral equations:

C =  c0 +  c1Yd
I  =  b0 +  b1Y
G  = G¯

And taxes (T) are exogenous.

(a) Write an expression for aggregate demand (Z). What are the slope and intercept? [Remember: the slope includes everything that varies with income, and the intercept includes all the terms that are constant (do not vary with income)].

(b) Use the Keynesian cross diagram and the specific equations here to show the solution for equilibrium income graphically. Label your graph completely (axes, each line, slopes and intercepts).

(c) Housing values crash, substantially reducing total wealth in the economy.

i. What is one way this shock could affect aggregate demand? Include in your answer (1) which component of aggregate demand is affected, and (2) which parameter. Explain briefly.

ii. Show the effect of this shock graphically. Does equilibrium income increase or decrease?

Question 3: Investment and income

Let's consider a case where investment depends on output. Suppose the economy is characterized by the following behavioral equations:

C =  c0 +  c1Yd
Yd =  Y −  T
I  = b0 +  b1Y

Government spending and taxes are constant. Note that investment now increases with output.

(a) Solve for equilibrium income.

(b) The multiplier:

i. What is the value of the multiplier?

ii. For the multiplier to be positive, what condition must c1+b1 satisfy?

iii. Is fiscal policy more or less effective when b1 is positive or when b1 is zero (if b1 is zero, then investment is exogenous)? Explain why (the intuition, not the mathematical mechanics).

[Hints: Another way to phrase this question would be "is the multiplier bigger when b1 is positive or when b1 is zero"? Your answer should also be consistent with your answer to Question 1(e), above].

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