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In Figure 9.2, K denotes the level of the capital stock required for investment to just cover depreciation. This is the steady-state level of capital stock, the only level from which the economy has no tendency to change, ceteris paribus. At other levels of capital stock, this is not the case. If K1 is the level of capital stock and Y1 the output of the economy, investment is greater than depreciation and the tendency is for the capital stock to rise with an impact on output also. For levels of capital stock above

K such as K2, depreciation is above investment, and investment is insufficient to replace depreciating capital stock, hence the tendency is for the capital stock level to decline and, therefore, for output to fall. Whenever the level of the capital stock is not at K , it tends to move towards K .

The steady-state level of capital stock K corresponds to a level of output of Y on the production function.

Another implication of the production function drawn here is that of convergence.

Convergence is the tendency for poorer countries to grow faster than richer countries for a given increase in capital stock. Hence, poorer countries would be expected to catch up with richer countries if the countries share similar steady states.

Richer countries (i.e. those with higher per capita income levels) have higher levels of capital stock than poorer countries. Given the assumption of diminishing returns to capital, this implies that for any increase in the capital stock the additional output produced from the capital will be lower in the richer country than the poorer country starting from a lower level of capital stock and lower level of income. The productivity of capital will be higher in the poorer country. Historically, following World War Two, Japan and Germany invested heavily in renewing and improving their capital stock relative to the USA and UK and this is one of the factors that is considered to explain their relatively better productivity. Similar arguments are used to explain the Asian Tiger phenomenon.

9.4.1MORE ON SAVINGS

Savings rates for many countries are published on a regular basis. A recent report by the Organization for Economic Cooperation and Development (OECD) provided the information presented in Table 9.4 on household saving rates across a range of industrialized countries. Countries’ ranking are presented in the final column while an indication of the general trend is shown in the second-last column of the table. The predominant trend in household saving has been a decline. In some countries,

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T A B L E 9 . 4 I N T E R N A T I O N A L H O U S E H O L D S A V I N G S R A T E S

Country	1985	1990	1995	2000	2002a	Change	Rank ’02
Australia	10.8	9.3	4.8	3.4	0.3	↓	19
Austria	10.5	14.0	11.7	8.3	7.5	↓	12
Belgium	15.9	18.0	18.8	13.4	13.7	≈	2
Canada	15.8	13.0	9.2	4.8	4.4	↓	17
Czech Republic	– b	–	20.6	13	11.3	↓	5
Denmark	–	11.2	6.9	4.8	6.2	↓	14
Finland	3.4	2.2	5.2	−0.9 −0.3		↓	20
France	8.9	7.8	11.2	10.8	12.2	≈	3
Germany	12.1	13.9	11.2	9.8	10.4	↓	7
Ireland	10.6	6.5	8.5	6.0	7.5	↓	12
Italy	30.7	27.8	22.5	14.5	16.0	↓	1
Japan	16.5	14.0	11.9	9.8	5.8	↓	15
Korea	14.8	22.0	16.8	11.5	9.6	↓	9
Netherlands	5.6	11.6	14.9	6.7	10.7	↑	6
New Zealand	–	0.5	−3.6	−3.8	−0.3	≈	20
Norway	−3.3	0.8	4.6	4.5	7.0	↑	13
Portugal	–	–	13.6	9.5	11.9	↓	4
Spain	11.1	12.3	14.4	10.6	10.1	↓	8
Sweden	3.2	0.0	8.3	2.4	8.2	↑	11
Switzerland	–	8.7	9.4	8.3	9.0	≈	10
United Kingdom	9.8	8.0	10.0	4.3	5.2	↓	16
United States	9.2	7.8	5.6	2.8	3.7	↓	18

Source: OECD, 2002

Notes: a 2002 figures are projections. b Data unavailable.

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the decline has been dramatic – Australia, Canada, Italy (from a very high share), Japan, the USA, and the UK.

There are many possible reasons why the savings rate varies a lot across countries. Different demographic patterns between countries lead to different savings rates as countries with a high proportion of the population in older age groups tend to have higher savings rates. National tax policies affect people’s saving/consumption incentives and decisions. Cultural differences also play a role, as does the level of development, and political and economic stability. Savings rates tend to be highest in countries with high income-levels, which could mean also that high income promotes high rates of saving. Economists have not identified which of the many possible explanations is most important to explain international differences in savings rates.

The Solow model can be used to consider what happens if a country’s savings rate changes. A decision to increase the proportion of income saved, for example, moves the savings = actual investment function up, as shown in Figure 9.3.

With the higher savings rate, at any level of capital stock the amount of investment is higher, so the new savings function 2 lies above the initial function. We can consider the implications of this change beginning at the initial steady state. Using savings function 2, we see that at K , savings = actual investment lies above the depreciation line. This means there is a tendency for the economy to move from its steady state and the capital stock rises due to increased net investment. In fact, the capital stock increases until K2 is reached (where the new savings function intersects the depreciation line and where savings = actual investment just covers capital depreciation). The higher capital stock of K2 denotes a new steady state involving both higher capital stock and higher output.

Governments sometimes intervene to affect savings. Remember consumers have the options to either save or spend on consumption goods. High levels

Output/
depreciation/	Y2		PF1
investment
	Y1		Depreciation
			Savings 2
			Savings 1
	K1	K*	Capital: K
			K2
F I G U R E 9 . 3 I N C R E A S E I N T H E S A V I N G S R A T E

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of consumption correspond to low levels of saving. High levels of aggregate demand correspond to booms and to encourage consumers to change their savings behaviour government might be anxious to try to reduce aggregate demand (if inflation or inflation expectations were rising, for example). Or to encourage greater savings for pensions, governments often offer tax concessions as an incentive to change savings behaviour. But is there an ideal or optimal savings rate for an economy?

Imagine that consumers wish to maximize their consumption out of the income generated in their economy and income is either consumed or saved (i.e. used for investment). There are, in fact, unique levels of capital stock (K ) and output (Y ) that correspond to maximizing consumption, which are shown graphically in Figure 9.4.

The production function indicates the maximum levels of consumption possible if no income/output is diverted for savings/investment (and if no taxes were diverted to government and if no external trade occurred!). Even if no income is saved a certain amount of capital depreciates each year, reducing the amount of income available for consumption. For Figure 9.4 panel A we can consider just by looking at the graph where the biggest difference exists between output and depreciation; this indicates the unique values of output (Y ) and capital stock (K ) at which consumption would be maximized. The intuition behind this result is that only at these points is the marginal return to capital (the slope of the production function) the same as the rate of depreciation. At any higher (lower) capital stock

A		B
Output/	Production	Output/
depreciation		depreciation	Production
	function		function
Y*		Y*
			Depreciation
	Depreciation
			Savings
K*	Capital: K	K*GR	Capital: K
		Golden rule
		level of capital

F I G U R E 9 . 4 S O L O W G R O W T H M O D E L : S A V I N G S A N D C O N S U M P T I O N