Aggregate consumption

Production-income are identical. Income generates demand for production. Production generates income.

Assume a closed economy. No export. No import.

$Y_d$ is the disposable income.

$C$ is the consumption.

$T$ is the taxes.

Consumption can be assumed to increase linearly with increase in disposable income. The slope $\tan\theta$ is called $c_1$.

Investment

Assume that investment is exogenous for simplicity. That is, we do not have an investment function.

Government expenditure or spending $G$. Assume exogenous also.

$G$, $Tx$ combined, are called fiscal policy instruments. (also subsidy)

Determination of equilibrium output

Aggregate demand,

Consider the goods market.

Equilibrium condition is, $Z=Y$. Demand is met by production. In equilibrium, $Y$ (production) equals demand $Z$. Demand in turn depends on income, which is itself equal to production.

$C_1$ is the marginal propensity to consume. Since $C_1$ lies between 0 and 1, $1/(1-C_1)>1$.

$C_0+I+G$ is positive, while $C_1Tx$ is negative. If the former is greater than the absolute value of the latter, then the combined term is positive. Else negative.

$C_0+I+G-C_1Tx$. Assume government has balanced budget (i.e: $G=Tx$). Then, $G-C_1Tx>0$.

When the government incurs a budget deficit. That is, $G>Tx$. Then, $G-Tx>0$ and thus $G-C_1Tx>0$.

Budget surplus, means $G<Tx$.

The first term $1/(1-C_1)$ is called multiplier. Because it magnifies the initial shock.

Plots.

Income on the x axis (which is equal to production) and production on the y axis and Z as well on the y axis. The intersection of the two curves (one of them 45 degrees), is the equilibrium point.

If propensity to consume increases, say from 0.6 to 0.7, the multiplier will increase. Higher $C_1$, higher the multiplier.

When expenditure increases, it immediately generates an increase in aggregate demand. When demand in creases firms produce more, producing additional income. This income increases the aggregate demand.