# Interest rate, consumption and investment

## The consumption function

Consumption C(r) is assumed to be negatively related to the real interest rate r

The aggregate demand for consumer goods is defined as the total amount of finished goods and services that households wish to buy under different conditions. There is no specific supply of consumer goods -firms offer final goods but do not distinguish between the supply to consumers, the supply to investors and the supply to foreigners.

We have used the symbol C for the observed consumption. To be consistent with the notation we should denote the demand for consumer goods by CD. However, this is not common practice in macroeconomics. Instead, the symbol C is used for the demand for consumer goods as well. Fortunately, it is almost always obvious from the context if the symbol C represents the observed consumption - it is then a variable -and when C represents the demand for consumer goods - it is then a function.

Moreover, the term "demand for consumer goods" is often shortened to the "demand for consumption" or simply "consumption". Whenever you see "consumption", you need to figure out if it means observed consumption or consumption demand.

In the classical model, the demand for consumption is assumed to be negatively related to the real interest rate r. Higher real interest rates makes it more expensive to borrow money for consumption today. Similarly, it will be more favorable to postpone consumption to the future.

Consumption is therefore denoted by C(r) and this notation makes it clear that we are talking about demand for consumption and not observed consumption.

## Investment demand

Investment I(r) is assumed to be negatively related to the real interest rate r

The total demand for investment goods is defined as the total amount of investment goods firms wish to purchase under different conditions. Again, as for consumption, there is no "investment supply" and we often use "Investments" as short for the demand for investment. We use the same symbol I for observed investments and for the demand for investments.

In the classical model, investments are also negatively related to the real interest r. Investments will lead to a higher income in the future and with a higher real interest rate, such future income is worth less today. Fewer projects requiring investments will be profitable and investments will declines. Investments are denoted by I(r) in the classical model.

## Government revenue, government spending and net exports

G, NT and NX are exogenous variables in the classical model

In the classical model (and in most macroeconomic models) government spending and net taxes are assumed to be exogenous variables determined by the government.

Net Exports NX is also an exogenous variable which means that both imports Im and exports X are exogenous variables. Exports are determined by the rest of the world and this variable is exogenous in most macro models. It is possible to assume that imports depend on the real interest rate by the same arguments we used for consumption. It would be possible to modify the classical model such that imports depended on the real interest rate but the results would be largely the same. Therefore, we assume that imports are exogenous as well.

## Household savings

Remember that consumption may refer to the observed consumption as well as to the demand for consumption. The same is true for "household savings", which may be the observed household savings as well as the supply of savings by the household sector. The supply of savings by the household sector is defined as the net amount that all households together which to lend under different conditions.

First note that for savings, we are always interested in the net. Some individuals will want to borrow and some will want to lend and some will want to do both. Household savings is the sum of all items where lending is defined as positive amounts and borrowing as negative amounts. If you borrow money in the bank, you are in effect reducing the total amounts of savings.

In the classical model the supply of savings SH depends positively on the real interest rate in the classical model. This follows by the fact that C depends negatively on r. When r increases, we consume less and save more. Therefore, household savings is denoted by SH(r).

## Total savings

Total savings S(r) depends positively on the real interest rate.

Remember that total savings is defined as S = SH + SG + Six, the sum of net savings from the household, the government and the rest of the world. As with SH, S may be the observed amount of savings or the total supply of savings. In the classical model, SG and SR are exogenous variables. SG = NT - G and SR = Im - X depend only on exogenous variables and are therefore themselves exogenous.

The only part of savings that is endogenous is household savings. Since household savings depend positively on the real interest rate, total savings will depend positively on the real interest rate. In the classical model we use S(r) to denote total savings and we have Note that SH, SG, and/or SR may very well be negative. For example, when SG is negative, G > NT and the government is a net borrower.

## Interest rate determination

The real interest rate r will be equal to the equilibrium real interest rate

In the classical model we define the equilibrium real interest rate r* as the real interest rate where savings is equal to investments, S(r*) = I(r*). From section 4.9 we know that S = I is a requirement for the financial market to be in equilibrium.

In the classic model, the real interest rate determines the flow of funds into and from the financial market. A higher real interest rates will lead to larger flows of funds into the market (savings depends positively on r) and the smaller flows out from the market (investment depends negatively on r). The real interest rate will be such that the flows into the market are precisely equal to the flows out of the market. Fig. 10.6:Determination of the real rate.

From this graph we can also determine the size of investments and savings. In equilibrium when r = r*, S = I which is what we need for the GDP identity to hold. Once we know savings, we can determine household savings from SH = S - SG - SR.

In the classical model, expected inflation 1 is an exogenous variable and since R = r + 1 we can determine the nominal interest rate from the real rate.

## Consumption

The final variable to be determined in the classical model is consumption C. Consumption may be found in several ways which will all produce exactly the same answer:

C = C(r) from the consumption function as we know r.

• By solving for C in the equation SH = Y - NT - C. We have found Y and SH while NT is exogenous.

• By solving for C in the GDP identity Y = C + I + G + NX. We have found Y and I, while G and NX are exogenous.

# Determination of all the variables in the classical model

The following diagram shows how all the variables are determined in the classical model: Figure 10.7 Determination of all the variables in the classical model.

1. Start at the top right. Here we determine L and real wage W/P.

2. Follow L down to the point on the production function in the middle to the right. Here you can find real GDP.

3. Follow GDP to the left to the graph of the left in the middle. This graph consists of a single 45-degree line. All points on a 45-degree line have the same x and y coordinates. Such graph is used to transform a variable from the y axis to the x axis.

4. Follow Y up to the top left graph. In this graph you find aggregate supply which is independent of P and aggregate demand which is just the quantity theory of money. From this graph, you get up P.

5. If you multiply P from the upper left-hand chart, by W/P from the upper right-hand chart, you get nominal wage W.

6. Follow Y from the middle left graph down to the bottom left graph. Here is S (r) and I (r) and a determination of real r and I in the balance. In C + + NX + G = Y, and since NX and G is exogenous, we can calculate C.

We will discuss the most impact from the classical model in the exercise book, but it may be interesting to also point out here the most important:

• Monetary and fiscal policy can not affect the GDP or unemployment in the classical model.

• In the classical model can no nominal variables affect a real variable. The price level, which is a nominal variable, for example, does not affect consumption, which is a real variable. This is known as the classic dichotomy.