Explain the operation of the Keynesian multiplier

University Degree Business and Administrative studies

Explain the operation of the Keynesian multiplier

a) Explain the operation of the Keynesian multiplier

The easiest way to explain the way in which the multiplier works according to Keynes is to construct a simple model. This model will have two particular simplifying features, in that it will focus exclusively on the demand side of the economy, and it will not include either government activity or the foreign sector. In order to construct this model, we will assume that all prices and wages are fixed within the economy, and that there are unemployed workers seeking jobs and firms that are not operating at their highest possible profitable capacity. From these two assumptions, it follows that the output of firms is being limited not by unavailability of labour, but demand. Firms will be producing at a level of output determined by demand.

Demand in this model will come from two sectors, namely households and firms, since these are the only sectors currently represented in the model. Households will be generating demand for consumption, which is defined as the part of their personal disposable income which households choose to spend rather than save, and firms will be generating demand for investment. We can make the general rule that the more personal disposable income households have, the higher their consumption will be. This is very much a rule of thumb, because the amount of the income which households choose to spend and the amount they choose to spend are affected by many factors, but for the purposes of this model this rule will suffice. From this we are able to graph the consumption function, which shows the relationship between personal disposable income and the level of consumption which households will desire:

Having said that demand in this model comes from households and firms, we can establish that in this model aggregate demand will be equal to consumption demand by households and investment demand by firms. Investment demand is defined as the amount which firms plan to invest in physical capital, such as machinery, and in building up their inventories. For the purposes of this model, we will assume that investment demand is constant. In fact there are a number of factors that affect the level of investment demand, but because there is no clear link between investment demand and any other of the variables in this model it will be easier to assume that it is constant. Having established this, we are able to graph aggregate demand, including the consumption function of households and the investment demand of firms:

This model will be in short-run equilibrium when the amount of desired spending is exactly equalled by the amount of output that is actually produced. The following graph shows all the points where output is equal to desired spending as a 45 degree line, and the one equilibrium point where this line crosses the aggregate demand schedule:

At this point in the model, we can introduce the notion of the multiplier by showing what will happen if there is, for ...

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At this point in the model, we can introduce the notion of the multiplier by showing what will happen if there is, for whatever reason, an increase in investment demand. On the graph below, an increase in investment demand has caused the aggregate demand schedule to shift upwards, and therefore has caused a change in the level of output, from A to B:

It is clear that there has been a greater change in output than there has in investment demand. The ratio of the change in output to the change in demand is the multiplier.

The gradient of the aggregate demand schedule is determined by household’s marginal propensity to consume, that is to say the fraction of each extra pound earned by households which they will spend rather than save. It follows that the multiplier will also be very closely related to the marginal propensity to consume, and it is. In this simple model, the multiplier is equal to 1 over 1 minus the marginal propensity to consume (1/(1-mpc). Therefore, if the marginal propensity to consume is 0.7 (that is to say, for each extra pound earned, households spend 70 pence), the multiplier will be equal to 1/(1-0.7)=1/0.3=3.33. Therefore, if demand increases by 1, output will increase by 3.33.

b) Discuss the effects of the introduction of the government and of foreign trade in the simple static multiplier model of the economy.

The effects of introducing the government into this model are twofold. Firstly, aggregate demand is changed to incorporate government spending on goods and services within the economy, and secondly the personal disposable income of consumers is changed because they have to pay some of their income to the government in taxes. We would expect the former to have a positive effect on output, and the latter to have a negative effect. In order to build government into the model, we will initially assume that all taxation takes the form of direct taxation, thereby avoiding the necessity of distinguishing between market and basic prices.

The effect of government spending is quite simply to shift the aggregate demand schedule upwards, because more demand has been introduced into the economy. It follows that the equilibrium point for output and income will also change, the precise amount of the change depending on the multiplier of the economy. This can be shown in a graph thus:

The effect of taxation, on the other hand, will be to rotate the consumption function, and therefore the aggregate demand schedule. The taxation which needs to be taken into account is net taxation. Since we are assuming that all taxes in the model are direct taxes, net taxes are equal to direct taxes minus transfer benefits, transfer benefits being the amount of money which the government pays out to households by way of benefits and social security. In order to show the effects of taxation, it will be easiest to present a worked example. Assume that the marginal propensity to consume in an economy is 0.7. Without taxes, we would therefore expect households to spend 70p for each additional pound they earn. However, if tax is set at 20% or 0.2, this changes things. They will now spend 0.7 times whatever they have left of their extra pound after taxation. Therefore, if they earn one extra pound they will pay 20p in taxes, and then spend 70 per cent of the remaining 80p, which comes to 56p. So their new marginal propensity to consume could be expressed as MPC*(1-t), where MPC is their old marginal propensity to consume and t is the level of net tax.

When government spending and net taxes are considered together, it will be noticed that although net taxes lower output and government spending raises output, if government spending is exactly equal to net taxes, output will go up. This is because all of the tax money is being spent, whereas if this money had been left with households some of it would have been saved. This is the principle of the balanced budget multiplier - an increase in government spending accompanied by an equal increase in net tax will increase output.

Introducing foreign trade into the model means taking account of both exports and imports. From these we can work out net exports as a percentage of GDP. For the purposes of this model, we will assume that export demand is independent of the domestic market and that it is constant. Import demand is decided by the marginal propensity to import (MPZ), which is defined as the proportion of each extra pound earned which a household desires to spend on imports. Net exports are equal to total exports minus total imports.

The effect of foreign trade on the aggregate demand schedule is once again to rotate it. The aggregate demand schedule which includes consumption demand (C), investment demand (I) and government spending (G) will have a slope equal to marginal propensity to consume (MPC). But having added in exports (E) and imports (Z), we can see that an extra pound of income would increase consumption demand by MPC, it would also increase import demand by MPZ. Therefore, the slope of the new aggregate demand schedule will be equal to MPC - MPZ.

From all this, we can find the final multiplier for the economy. Without government or foreign trade, we discovered that the multiplier was:

multiplier = 1 / (1 - MPC).

The introduction of government means that we must redefine MPC to account for taxes, so that the multiplier becomes:

multiplier = 1 / (1 - (MPC * (1 - t))).

With the introduction of foreign trade, we must also account for the marginal propensity to import, so that the multiplier becomes:

multiplier = 1 / (1 - (MPC * (1 - t)) - MPZ)

Therefore, if we assume a marginal propensity to consume of 0.7, a tax rate of 0.2 and a marginal propensity to import also of 0.2, we can see that the multiplier will be equal to:

multiplier = 1 / (1 - (0.7 * (1 - 0.2)) - 0.2)

1 / (1 - (0.7 * 0.8) - 0.2)

1 / (1 - 0.36)

1 / 0.64

1.5625