Question

Question 3: Multiplier Model (20 Points] Suppose the components of a closed economy can be described by the following set of equations: Y=C+I+G C= 1200 +0.8 (Y-T) I = 750 G = 900 T=950 (a) Is the government currently running a balanced budget, a budget deficit or a budget surplus? Explain. [3 Points (b) Calculate the equilibrium income. [6 Points) (c) Graphically illustrate, using the Keynesian Cross Diagram, the effect of a decrease in government spending on equilibrium output. [5 Points) (d) Suppose that government spending (G) decreases by 60 so that G = 840. Calculate the value of the new level of equilibrium income. How much did equilibrium income change as a result of the decrease in government spending? Calculate the government purchases multiplier. [6 Points)

Answer 1

a). An economy run on balanced budget when tax revenue (T) is equal to government expenditure (G). It run on budget deficit when G > T and it runs budget surplus when G < T.

This economy is currently a budget surplus because tax revenue (T) is $950 which is more than and government expenditure (G) which is $900. As T > G we can say the economy is currently in budget surplus. As we know when tax revenue (T) is more than government expenditure the economy is in budget surplus.

(b). In Equilibrium, aggregate income = aggregate expenditure. Here Y is aggregate income and C+I +G is aggregate expenditure.

In Equilibrium, Y = C + I + G

Putting the values of C, I and G we get,

Y = 1200 + 0.8(Y - T) + 750 + 900

Or, Y = 1200 + 0.8(Y - 950) + 750 + 900 ; ( as T = 950)

Or, Y = 1200 + 0.8Y - 760 + 750 + 900

Or, Y - 0.8Y = 2850 - 760

Or, 0.2Y = 2090

Or, Y = 2090/0.2 = 10,450

Therefore Equilibrium income say Y_{​​​​​​0} = 10,450. (Ans)

(c).

AD A AS ADO ADI Eo EL o Y, Yo Y

In the above initial AD curve is AD_​​​0 and new AD curve is AD_​​1 . AD curve has shifted downward because of decrease in government expenditure. Initial equilibrium Y is Y0 and new equilibrium Y is Y1. Due to decrease in government expenditure equilibrium output has decreased from Y0 to Y1. Here in the figure Y1 is less than Y0.

To understand more clearly we can show it in below figure

AD AS AD G=bro GG Go Izlo Io c-Co 1. C=C. I co I lo 0 Yo Y Y, Y

In these two figures we have shown how decrease in government expenditure reduces equilibrium output Y. In the first figure G = G0 and in second figure G= G1, where G1< G0. Other things remain same in both figure. In the first figure equilibrium output Y0 is greater than equilibrium output of second figure which is Y1. Here Y1<Y0. It happens because G1 < G0 . So we can say decrease in government expenditure leads to decrease in equilibrium output.

(d). Suppose the government spending decreases by 60 and new G is 840.

We can calculate new level of equilibrium income by using same data as above and only change is G = 840

In equilibrium, Y = C + I + G

Or, Y = 1200 + 0.8(Y - T) + 750 + 840

Or, Y = 1200 + 0.8(Y - 950) + 750 + 840 ; (as T = 950)

Or, Y = 1200 + 0.8Y - 760 + 750 + 840

Or, Y - 0.8Y = 2790 - 760

Or, 0.2Y = 2030

Or, Y = 2030/0.2 = 10,150.

Therefore new level of equilibrium income Y_{​​​​​​1} say is 10,150. (Ans).

Therefore change in equilibrium income is Y_{​​​​0} - Y​​​​​_{​​​​​​1} = 10,450 - 10,150 = 300.

So, change in equilibrium income is 300 as a result of decrease in government spending. (Ans).

Government purchase multiplier is ∆Y/∆G = 1/1-MPC

Here ∆Y = is change in equilibrium Y and ∆G is change in government spending.

Therefore, ∆Y/∆G = 300/60 = 5

1/1-MPC = 1/1-0.8 = 1/0.2 = 5

Government spending multiplier is 5. (Ans).