Question 1: Fiscal policy in the Keynesian cross model Consider an economy descr

Question

Question 1: Fiscal policy in the Keynesian cross model Consider an economy described by the following behavioral equations:

C = C0 +C1  (Y-T)

I =bo +b1 Y

T = t1 Y

Government spending and investment are exogenous; Yd refers to disposable income; and 0 < C1 < 1, c1 + b1 < 1, and 0 < t1 < 1.

a. What is the expression for equilibrium income?

b. What is the government spending multiplier in this economy? Explain (intuitively) why the multiplier is greater than one.

c. Consider a change in government spending. Calculate the effect of a one-dollar increase in government spending on the government budget. [Hint: the government budget is the relationship between taxes and government spending, specifically T G. So, you want to know how much taxes change when government spending changes by $1, and compare this to the $1 change in G. Notice that taxes change when output changes!].

Explanation / Answer

(a) Yd = Y - T = Y - tY

In goods market equilibrium, Y = C + I + G

Plugging in given values and equations, we get

Y = c0 + c1[Y - (t1Y)] + (b0 + b1Y) + G0 [where G0: Autonomous government spending]

Y = c0 + c1Y - c1t1Y + b0 + b1Y + G0

(1 + c1t1 - c1 - b1)Y = c0 + b0 + G0

Y = (c0 + b0 + G0) / (1 + c1t1 - c1 - b1)

(b) Government spending multiplier = 1 / (1 + c1t1 - c1 - b1)

Government spending multiplier is greater than 1, because when government spending increases in round 1 of consumption, income rises, therefore increaseing disposable income (= Y - tY) and as a result, increasing consumption. In round 2, increase in consumption further raises income which again raises disposable income and consumption. This process continues until the last round of income-expenditure cycle ends.

(c) Tax multiplier = -[c1 x (1 - t1)] / (1 + c1t1 - c1 - b1) = [c1 x (t1 - 1)] / (1 + c1t1 - c1 - b1)

Using government spending multiplier,

When Government spending increases by $1, Y increases by $[1 / (1 + c1t1 - c1 - b1)].

Using tax multiplier,

When Tax decreases by $1, Y increases by $[c1 x (t1 - 1)] / (1 + c1t1 - c1 - b1).

Therefore, when Y increases by $[1 / (1 + c1t1 - c1 - b1)], Tax has to fall by {[1 / [c1 x (t1 - 1)]}.

Government budget balance = Tax - Government expenditure, therefore

Change in government budget = Change in Tax - Change in Government expenditure

= - {[1 / [c1 x (t1 - 1)]} - 1

= - 1 x [{[1 / [c1 x (t1 - 1)]} - 1]

= - 1 x [(1 + c1t1 - c1) / ([c1 x (t1 - 1)]

= (c1 - 1 - c1t1) / ([c1 x (1 - t1)]

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