Question

Using Total Expenditures, the money market, and the investment market describe and graphically depict the effect of a decrease in Lump Sum Taxes on the equilibrium level of output and the interest rate.

Answer 1

The effect of decrease in tax on equilibrium output and the interest rate can be explained by the IS-LM model.

The total expenditure function is

TE= (C + c(Y-T)) + I + G + (X-M)

At equilibrium TE (total expenditure) = Y (output)

At equilibrium, Y = C + c (Y-T) + I + G + (X-M)

This is also known as the IS equation

Y-T = disposable income

T= tax

C= autonomous consumption

c = marginal propensity to consume

I= investment

G= government expenditure

X-M = net exports = exports - imports

If the interest rate increases, the investment drops, which pushes down the demand for goods and the equilibrium output is lower. Hence there exists an inverse relationship between the interest rate and the equilibrium output.

If there is a decrease in the lumpsum tax, the disposable income increases, this in turn increases the consumption of the consumer and thereby increasing the output Y of the economy. Thus a decrease in lumpsum tax will shift the IS curve to the right.

In the money market the money, demand is equal to the money supply at equilibrium. Money demand comprises of the transactions demand and the speculative demand. When the money demand depends on the interest rate and the output, the LM curve is upward sloping as shown in the figure.

MS = MD

This is the LM equation.

Where MS = money supply = M/P

MD = money demand

If income increases, the demand for money increases at any given interest rate. Assuming money supply is fixed, the interest rate, must increase to lower the demand for money and maintain the equilibrium. Thus there exists a positive relationship between interest rate and output.

A decrease in the lumpsum tax will cause the consumption to increase, leading to an increase in the output. This increase in the output increases the demand for money and cause a rightward movement along the LM curve.

THUS,

when taxes decrease, the consumption increases, leading to an increase in the output.

The increase in income increases the demand for money. Given a fixed money supply, the interest rate increases to pull the demand for money down to maintain the equilibrium.