The Growing Economy

and measure l instead of l along the horizontal axis of Figure upon the working-class standard of living Figure 11(i) and (ii). The area OABC in Figure ll(i) will then represen (11.1) (11.2) But since in a state of steady growth

Condition 2 can be intuitively interpreted as implying that in order to be in a state of steady growth of this kind at any given point of time L must be sufficiently small for the pressure of population on the resources of N and k then available to be so slight that output per worker is above the critical level Thusprovided and provided that the absolute size of , D will be constant at D. But if D is constant, L = I. But if n—from equation (11.2)— constant, and

head to be rising (i.e. l so that Ŷ would move towards Ŷ conversely if at any time the population were in absolute size rather smaller than was appropriate to this steady-state stagnation level, output per head would

In this case with y the steady-state value The capital stock must have been adjusted to the other factors that is at a level which Only on this condition can workers' standards pro­ gressively rise.

so that there can be a stagnation level of Ŷ which equates and so to y, so that Ŷ remains constant. (3) Wi = The absolute size of the working population must be such as to have brought the wage rate into the region of the stagnation level. (4) Ŷ = Ŷ. The absolute size of the capitalist population must be such as to have brought property income per property owner into the region of the stagnation level.

may now be some unemployment, if L (the demand for labour to man up the K) < L (the available supply of labour), i.e. if labour as well as of capital. One of our purposes in the following exercises is to see in what conditions labour will be fully employed.

living upon the steady-state the growth rate of population (l), and the dependency ratio (D). For convenience of exposition the of the Figure is reproduced, after multiplication by the constant and D must be and rising so that S, l and remain constant at , . can then have a constant rate of growth for total output Yof for the standard of living

and D. If this sustain a state of steady growth with S, l and D at these constant

capital the proportion of the national output going to wages would fall and that accruing to property owners would rise; and since in a Plantcap no wages, but some property incomes are saved, this shift of income from wages to property incomes would increase the proportion of the national income which was saved and so raise the

n any state of steady growth D will be constant and with portion of income going to profits and since S is the proportion of property incomes saved, (1 saved. Now we know from equation (11.6) that in all Zero cases, (11.8) These expressions give the distribution between wages and profits which, on the principles discussed in the last paragraph, is necessary

Output must rise at a steady rate equal to the sum of the growth rate of the number of workers plus the rate of labour-expanding technical progress. Capitalists' standards (1 - Q)Y can stagnate if These conditions can be fulfilled if the capitalists' standard of living But if Ŷ is at this level in Figure 16, so that y = α(l — Q)S = + l' = l. From this it is clear that Only if Q has this value will the rate of growth of the capital stock — Q)S be kept in line with the expansion of the effective labour

rather than another from the particular conditions displayed in Figure appropriate size relatively to the capital stock K and the state of technical knowledge interested. As the reader can easily verify for himself this possibility a new stagnation state with a still

lower standard of living. The decreased mortality due to the elimi­ nation of malaria would be replaced by the higher mortality due to the starvation levels of income resulting from the increased pressure of population on resources. On the contrary a shift of the l-curve to the left would lead to a new stagnation situation but at a higher

every unit of consumption which he forgoes this year in order to increase this year's savings. The citizen is then assumed to plan his savings and so the time pattern of his consumption so as to satisfy his preferences under (i) to the best extent made possible by the market conditions under (ii).

Rates expected to rule over the period of the loan (see page 35 above and pages 314-318 below). We can for the time being conduct our analysis as if all borrowings and lendings were made solely on a daily basis, each loan which remains unpaid for a longer period being renewed from day to day at that day's Bank Rate. on day 1, W on day 2, and so on; and (ii) that in fact these firm expectations happen to turn out to be correct. This assumption of perfect foresight raises very great difficulties to which we shall return in due course (see Chapter XVIII below). For the time being in order to isolate one part of our problem we assume simply that in fact every citizen does

e must put aside a sum equal to to cover his bequests to his children, because this sum invested at the beginning of day beginning of day 2, (1 + i)(1 + i) times itself by the beginning of and so on, until it (1 + i) (1 + i)(1+i) (1 + i)(l + i)(1 + i) i)(1 + i)(1 +i) + (1+i (12.2) Suppose now that our citizen plans a stream of consumption Ĉ will have at the beginning of day 1 to set aside to finance a (12.3) He can choose any combination of Ĉ Ĉ Ĉ Ĉ and Ĉ which he likes provided that the expression in (12.3) does not exceed the expression in (12.2).

shape of the consumption stream and, second, the choice of the absolute starting level for that stream. For examples of the first part of the choice level of consumption over his life (i.e. Ĉ = Ĉ = Ĉ = Ĉ = Ĉ); or a level of consumption which starts relatively low, rises as his needs

salary of GE; and this is assumed to rise slowly at first and then more rapidly to a height of JF at the time of his retirement after GJ days of any earnings. We can draw another curve CD the height of which represents days of his adulthood (GH) his low needs plus the gain in total consumption obtainable from the postponement of consumption have brought his con­ sumption below even his modest starting salary. For the inter­ mediate period of his life as an earner (HI) his heavy family needs have brought his consumption above his earnings. For the last years

our citizen, given the pattern of his needs, should not prefer to transfer a unit of consumption at the current rate of interest from any one day to another. Suppose now that our citizen were faced at the outset of hood with a set of higher expected interest rates for each day of his

It follows that the utility index for consumption at the level of $35 will be greater than 0.6. But 0.6 is the height of the line HJ whose height is half words the point G will lie above the point H. We have therefore shown that the slope of the curve O D G A K Q

was the case with the C'D'-curve in Figure 20). We assume for the purpose of Figure 25 that a citizen's adulthood lasts for 40 years and that after 30 years of adulthood his own sons leave home to start their own 40 years of adulthood; and so on from generation to generation.

will start at a higher earnings level than their fathers. If the wage rate is going up at 2 per cent per annum, then after 30 years it will be 80 per cent greater than AE. If the second generation plans the same time shape for its consumption stream, AC will be

Conversely in the case of Figure 25(ii) it is only necessary for each son to be concerned with the welfare of have been passed back in history up the generations. The son helps the father to raise the father's standard to the son's, but the father's standard needs to be raised all the more because the father has used returns to scale (so that U + Q + Z = 1), in which the growth rate of population is constant at l, and in which the growth rate of technical progress is constant at r. We know from equations (7.14) and (7.15) that in these conditions, provided the proportion of income saved is constant, a state of steady growth is possible in which the

If, on the other hand, today's S is set too high, the consumption pattern will not break down; but on the other hand, the consumption pattern could have been maintained even if a higher initial level of consumption had been chosen. If a very high level of S is chosen today, then there will be a large addition to the amount of capital and Z are all constant, there exists a value of today's S which will cause S to move to its steady- state value of at which it can continue indefinitely. Any value of today's S greater than this would be unnecessarily high since

impeded from exercising freely their own individual inter-generation altruism. The State may need to save in order to compensate for the reduced accumulation of capital by private individuals. We will return to these problems in the final chapter of this volume (Chapter XXIII, pages 489-499).

story—the starting level of consumption for each individual (equation 13.12) and the amount which each individual must leave to his children (or will receive from his children) (equation 13.10). If the parents refuse to die (G is great) that will no doubt burden the population of working age, keep their consumption low, and make (13.21) Now we have seen in Chapter VIII that the highest possible level of consumption at each point of time in a state of steady growth is obtained if S = If S > then total national consumption is held permanently below the level which it could at any one time have attained with a lower value of S. This will be so if σ > Thus altruism by leading to parents saving to leave proper to their children could possibly raise S above the critical level, If S = U,

value should exceed unity, minimum value {(l+ l')A}. But the value of U = Ai increases as

1. Therefore i > l + l'. falls towards so that a ∞. With ∞, a 1, so that we have curve of the kind shown in Figure 32.

In case I with perfect selfishness and is possible. We could, however, have steady-state position with perfect altruis provided . But in this case we must have these conditions with perfect I to IV it should be borne in mind that the perfect altruism

In case II there is a perfect-selfishness steady-state position at the intersection A. This is at a value of i < l + l' so that S > U and perfect selfishness leads to more than golden-rule savings. Case III is similar to case II except that the perfect-selfishness steady-state position at the intersection B is at a value of i > l + l', so that the this case parents will help their children if lies to the hildre ill help parent r s lies to the right

already considered (pp. 206-207 above) reasons why the very poor and the very rich may plan the pattern of their consumption levels over time to rise at a lower rate than the moderately rich (the elasticity of substitution between today's and tomorrow's consumption may be numerically smaller at very low and very high incomes than at

s no saving and owns no capital. accumulation is supplemented by that financed by savings from capitalists' earned incomes. In fact we have Suppose now we have the case in which cap s do no work (i.e. = 0) but workers do some saving (S > 0) as well as working by workers is less than the proportion of income saved by capitalists (S < S ). Since λ' = 0, the curve JAK coincides with the axes XO'E. Since neither λ' nor S = 0, the curve FABG does not coincide with the axes X00. As drawn in Figure 36 the two

those of class 2 Fourth 1.38 0.23, which shows that income per head for a member of class 1 and similarly From this we obtain Q =0.646 and Q = 0.298. About 65 per cent of income in class 1 and 30 per cent of income in class 2 will be earned income.

VII, pages 99-103, above the economy will move into a state of steady growth in which from (7.14) the growth rate of output and rate of capital accumulation will be Moreover , we shall have also k = k = k = l + since on the at a different level. But in Chapters XII and XIII we tried to go behind the savings proportion by examining the substitutability between present and future consumption on which the motive to save depends. If we try to explain in these terms why the savings pro­ portion in class 1 may be less than the savings proportion in class 2,

the ablest citizen someone less able than citizen someone less feeble than A further factor which may tend to increase or to decrease in­ equalities is differential fertility. If the wealthy have smaller families than the p∞r, then the large properties will be split up among few

capacities so that although in Table VI we allow only for one type of labour, L, we do not need to assume that there is only one input in this category. (ii) We have the inputs of natural resources such as the inputs of N into the various processes, i.e. inputs of those factors of production etc.) and outputs etc.) though they may well, of course, be inputs of one process and outputs of another. (iv) Finally we have the goods and services (e.g. X and Y) which are outputs but not inputs of the productive processes. These are the goods and services which are ready for final consumption by the citizens in the economy.

since N may differ from N and indeed N may differ from N, just as our model in terms of the actual gross inputs and outputs of the instruments themselves rather than in terms of the hire of their net services. The reasons for doing this and its implications will be dis- cussed in more detail later (cf. pp. 295–298 below). In considering the instruments of production such as J and K it

the amount to final consumers the firm; the whole has output

In this last expression the terms in the first row are simply the receipts at goods. The terms in the second row are the values (at the prices ruling at 8 a.m. on day 1) of the net outputs (if J > J, etc.) or the cost (also at the prices ruling at on day 0 any entrepreneur has a given set of expectations about the prices which will rule at 8 a.m. on day 1; in accordance with the notation described on page 38 above, we will call these prices which at the beginning of day 0 are expected to rule at the beginning of day 1 If the prices, wage rate, and rate of

(iii) the input and output co-efficients of each process are determined technically (L, X, Y, J, J, etc.), (iv) there will be certain total quantities of labour (L) and of land (N), seeking employment; and (v) yesterday's (i.e. day products will have determined the quantities of the intermediate

some more and some less optimistic about prices, are taking on quantities of inputs in many processes. We will examine these effects of uncertainty in Chapters XXI and XXII below. In the second place, we could assume that while expectations were held with certainty there were always a large number of entre-

goods. The price of to users inJ would tend to expand. The prices of other inputs which intensive in these processes would be driven up. There would be a general reshuffling of very large) number of separate processes a, b, c, etc., each of which had a set of fixed co-efficients of inputs and outputs. An alternative model would be to assume that co-efficients were not fixed but that there was a continuous possibility of substitution between one input and another, and between one output and another and a continuous

production among the inputs or the outputs; now there are. Other- wise the principles of profit maximization are the same: industries which are showing a profit will be expanded and those which are showing a loss will be contracted; within any industry one input consume a fixed amount of raw material per day. Here there is no possibility of substitution between labour and machine or raw material and machine. But it may be possible, when the time comes, to replace the machine with a different machine which is itself more expensive, but which uses less labour and/or less raw material input

which we have constructed in the present chapter we assume that consumption goods (X, Y) cannot be used as instruments of pro- duction (J, K) nor instruments of production as consumption goods. But there are certain products of can be bought by an entrepreneur to raise steam in a factory's boilers. Corn can be eaten as food or put back as seed or as feeding stuffs for animals into the productive system of the farm. Normally, however, if not universally, there are at least some slight differences in the product as sold for the two purposes. Domestic coal is likely to differ in size or

we are assuming that the cost of living is stabilized. We have assumed a policy of budgetary taxation or subsidization of incomes of a kind which so adjusts each day the amount of net spendable incomes to the available supplies of consumption goods that the price index,

are expected to rule in the future, inputs will be devoted to the production of instruments of production rather than of consumption goods. The output of instruments of production will rise relatively to the output of consumption goods and income subsidies will no longer be required to maintain the demand price of consumption goods.

of the instrument the instrument Suppose that the future course of the rate of interest of all other prices, other than the price of the instrument itself, were precisely known. Suppose further that the instrument one possible future use. If it is used at all, then all the various inputs (of labour and of other instruments) and outputs (of consumption goods and of other instruments) which will be associated with it on the daily rates at which interest will be charged for loans used during days 1, 2, 3, etc. Let P be the price which entrepreneur A will offer etc., be the value which the instrument itself is expected at 8 a.m. on day 1 by entrepreneur A to at 8 a.m. on days 2, 3, etc. We assume further that entrepreneur

In other words if the rent received from the house is at a rate of $1 a day ($100 per annum) and the rate of interest is 10 per cent per annum, the value of the house were only 5 per cent per annum, the value of the house would be $2000. $100 a year represents a return of 10 per cent per annum on

where G may be called the 'cash flow' of day 2—i.e., the excess of receipts (O) over expenditures (W + I) expected to result on day 2 from the investment—and where T measures the useful life of the investment. We can say then that the value of the machine on day 1 (P) together with any other expenditure necessarily incurred with it given expected cash flows (G, G, . . . G) the present value of the investment will be greater the higher are the discount factors interest. But while a reduction in the rate of interest which is expected to be

would 0 37; in Situation I this would rise only to 0 39 but in Situation II it would go up to 0 61. The permanent fall in the rate of interest would have a very much greater effect in raising the present value of distant future yields on any capital instrument. But so far in this volume we have assumed that the Central Bank lend for the current day at a given daily rate of interest (i at 8 a.m. on day 0, i at 8 a.m. on day 1, and so on). If the Central Bank fixes only the rate of interest for each day, how can it influence the expectations of the citizens about the future rates of interest? If in fact it could reduce only the rate of interest for one day (without any

per annum rate of interest on two-year loans. Accordingly we shall now assume that our Central Bank at 8 a.m. on day 0 offers to borrow or lend on stated terms not only money for one day, but money for two days, money for three days, money for

of a day's duration). This, as we have seen, will enable it not only to lower (or raise) the spot rate of interest on day 0 (i.e. i) but also the whole structure of rates for long-, middle-, and short-term loans. This in turn will enable entrepreneurs who are considering what price to pay for an instrument on which the net returns will be earned only in line 1) the only direct payment from the firms and farms to the

homes is for the wages of the labour services; (ii) that (broken line 2) there are daily transfers of money from one firm to another in pay- ment of the instruments of production transferred from one firm to another, (iii) that (broken line 3) there is a daily payment from the firms and farms to the money and capital market of interest, profits, firms and farms; (vii) that (broken line 7) there is a daily flow of funds from the money and capital market to the homes in the form of interest, dividends, profits, repayments of principal, etc., to the

would be paid on capital stock if all capital goods continued to be available at current prices. But current prices would, of course, change. The fall in the rates of rent and of wages which would be caused by the indirect fall in demand for N and L would cause rent- and wage-intensive products

the world be imputed in the plan to the supplies of capital goods which will be left over as a result of the plan to carry on productive operations after the end of the plan. to fix the social valuations V and V at certain positive values,

asking whether this implies that V ld al so be set equa But we can show that this will not necessarily be the correct valuation policy for the Central Authority to adopt by considering

indifference curves between X and (as determined by the planning authority) are such that the combination at C is the most desirable one. At this point the social valuation of X in terms of Y should be given by the slope of the line γ which is tangential to th e social indifference curve at the point C. But if the computer is told to work out the best plan on the social valuations represented by

valuation such as that given by the line β, which represents a higher he computer will now state that D is the best output combina- If at D the planning authority were to consider that, with the large supply of X and shortage of Y, a lower valuation of as that depicted by the line δ—were appropriate, then the computer would report the combination B once more as being that which would maximize the value of the plan. For no valuations would the com­

progress markedly biassed against wages. Let us suppose that the additional employment given by the heavy, but biassed new invest- ment is just equal to the increase in the manpower seeking work. it became unprofitable to use old machinery; there would on balance

lending out their own property at interest in the ordinary way like other citizens. They have, therefore, incomes from wages and from interest on their property. The entrepreneurial profits (or losses) which they make on running firms and farms are thus net sums additional to (or to be subtracted from) their normal incomes from

his employees and his creditors. We have argued that the scale of his entrepreneurial activities will be necessarily limited, being restrained to a proper relationship with his own total personal resources. Thus we assume in Figure 46 that the largest possible loss which Mr A can incur on day 0's operations is $100. Theoretically there is no upper

43½ to 38¼ per cent.

But would Mr A necessarily in fact react in the same way in the two situations? Compare columns (a) and (i) of Table XXVII. The average chance of profit in the first case is 49 per cent and in the second case is only 39 per cent. If other conditions (e.g. the possi- bilities of profit in other industries and the amount of Mr

may experience. If each insurance company covers a large number of these independent risks, the probability is overwhelming that the company's daily payments of claims averaged over a series of days will be very nearly exactly equal to 100,000 h part of property insured.

spreading their own risks over a larger number of smaller firms. Consider Mr A, an entrepreneur running a firm which produces X. 100,000 of his daily output, he would in fact have pooled the risk of fire with the But if there are literally no economies of scale and literally no indivisibilities and if there were literally no costs of management but only costs of facing risks and uncertainties, there would be nothing to prevent Mr A from producing his same output X in 50,000 inde- pendent hazard, if it is wet for Mr A it will also be wet for Messrs B, C, D, E, etc., as well. It is not, therefore, like fire a hazard against which simple insurance will spread the risks. If Messrs A, B, C, D, and E all pay premiums to an insurance company of one third of the value insured against destruction by wet weather tomorrow and if tomorrow is wet, then the insurance company will

shifted to the insurance company. But something can be done to reduce the burden of risk and uncertainty if there are some persons to whom wet weather brings gain (say, the cinema industry) and others to whom it brings loss (say, the hotel industry). As we shall see shortly, a 'betting' market can be set up in which the risk of gain to the hotel keepers will owe the cinema operators money on the bet, and this will transfer some of the fine-weather profits of the hotel keepers to make up for the fine-weather losses of the cinema

income of H if and a minimum of H if it is wet. We can, therefore, take incomes of H and H as the maximum and minimum benchmarks against which we can construct (in the manner described on pp. 419-420 for the construction of Figure 46) the hotel keepers' chance-utility index for all incomes between the minimum H and the maximum H. In Figure 47 we draw the

buyer and seller in respect of the amount of X covered by the bargain. Just as in the cases of betting these transactions need not take place directly between an actual buyer and seller of X, but can be developed in a competitive market by specialized entrepreneurs who deal in forward transactions in X. Thus a market 'forward' price for X (i.e. turn out to be lower than this they gain from the quantity which they can sell at the higher forward price fixed today, but if tomorrow's

essential difference between the offsetting of risks which (like Wet or Fine weather) cannot themselves be affected by the process of offsetting and the offsetting of risks which (like a high or low price tomorrow) can themselves be much affected by the process of setting. Suppose that the forward price of X

relatively to other products. There will indeed remain a thousand and one reasons why the outputs and prices of change in the future relatively to each other. But suppose now that there is a fully organized forward market for every single good and service to be exchanged at every single day in

forward prices will give perfect foresight of the actual price develop- ments that will in fact take place. It can now be seen why, in order to achieve perfect foresight through forward markets, we had to make such strict assumptions as those made above (p. 467). If new members of the population were to

independent estimate of what every other producer and consumer will do, the total planned outputs and inputs may be very inappro- priate. Individual producers may on balance seriously underestimate (or overestimate) either the amount which their competitors are planning to produce or else the total amount which all the users

at various future dates on the basis of the totality of the individual planned demands and supplies. The central authority could then revise its plan for future price movements, raising those future prices where excess demand was threatened and buyers and sellers in every market would then be asked to revise their

in this chapter is to be a success in market conditions of this kind, a delicate institutional set-up must be achieved. The individual firm must reveal its detailed plans to the central authority; but the central authority, although it openly publishes the central Indicative Plan which it has formed on the basis of these detailed plans of individual

The computer in the Dual (cf. pp. 368-371 above) will tell the Central Authority that the shadow price of J (V) is equal to the expression given in (23.1). Let us now consider the analogy with a perfectly competitive system. We know (cf. page 381 above) that the social valuation in As far as the effect of (1) on the present valuation (P) of J is

and more food-tomorrow in quantities which would enable Mrs A being affected. One form of the optimization of trade (cf. The

On the contrary in an economy in which standards are continuously improving, the member of the younger generation will at each age of his life be better off than the member of the older generation was in the past at each corresponding age of his life; but it is perfectly compatible with this that at any given date when the member of the

discounting future utilities, simply because they are to be enjoyed in what is still the future. This is something quite different from (i) preferring $100 of income now rather than in the future because present income can be accumulated at a positive rate of interest to build up a larger income in the future or (ii) preferring an additional

instead of, as on page 205 above, at a rate equal to where c is the growth rate in the individual's consumption level and time, between the utility of different levels of consumption. (23.5) measures the rate at which he can obtain extra units of consumption in year 2 for each unit of consumption given up in year 1. Suppose now that there are taxes at and t on consumption goods bought in years 1 and 2 respectively. Then our citizen by giving up of consumption releases purchasing power of this be accumulated to ΔĈ(l + by the beginning of year 2; and this total sum is available then to be spent on consumption

The three equations in (23.8) tell us what the value of ε must be in order to make S = U. Eliminating i and k between these three equations we get (23.9) We know from (13.2) on page 226 above that the problem of a con- stant arises only The expression in (23.9), therefore, gives one the negative value of ε which is necessary to remove this anomaly if it should arise.

sum gratuity) as he was assessed to be a potentially exceptionally wealthy (or exceptionally poor) citizen. It would make no difference in our present simple model of the world when this lump-sum tax was levied or this lump-sum gratuity paid. Given the rate of interest at which money could be borrowed or savings could be invested, a

redistribution by lump-sum taxes and subsidies combined with the consumption tax-subsidies designed so as to make ε = ρ without disturbing the balance between work and leisure, left the Govern­ ment's budget in balance. In that case we would have (i) a correct intertemporal choice by every individual between consumption now

there briefly noted in this volume, namely the case where invention and technical improvement brought about by the costly effort of the innovator can nevertheless be used without cost by other beneficiaries (cf. pp. 113-115 above). For this reason, although technical progress

there briefly noted in this volume, namely the case where invention and technical improvement brought about by the costly effort of the innovator can nevertheless be used without cost by other beneficiaries (cf. pp. 113-115 above). For this reason, although technical progress