#### Building Up Aggregate Demand, Income-Expenditure Diagram and Consumption Function

Building up Aggregate Demand:

If prices are sticky the level of real GDP is resolute by the level of aggregate demand:

Y = E

And not by the level of possible output:

Y = Y*

The Consumption Function:

C = Co + Cy (1-t) Y

If alter in incomes are considered permanent the MPC will be high: a \$1 raise in incomes will lead to a raise in consumption of as much as 80 cents. However if changes in income are considered transitory the MPC will be low: a \$1 increase in incomes will lead to an increase in consumption of only 30 cents or so. Transitory raises in income have only a small effect on consumption because people seek to smooth out their consumption spending over time.

The stage of investment spending, I, is figure out by the real interest rate and assessments of profitability made by business investment committees:

I = Io - Ir x r

In our model we symbolize these determinants by making investment spending I a function of the real interest rate r and of the parameters I0 and Ir, the baseline level of investment expenditure and the interest sensitivity of investment.

The stage of government purchases G is set by politics. Net exports are equivalent to gross exports (a function of the real exchange rate ε as well as the level of foreign real GDP Yf) minus imports. Imports are a task of national income Y:

NX = GX - IM = (XfYf + Xε ε) - IMyY

Let’s obtain the equation for aggregate demand:

E = C + I + G + NX

And reinstate the two components of aggregate demand that depend directly on national income Y by their determinants:

E = (Co + Cy (1-t) Y) + I + G + (GX - IMyY)

We are able to now classify the components of aggregate demand into two groups. The first group is so-called as autonomous spending which we will call ‘A’. Autonomous spending is invented of those components of aggregate demand that don’t depend directly on national income Y. The second group comprises all the other components of aggregate demand. It is equivalent to the marginal propensity to expend or MPE for short on domestic goods times the level of national income Y. Therefore with these new definitions of:

A = Co + I + G + GX

and:

MPE = Cy (1-t) - IMy

We can reschedule our equation for aggregate demand to fit these new definitions:

E = (Co + I + G + GX) + (Cy (1-t) - IMy) x Y

And rephrase aggregate demand in the more compact form:

E = A + MPE x Y

The intercept of the planned spending or aggregate demand line is the level of autonomous spending A the slope of the planned spending or aggregate demand line is the marginal propensity to expend MPE.

The Income-Expenditure Diagram:

Legend: On the income-expenditure diagram the line shows the relationship between total economy-wide income on the one hand total aggregate demands on the other--the planned expenditure line--is determined by two things. Autonomous spending is the level at which the planned spending line intercepts the y-axis. The marginal propensity to spend is the slope of the planned expenditure line.

An Increase in Autonomous Spending:

Legend: A raise in autonomous spending shifts the planned expenditure line upward.

An alter in the value of any determinant of any component of autonomous spending--the baseline levels of consumption C0 of investment I0 or government purchases G the real interest rate r and foreign-determined variables like foreign levels of real income Yf, foreign interest rates rf or speculators' view of exchange rate fundamentals ε0—will shift the planned expenditure line up or down. The elevated is autonomous spending the further from the x-axis the planned expenditure line will be.

Alterations in the marginal propensity to consume Cy and in the tax rate t or in the propensity to spend on imports IMy will change the MPE as well as the slope of the planned expenditure line. The elevated the MPE the steeper is the slope of the planned expenditure line. Above figure is an example of how to calculate the MPE.

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