# government spending multiplier

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Consider a closed economy, with fixed prices, represented by the following set of equations:

D = C + I + G

C = cYd

Yd = (1 - t)Y

t = 0.25, c = 0.8

I = 700 - 100r

G = 300

L = 2500 + 2Y - 500r

Where, D is the aggregate demand, C is consumption, Yd is the disposable income, t is the tax rate, I is investment, r is the interest rate (measured as a %), G is government spending and L is money demand.

(a) Let the government pursue an interest rate target of 7%. How does it achieve this target? Hence determine the equilibrium level of income Y, the government surplus tY-G and the private sector surplus (1-c) Yd - I. Comment on why D = Y in equilibrium.

(b) Using the same data, calculate the effects of increasing G to 400.

(c) Now let the government pursue a policy of holding the money supply constant at 500, and spending G = 300. What will be the level of income and the rate of interest?

(d) Using the above data, and continue to pursue a fixed money supply target of 500, recalculate your result when government spending increases to G = 400. Comment on the effects, of monetary factors, on the government spending multiplier.

#### Solution Preview

Consider a closed economy, with fixed prices, represented by the following set of equations:

D = C + I + G

C = cYd

Yd = (1 - t)Y

t = 0.25, c = 0.8

I = 700 - 100r

G = 300

L = 2500 + 2Y - 500r

Where, D is the aggregate demand, C is consumption, Yd is the disposable income, t is the tax rate, I is investment, r is the interest rate (measured as a %), G is government spending and L is money demand.

(a) Let the government pursue an interest rate target of 7%. How does it achieve this target? Hence determine the equilibrium level of income Y, the government surplus tY-G and the private sector surplus (1-c) Yd - I. Comment on why D = Y in equilibrium.

When r = 7%,

I = 700 - ...

#### Solution Summary

The government spending multiplier is found.