The IS Curve

Expenditure = C + I + G + (X – M)

Personal disposable income = Y + F – S_B– R = C + S_H

Where F = transfer payments, R = direct and indirect taxes.

Y = C + S + T

where T = (R – F) denotes net taxes and S = (S_B + S_H) denotes total private sector saving.

Total expenditures must be identical to aggregate income (Y):

C + S + T = C + I + G + (X – M)

S = I + (G – T) + (X – M)

Government deficits and surpluses:

G – T = (S – I) – (X – M)

Disposable income = Y – S_B– T

C = C(Y – S_B– T)

or, C = C(Y – T)

The marginal propensity to consume (MPC) represents the proportion of an additional unit of disposable income that is consumed or spent.

Because the amount that is not spent is saved, the marginal propensity to save (MPS) is MPS = 1 – MPC.

Companies are the primary source of investment spending (I).

Total investment, including replacement of worn-out capital, is called gross investment.

GDP includes gross investment.

Investment decisions depend primarily on two factors: the level of interest rates and aggregate output/income.

The level of interest rates reflects the cost of financing investment.

The level of aggregate output serves as a proxy for the expected profitability of new investments.

I = I(r, Y)

where r = the real interest rate

Net exports (X – M) are primarily a function of income in the domestic country and in the rest of the world and the relative prices of domestic and foreign goods and services.

As domestic income rises, net exports will decline.

An increase in income in the rest of the world will lead to an increase in net exports.

A decrease in the relative price of domestically produced goods and services will increase net exports.

Equality of expenditure and income

S – I = (G – T) + (X – M)

Equilibrating income and expenditure entails an inverse relationship between income and the real interest rate. – The IS curve.