2 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.

2.1 Consumption and saving

Like the Solow model, we’ll assume a closed economy, although we will explicitly include government spending and taxes.

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

For our basic model, we’ll focus on current disposable income (current income minus current taxes), and add up all of the households. For analytical simplicity, we’ll assume that aggregate consumption is a linear function. Notice that since aggregate household income is total income for the economy, we can write household income as a function of \(Y\) (real GDP) and an aggregate taxes/transfers term \(T\). We are going to assume that aggregate household consumption \(C\) is a linear function of aggregate disposable (post tax) income:

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

Notice we are making the simplifying assumption that all taxes are “lump sum” . This assumption means we ignore “automatic stabilizer’’ programs – features of government policy that lead the government to spend more (or tax less) when income is low. (Although we can think about how to incorporate those into the model).

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.

\(b\), 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 aggegate saving function, which will also be linear.

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

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, households are net borrowers, and for others, they are net savers.

Exercise:. On the same set of axes, sketch the aggregate consumption and savings functions described by the lines you worked out above.

2.2 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 (which consists of planned investment, and unplanned inventory changes).

Remember that 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 make up for the cost of borrowing. 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:

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