What would we do to find the mpcof a non-linear (curved) consumption function? The procedure is the same.
Assume that the consumption function is given by the following equation:
C=20 +0.9Y−0.001Y2 (3)
First of all, try constructing a table like Table 17.1 and then graph the consumption function that it gives. What is it about equation (3) that gives the graph its particular shape?
The mpcis given by dC/dY:
mpc=0.9 −0.002Y
1. What are the values of mpcat incomes of (a) 20;
(b) 100?
2. What happens to the value of mpcas national income increases? Is this what you would expect by examining the shape of the consumption function?
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The consumption function can be expressed as an equation. For example, the consumption function of Table 17.1 and Figure 17.3 is given by the equation:
C=10 +0.8Y (1)
Try using this equation to derive the figures in Table 17.1.
From this equation we can derive an equation formpc.
It is found by differentiating the consumption function.
Remember from previous calculus boxes what it is we are doing when we differentiate an equation. We are finding its rate of change. Thus by differentiating the consumption function, we are finding the rate of change of consumption with respect to income. But this is what we mean by the mpc.
The difference between using differentiation and the formula ΔC/ΔYis that with the former we are looking at the mpcat a single point on the consumption function. With the ΔC/ΔYformula we were looking at the mpcbetween two points.
Differentiating equation (1) gives
mpc=dC/dY=0.8 (2)
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and many other countries, however, income tax became much less progressive in the 1980s and 1990s, but the mpt remained roughly the same because of rises in indirect taxes.
Imports
The higher the level of national income, the higher will be the amount spent on imports. The marginal propensity to import(mpm) is the proportion of a rise in national income that goes on imports:
mpm= ΔM/ΔY
Note that we only count that part of the expenditure on imports that actually goes abroad. Amounts retained by the
retailer, the wholesaler and the importer, and amounts paid in indirect taxes are excluded.
Whether the mpmrises or falls as national income rises depends on the nature of a country’s imports. If a country imports predominantly basic goods, which have a rela- tively low income elasticity of demand, the rate of increase in their consumption would tail off rapidly as incomes increase. The mpm for such a country would thus also rapidly decrease.
If, however, a country’s imports were mainly of luxury goods, they would account for an increasing proportion of any rise in national income: the mpmwould rise.
If a country imports a whole range of goods whose average income elasticity of demand is the same as for home- produced goods, will the mpm rise or fall as national income rises?
The determinants of the level of imports. Apart from national income, there are a number of other determinants of the level of imports:
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BOX 17.2 CONSUMPTION AND SAVING IN PRACTICE
with consumption actually falling in quarter 1 of each year. The gap between consumer expenditure and disposable income represents that fraction of disposable income that is saved. Where consumer expenditure exceeds disposable income, as it has in several quarters in recent years, this represents ‘dissaving’: i.e. negative saving.
Consumer spending follows a regular cyclical pattern each year, reaching its peak in the fourth quarter as Christmas approaches. The graph shows the levels of UK personal disposable income and total consumer expenditure (i.e. consumption before indirect taxes and imports have been deducted) from 1997 Q1 to 2008 Q3. The annual cyclical pattern can clearly be seen,
UK disposable income and total consumer expenditure, 1997Q1–2008Q3
Source: Financial Statistics(National Statistics, various years).
Marginal propensity to import The proportion of an increase in national income that is spent on imports:
mpm= ΔM/ΔY.
Definition
• Relative prices. If the prices of home-produced goods go up relative to the prices of imports, the level of imports will rise. The rate of exchange is a major influence here. The higher the rate of exchange, the cheaper will imports be and hence the more will be spent on them.
• Tastes. If consumer tastes shift towards foreign goods and services, imports will rise. For example, it might become more popular to go abroad for your holidays.
• Relative quality. If the quality of foreign goods and ser- vices increases relative to that of domestic goods and services, imports will rise.
• The determinants of consumption. Since imports of goods and services are part of totalconsumption (as opposed to Cd), the various determinants of consumption that we looked at on page 477 will also be determinants of imports.
The total withdrawals function
Remember that withdrawals consist of the three elements:
net saving, net taxes and imports, all of which rise as
national income rises. A withdrawals function along with the corresponding consumption of domestic goods func- tion is shown in Figure 17.6.
CASE STUDIES AND APPLICATIONS the ‘virtues’ of saving have gradually been eroded. A similar decline in the saving ratio has emerged more recently in the UK (see graph), with more and more people being prepared to ‘live on credit’. Other changes reflect changes in government policy. For example, Sweden after 1990 was concerned to prevent its exchange rate falling relative to EU currencies. This involved pursuing a policy of high interest rates, which had the effect of encouraging saving and discouraging borrowing (negative saving).
Comparing the saving ratios in France and New Zealand, what do the differences imply for the balance between government expenditure and taxation if both countries want to achieve similar rates of investment and want to maintain a balance between imports and exports?
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As well as there being a clear annual pattern for consumption and saving, patterns can also be observed over the years. For example, saving ratios tend to fluctuate with the business cycle. In booms the saving ratio tends to fall, especially if real interest rates are low and people are keen to spend, perhaps anticipating rising inflation. This can be seen in the boom of the late 1990s.
The table below shows that there are marked differences in saving ratios between countries. This is partly a reflection of national attitudes towards saving and spending, and partly a reflection of the encouragement given to saving by government and financial institutions.
Some of the changes in saving ratios reflect long-term trends. For example, Italy’s and the USA’s saving ratios have shown a long-term decline, as traditional beliefs in
Household saving (% of household disposable income)
1987–91 1992–6 1997–2001 2002–6 2007–9a
Australia 7.9 5.4 2.6 −1.6 2.1
Belgium 16.1 18.6 14.4 14.0 10.6
France 7.4 10.2 11.0 10.6 12.4
Germany 13.2 11.8 10.1 10.9 10.8
Italy 23.8 19.7 11.4 10.7 6.8
Japan 13.8 12.4 9.6 5.5 2.8
Netherlands 13.5 14.3 10.4 10.3 6.9
New Zealand 2.6 −1.8 −4.4 −6.6 −6.7
Sweden −0.1 9.4 4.1 8.3 8.0
UK 7.2 10.2 6.4 6.5 1.3
USA 7.1 5.4 2.9 1.2 1.2
aYear 2009 figures forecast.
Source: Based on data in Economic Outlook(Organisation for Economic Co-operation and Development [OECD], various years).
Figure 17.6 The Wand Cdfunctions
Note the relationship between the Cdand Wcurves. The steeper the slope of the one, the flatter the slope of the other. The reason for this is that Cdand Wadd up to total national income (Y):
Y =Cd+W
Since the 45° line measures Cd+W, the distance between the Cdfunction and the 45° line must equal withdrawals.
Thus at point x, where national income is £100 billion and Cdis £70 billion, Wmust be £30 billion – the gap between Cdand the 45° line.
The marginal propensity to withdraw
The formula for the marginal propensity to withdraw (mpw) is as we would expect:
mpw = ΔW/ΔY
The mpwis the slope of the withdrawals function. Note that, since W=S+T+M, mpwmust equal mps+mpt+mpm.
For example, if for any rise in national income, 1/10 were saved, 2/10 paid in net taxes, and 2/10 spent on imports, then 5/10 must be withdrawn.
Note also that, since Cd+W=Y, mpcd+mpwmust add up to 1. For example, if the country spends, say, 3/5 of any rise in income on domestically produced goods, the remaining 2/5 must go on withdrawals.
If the slope of the Cdfunction is 3/4, what is the slope of the W function?
Injections
In simple Keynesian theory, injections are assumed not to depend on the level of national income: they are exogen- ouslydetermined. This means that the injections function is drawn as a horizontal straight line. Injections will be at a given level irrespective of the level of national income. The injections function is the vertical addition of the invest- ment, government expenditure and export functions, each of which is a horizontal straight line.
The assumption that injections are independent of national income makes the theory simpler. (It is possible to drop this assumption, however, without destroying the theory.) But is the assumption sufficiently realistic? Let us examine each of the injections in turn.
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Investment
There are four major determinants of investment.
Increased consumer demand. Investment is to provide extra capacity. This will only be necessary, therefore, if consumer demand increases. The bigger the increase in consumer demand, the more investment will be needed.
You might think that, since consumer demand depends on the level of national income, investment must too, and that therefore our assumption that investment is independent of national income is wrong. But we are not saying that investment depends on the levelof consumer demand; rather it depends on how much it has risen. If income and consumer demand are high but constant, there will be no point in firms expanding their capacity: no point in investing.
The relationship between investment and increased consumer demand is examined by the ‘accelerator theory’.
We will look at this theory in section 17.4.
Expectations. Since investment is made in order to produce output for the future, investment must depend on firms’
expectations about future market conditions.
The cost and efficiency of capital equipment. If the cost of cap- ital equipment goes down or machines become more efficient, the return on investment will increase. Firms will invest more. Technological progress is an important deter- minant here.
The rate of interest. The higher the rate of interest, the more expensive it will be for firms to finance investment, and hence the less profitable will the investment be. Just how responsive total investment in the economy is to changes in interest rates is a highly controversial issue and we will return to it later.
So if these are the main determinants of investment, does it mean that investment is totally independent of the level of national income? Not quite. Replacement of worn-out or outdated equipment willdepend on the level of national income. The higher the current level of national income, the greater will be the stock of capital and therefore the more will need replacing each year. It is also possible that, if the level of national income is high and firms’ profits are
Marginal propensity to withdrawThe proportion of an increase in national income that is withdrawn from
the circular flow: mpw = ΔW/ΔY, where mpw=mps+mpt+ mpm.
Definition
KI 10 p71
high, they will be able to affordmore investment. However, it is not a gross distortion of reality to assume that invest- ment and the level of national income are independent, at least in the short run.
Government expenditure
Government expenditure in any year is independent of the level of national income. The reason is as follows. In the months preceding the Budget each year, spending depart- ments make submissions about their needs in the coming year. These are discussed with the Treasury and a sum is allocated to each department. That then (excepting any unforeseen events) fixes government expenditure on goods and services for the following financial year.
Thus, again, for our purposes we can take government expenditure as independent of national income in the short term. Even if tax revenues turn out to be more or less than expected, this will not influence that year’s govern- ment spending. The government can end up running either a budget surplus (T>G) or a budget deficit (G>T).
Over the longer term, however, government expendi- ture willdepend on national income. The higher the level of national income, the higher is the amount of tax rev- enue that the government receives, and hence the more it can afford to spend. The governments of richer nations clearly spend much more than those of developing countries.
Exports
Exports are sold to people abroad, and thus depend largely on theirincomes, not on incomes at home. Nevertheless, there are two indirect links between a country’s national income and its exports:
• Via other countries’ circular flows of income. If domes- tic incomes rise, more will be spent on imports. But this will cause a rise in other countries’ incomes and lead them to buy more imports, part of which will be this country’s exports.
• Via the exchange rate. A rise in domestic incomes will lead to a rise in imports. Other things being equal, this will lead to a depreciation in the exchange rate. This will make it cheaper for people in other countries to buy this country’s exports. Export sales will rise.
However, it is useful in simple Keynesian models to assume that exports are determined independently of domestic national income.
Note that, although the injections function is assumed to be constant with respect to income and is drawn as a horizontal straight line, this does not mean that it will be constant over time. Investment can suddenly rise or virtu- ally collapse as the confidence of businesspeople changes.
Exports can change too with shifts in the exchange rate or with speculation. The injections line, then, is constantly shifting up and down.
Section summary
1. In the simple Keynesian model, equilibrium national income is where withdrawals equal injections, and where national income equals the total expenditure on domestic products: where W=Jand where Y=E.
2. The relationships between national income and the various components of the circular flow of income can be shown on a 45° line diagram. In the diagram, C, Cd
and Ware endogenous variables. Each one rises as income rises. The relationships can also be expressed in terms of marginal propensities. The marginal propensity is given by ΔV/ΔY(where Vis the variable in question).
3. Apart from being determined by national income, consumption is determined by wealth, taxation, the availability and cost of credit, expectations about future prices and incomes, the distribution of income, tastes and attitudes, and the average age of durables.
Consumption of domestic product (Cd) is total consumption minus imports of goods and services and minus indirect taxes and plus subsidies on goods and services.
4. Like consumption, withdrawals (S, Tand M) vary with national income. Net saving is also determined by the various factors that determine consumption: if these factors cause consumption to rise, then, except in the
case of a cut in income taxes, they will cause saving to fall and vice versa. Net tax revenues, apart from being dependent on incomes, depend on the rates of tax and benefits that the government sets and how progressive or regressive they are. Imports depend on the relative prices and quality of domestic and foreign goods, total consumption and tastes.
5. In the simple Keynesian model, injections are assumed to be exogenous variables. They are therefore drawn as a horizontal straight line in the 45° line diagram.
In practice, there will be somerelationship between injections and national income. Replacement investment depends to some extent on the level of output; government expenditure depends to some extent on the level of tax revenues; and exports depend on exchange rates and foreign incomes, both of which will depend on the level of imports.
Nevertheless, in the short run it is reasonable to assume that injections are independent of national income.
6. The determinants of investment include the rate of interest, the size of increases in consumer demand, the cost and efficiency of capital equipment, and expectations about prices, consumer demand, interest rates and other costs.
BOX 17.3 BUSINESS EXPECTATIONS AND THEIR EFFECT ON INVESTMENT Recent European experience
After 1993, pessimism began to decrease, and by the last quarter of 1994 the average EU industrial confidence indicator became positive. From 1995 to 2000, the indicator was mainly positive, as the European economy experienced growth rates averaging 2.6 per cent.
Investment grew rapidly. Notice how the industrial confidence indicator mirrored the rate of economic growth. For example, both the rate of growth and the confidence indicator fell in 1996.
But then, in 2001, with the world economy slowing down and the 11 September attack on the World Trade Center in New York, industrial confidence plummeted, and so did investment, only to recover again as economic growth and business confidence returned.
In 2007/8, however, with rising oil and food prices, with less credit available (the ‘credit crunch’) and talk of an impending recession, industrial confidence began to fall once more. Then as recession became a reality and turned out to be much worse than had been forecast, so confidence took a nosedive.
Another useful indicator of the state of the economy is the degree of industrial capacity utilisation. The lower this is, the greater the slack in the economy. Figure (b) shows the percentage capacity utilisation in manufacturing industry in the EU. You can see how this mirrors industrial confidence (and hence economic growth).
If the economy expands and firms respond by investing, there will be a time lag before this can be In the boom years of the late 1980s, business optimism
was widespread throughout Europe. Investment was correspondingly high, and with it there was a high rate of economic growth.
Surveys of European business expectations in the early 1990s, however, told a very different story.
Pessimism was rife. Europe was in the grip of a recession, and output was falling (see Table (a)). Along with this decline in output and deteriorating levels of business and consumer confidence, there was a significant fall in investment.
Table (b) gives the indicator of industrial confidence in various EU countries and the indicator for the EU as a whole is plotted in Figure (a). The indicator shows the percentage excess of confident over pessimistic replies to business questionnaires: a negative figure means that there was a higher percentage of pessimistic responses.
You can see that the indicator was strongly negative in 1993.
Not only was the total level of investment falling, but the proportion of that investment used to expand capacity was also falling. By contrast, the proportion of investment devoted to rationalisation schemes had risen. Firms were increasingly having to look for ways of cutting their costs through restructuring their operations. One of the consequences of this was a growth in structural unemployment (as well as in demand-deficient unemployment).
(a)Macroeconomic indicators for the EU-15 countries
1989 1990 1991 1992 1993 1994 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008
GDP growth (%) 3.5 3.0 1.8 1.1 −0.4 2.8 2.4 1.6 2.9 3.8 1.9 1.1 1.2 2.3 1.7 2.8 2.6 1.0
Investment (% change) 6.9 3.6 −0.6 −0.4 −5.8 2.8 2.8 1.9 7.1 4.7 0.8 −0.6 1.3 3.0 3.0 5.6 4.7 2.0
Unemployment (%) 7.8 7.3 7.8 8.9 10.1 10.5 10.1 10.2 9.3 7.7 7.2 7.6 7.9 8.0 8.1 7.7 7.0 7.3
Note: EU-15 =the 15 members of the EU prior to its expansion in 2004.
Source: Based on data in Statistical Annex of the European Economy (Commission of the European Communities, 2007).
(b)Industrial confidence indicator
Country 1989 1991 1993 1995 1996 1998 2000 2001 2002 2003 2004 2005 2006 2007 2008
Belgium 0 −15 −29 −9 −18 −8 2 −14 −12 −15 −3 −9 2 1 −8
Denmark 4 −8 −12 5 −8 −1 6 −2 −4 −6 4 0 8 5 −8
France 8 −20 −35 −2 −18 5 12 −4 −9 −9 −3 −8 −2 2 −11
Germany 5 0 −34 −6 −21 −5 −2 −15 −18 −17 −8 −10 4 7 −8
Ireland 10 −9 −13 7 −1 3 10 −8 −7 −9 −4 −4 4 3 −12
Italy 8 −13 −17 6 −12 0 12 −3 −3 −4 −2 −5 5 3 −9
Netherlands 1 −5 −10 2 −2 2 4 −4 −3 −8 −3 −2 4 5 −1
UK −2 −32 −11 3 −5 −16 −7 −15 −15 −17 −2 −10 −6 3 −11
EU 4 −14 −26 −1 −14 −3 4 −9 −11 −11 −4 −7 1 5 −9
Source: Based on data in Business and Consumer Surveys (Commission of the European Communities, 2008).
KI 32 p388