1 Components of aggregate demand

In this section, we’ll talk about the components of “aggregate demand” – the things that people spend their money on. We’ll think about it in terms of some simple equations that describe peoples’ behavior in the aggregate.

1.1 Consumption and saving

We’ll assume a closed economy, although we will explicitly include government spending and taxes.

We start with consumers. As we’ve seen earlier in the course, households consider a number of different factors when they’re making consumption plans – including things like their permanent income and interest rates.

For our basic model, we’ll focus on current disposable income (current income minus taxes). For mathematical simplicity, we’ll assume that aggregate consumption is a linear function of disposable income. Notice that since aggregate household income is total income for the economy, disposable income is just aggregate real GDP \(Y\) minus aggregate taxes \(T\), which we’ll assume are “lump sum,” so that the aggregate consumption function is

\[C(Y,T) = a + b(Y-T)\]

The assumption we’re making says that the “C’’ part of the GDP accounting identity is a function of real GDP and real taxes minus transfers. We’ll call this expression the aggregate consumption function.

\(a\) in the aggregate consumption function is called “autonomous consumption.’’ It is a catch-all variable for any consumption that occurs which is unrelated to the current level of disposable income. For example, if (in the aggregate) household wealth matters for income, it’s captured in \(a\).

\(b\), the slope of the aggregate consumption function, is the marginal propensity to consume (MPC). It has the natural interpretation of the amount that consumption increases for every additional dollar of disposable income the household receives.

Assuming that all disposable income is consumed or saved, we can also define an aggregate saving function, which will also be linear. (To see this, note that \(Y-T = C + S\), substitute the aggregate consumption function in for \(C\), and solve for \(S\).)

\[S(Y,T) = - a + (1-b) (Y-T) \]

If you’re feeling concerned about the intercept of this savings function being negative, remember that borrowing is like negative saving. For certain levels of GDP and net taxes, the household sector is a net borrower, and for others, they are net savers.

Exercise:. Sketch the aggregate consumption and savings functions described by the lines you worked out above.

1.2 Investment and government spending

Given that we’ve assumed a closed economy, we know that all output can be assigned to three uses: Household consumption (\(C\)), Government purchases (\(G\)), and investment \(I\).

Remember investment has many components: residential investment, business fixed investment, and inventories. We will simplify by assuming there are two kinds: planned investment and unplanned inventory changes, which happen when consumers buy more or less of the firms’ output than expected.

We will assume planned investment is mainly determined by the interest rate \(r\). When \(r\) is high, it is expensive to borrow. All else equal, investors want to borrow less because few projects have a high enough return to have a positive net present value. The reverse is true when \(r\) is low.

Exercise:. What might cause planned investment to change besides interest rates (that is, what will cause in the investment curve at a given \(r\)?)

Unplanned investment does not directly depend on the interest rate. It is merely the result of the fact that consumers may buy more or less than firms anticipated in a given period.

Overall investment is therefore

\[ I(r) = PI(r) + \text{Unplanned inventory changes}\]

This means we can write the overall uses of income as the sum of consumption, investment, and government spending:

\[ Y = C(Y,T) + PI(r) + \text{Unplanned Investment} + G \]