Summary of chapter 4: Government Money with Portfolio Choice

Model PC (portfolio choice) is a continuation on the Model SIM. Agents must choose between money and financial assets. Their decision is aided through the rate of interest on other assets; hence it is called Porfolio choice.

The Matrices of Model PC

Government bills, interest payment and a central bank are all added to Model SIM to make up Model PC. In the balance sheet of Model PC, the first column is for Households, which contain money H or bills Bh, the sum of these 2 is private wealth (V). There is no production sector as it is assumed to be a pure service economy, which means the value of the household sector is also the value of the private sector. Column 3 consists of public debt – amount of outstanding bills B issued by the Government to households and the central bank together. In column 4 includes the central bank purchasing bills from government, which increases its stock of assets Bch. On the other side the central bank provides money to households.

The two differences from the Model SIM flow matrix are that flow-of-funds accounts include two financial assets and there are interest payments on government debt. National income doesn’t include these interest payments; it consists of income derived from the sales to households and to the government. The new central bank sector consists of a current account (involves the inflows and outflows of daily activities) and the capital account (shows changes in the balance sheet). It is assumed that the central bank has zero net worth and profits are always paid to the government.

The equations of the Model PC

The first model assumes that producers sell exactly what is demanded and that households have correct expectations regarding their incomes. It begins with production is equal to consumption plus government expenditure. Godley follows by defining disposable income (4.2) and taxable income (4.3). Both (4.2) and (4.3) are includes interest payments.

• Y = C + G (4.1)
  
• YD = Y – T + r-1. Bh-1 (4.2)
  
• T = Ơ . (Y + r-1 . Bh-1) (4.3)
  

Keynes two-stage decision means households decide how much they will save and how they will allocate their wealth between money and bills. V is total wealth.

• V = V-1 + (YD – C) (4.4)
  

Consumption now includes total wealth;

• C = α1 . YD + α2 . V-1 0< α2< α1<1 (4.5)
  Wealth is allocated between bonds and money dependent on the interest rates and liquidity preferences. However the allocation will always sum to one to satisfy the following formulas;
• Hh/V = (1- λ0) – λ1 . r + λ2 . YD/V (4.6A)
  
• Bh/V = λ0 + λ1 . r - λ2. YD/V (4.7)
  
  

To solve the model, with the demand for cash a residual equation (4.6A) is dropped and (4.6) is used.

• Hh = V – Bh (4.6)
  

Money holdings is the total wealth and the demand for bills by households.

Equations (4.8)-(4.11) involve the government and central bank.

• ∆Bs = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . BCB-1) (4.8)
  
• ∆Hs = Hs – Hs-1 = ∆Bcb (4.9)
  
• Bcb = Bs - Bh (4.10)
  
• R = r (4.11)
  

Equation (4.8) explains the government budget constraint. Equation (4.9) shows the capital account of the central bank. Equation (4.10) and (4.11) are related to the fact that the central bank purchase all governmental bills that households don’t want. The interest rate will affect this amount.
Given these equations, the cash household’s have is equal to the cash provided by the central bank.

• Hh = Hs (4.12)
  

Expectations in Model PC

Consumption will depend on expected income and that expectation is usually incorrect. Therefore the Consumption function is now;

• C = α1 . YDe + α2 . V-1 (4.5E)
  

YDe is the expected disposable income. The rest of the equations must be changed because wealth as well as income is unknown.

Any miscalculation of expected disposable income is balanced by a change in money balances. This means, households actually invest in bills on the basis of their expectations with respect to disposable income from the beginning of the period.

• Therefore Bh = Bd (4.15)
  

Expected disposable income including the possibility of a random process is defined as;

• YDe = YD . (1 + Ra) (4.16)
  
  

Our conclusion from earlier equations is that the difference in the amount of money held and demanded by households is dependent on expected income, which is equal to the difference between realised and expected income.

• Hh – Hd = YD -YDe (4.17)
  
  

The Steady State

The effect of rising interest rates on the allocation of wealth between cash and bills is examined, assuming no change in external variables and opening from a full stationary state.

A higher interest rate means that households would hold more interest paying bills as would be expected due to the rate of return being higher at a constant level of risk.

Although it is also found that a higher interest rate encourages an increase in disposable income and consumption both in the short run and in the new stationary state.To explain this unusual result, the steady state solution for national income is established. The government budget must be balanced (government revenue plus central bank profits equal to government expenditures plus cost of servicing government debt)

The steady-state solution for national income is determined:

• Y* = G + r.Bh*.(1 - θ)/θ (4.18)
  
  

The steady state solutions for disposable income can also be obtained keeping in mind that in the stationary state consumption equals disposable income:

• C* = YD* = Y* + r.Bh* - T* = Y* + r.Bh* - θ.(Y* + r.Bh*) (4.18)
  
  
  

It can be seen that in the full stationary state the aggregate income flow and disposable income flow are an increasing function of the interest rate. As higher interest payments accumulate on government debt, disposable income increases as does consumption and national income. . As disposable income increases households hold more wealth and a larger absolute amount of bills as well as a larger proportion of their wealth in bills. All of this leads to even larger interest payments on debt. Higher interest rates generate more economic activity.


Fully developed solutions

The solutions need to be examined further because the value of Bh* needs to be found in terms of the different limits and need to put this value into the equations to reach the fully developed stationary solutions of the Model PC.

To do this the wealth accumulation function is obtained

• ∆V = α2 . (α3 . YD – V – 1) (4.20)
  
  

Noting that in the stationary steady state households accumulate no additional wealth and so ∆V equals zero. Thus wealth and disposable income are in a constant ratio, combining this ratio with the portfolio decisions of households eventually highlights that the steady state level of GDP is dependant on the fiscal stance which, whatever the target wealth to disposable income ratio and the average interest rate payable on overall government liabilities depends on the G/ θ ratio.

• Y* = (G/ θ ) { 1 + α3. (1 – θ) . ѓ (4.26)
  [θ/(1- θ)] - α3 . ѓ }
  
  

Implications of changes in parameter values for temporary and steady state income

Puzzling results

An increase in the permanent level of government expenditure boosts the stationary level of income and disposable income; dY*/dG >0.

Any permanent decrease in the on the whole tax rate θ has the same effect; dY*/d θ <0.

Alternatively an increase in the interest rate or in the rate of interest payable on government liabilities leads to an increase in the steady state level of income and disposable income as the higher rate increases payments arising from the government sector thus leading to more consumers spending from households. Also the higher rate of return on bills means households will hold more interest paying government debt.

An increase in the desire to hold bills increases the proportion of government debt taking the form of bills, thus raising ѓ leading to an increase in the steady state value of national income. So holding more bills leads to an increase in national income.

The model also shows that any increase the wealth to disposable income ratio (a3), leads to an increase in stationary income or disposable income. This is because dY*/a3 >0 where a3 = (1-a1)/ a2. (Where a1 and a2 are the propensities to consume out of current income and out of accumulated wealth.) Thus if households decide to save larger amounts of both their income and wealth then the level of steady state income will be higher.

This result challenges a ‘paradox of thrift’ that has been stated by Keynes. If people decide to save more at each level of income one might expect that this would increase the total amount of savings, but Keynesian multiplier model predicts a paradox of thrift, that total savings will remain the same and income will decline. The reason that higher thrift leads to higher stationary level of income is because a larger a3 parameter suggests households aim for a higher wealth level, but a higher wealth objective implies higher interest payments on government debt held by households and in due course higher absolute consumption and income levels once the steady state is reached.

Graphical Analysis

Assuming that:

• Expectations about current disposable income are based on actual disposable income in the previous period and
  
• An increase in the propensity to consume implied a decrease in the target wealth to disposable income ratio

An increase in the propensity to consume out of disposable income causes GDP to rise in the short run, but in the long run a lower steady state value is achieved which is lower than the original steady state National Income operates as follows.

National income first rises in the short run because for a given level of accumulated wealth when households increase consumption out of current income there is an increase in aggregate demand leading to an increase in national income. However, the propensity to save decreases, reducing the stock of wealth as consumption exceeds disposable income. Ultimately the reduced consumption out of the wealth compensates for higher consumption out of current income. Wealth and consumption keep falling and national income falls to reach steady state level which is lower than the initial steady state.

Why then with a higher propensity to consume does both household wealth and government debt fall? This is due to fact the starting point is a stationary state which indicates the private sector is neither saving /dissaving and the government budget is balanced. As household consume more, their wealth is falling. There is increased revenue for government which means the budget is in surplus and the debt level can be reduced. So both household wealth and government debt decrease by the same amount.

The consequences of an increase in the rate of interest set by the central bank is also shown assuming we begin from a stationary position where accumulated wealth is the targeted level of wealth. Any increase in the rate of interest or the propensity to consume leads to a brief increase in disposable and national incomes. The target level of wealth also increases, suggesting that households will be increasing savings and their demand for bills. In the next period, consumption and income rise, leading to a higher stationary level of income.

The effect of a decrease in the propensity to consume out of current income is examined. The target wealth to income ratio would rise as a result. There would be an initial fall in national income but there would also be a difference between current wealth and target levels of wealth, making it appealing for households to buy bills.

The puzzling impact of interest rates reconsidered

Assuming the propensity to save is not constant, but is a value which depends negatively on the interest rate on bills.

The first result of the increased interest rate is that it causes a fall in consumption, disposable income and national income.

However this model takes stocks into account. A reduction in the propensity to consume increases the target wealth to income ratio, leading to an increase in the stock of wealth. If households’ wealth keeps increasing consumption demand is lower than disposable income once household wealth is increasing.

There is also an increase in government debt. The short term recession caused by the higher interest rates on consumption drives tax revenues down. This negative effect is heightened by an increase in government expenditures due to higher cost of debt. This causes a budget deficit. This deficit gets smaller as government expenditures and taxes continue to increase up to stationary level where the government budget is balanced, and eventually the deficit flow is wiped out by rising consumption expenditures encouraged by increasing household wealth.


A Government target for the debt to income ratio


Godley asks can the government do anything about the debt to income ratio in the long run.

In this model the ratio is defined as V/ Y where V is the wealth of households which corresponds to government debt and Y is national income or GDP This ratio is determined by the behaviour of households.

If households are trying to achieve a high wealth ratio government could attempt to achieve a budget surplus (e.g. by reducing expenditure) but this would be unsuccessful as there would be a reduction in disposable income, but no change in the ratio unless the reduction in income led to households revising their saving propensities.

Government and securities rating agencies are more concerned with public debt as a ratio of GDP, which is easier to adjust. If households are targeting too high a wealth ratio, the government can reduce its stationary debt to GDP ratio. If government wishes to decrease this, they need to increase tax rates or reduce interest rate on bills, resulting in a reduced level of stationary income. Thus, the debt to income ratio must be disregarded to sustain full employment income. This is irreconcilable with maintaining full employment in the long run.

Table 3.4 of Godley/Lavoie

(1) Complete values for table if tax rate is 20%
(2) Complete values for table if tax rate is 30%
(3) Complete values for table in period 2 if tax rate is 30%


(1)

Y = G/(1-a1+a1θ) 38.5
T = θ *Y = 38.5*0.2 7.7
YD = Y - T = 38.5 - 7.7 30.8
C = a1*YD + a2*H-1 = 0.6*30.8 + 0.4*0 18.5
∆Hs = G - T = 20 - 7.7 12.3
∆Hh = YD - C = 30.8 - 18.5 12.3
H =∆Hh + H-1 = 12.3 + 0 12.3

(2)

Y = 34.48
T = 0.3*34.48 10.34
YD = 34.48 - 10.34 24.14
C = 0.6*24.14 + 0.4*0 14.48
∆Hs = 20 - 10.34 9.66
∆Hh = 24.14 - 14.5 9.66
H = 9.64 + 0 9.66


(3)

Y = 34.48 + a2*H-1 34.48 + 0.4*9.65 = 38.36
T = 0.3*38.36 = 11.5
YD = 38.36 - 11.5 = 26.86
C = 0.6*26.86 + 0.4*9.65 = 16.11 + 3.86 = 19.98
ChangeHs = 20 - 11.5 = 8.5
ChangeHh = 26.86 – 19.98 = 6.88
H = 6.88+ 9.65 = 16.53

3.1:
Outside money means the government makes a draft and banknotes for its payments. Inside money (private money) is made by commercial banks or private institutions. Both these ways of money creation and destruction is important to study the complete monetary economy in the real world. However, a hypothetical economy is assumed in which there is a world without any private money, banks, borrowing and interest. This assumption explains why the private bank loan is an important item in the real economic world. It is essential to understand the stock-flow macro-economics rules.

3.2:

A simple model SIM is the starting point for this analysis and built from there. SIM assumes:
A closed economy- No imports/exports
All production undertaken by service providers - no capital equipment and no intermediate costs of production.
Services are instantly provided so unlike manufacturing no inventories exist.
No private banks - government buys services and pays them with the money it printsThe economy is demand-led, i.e. unlimited labour force etc as production responds to demand.

SIM introduces a behavioural matrix explaining each sectors stock of assets and liabilities and how each sector relates to another such that all columns and rows in this matrix sum to zero. It’s players are: households, producers and the government and the transactions are: consumption, government expenditure, output, wages, taxes and change in money stock -Hh +Hh. The balance sheet has money (H) which is an asset to households and a liability to government. Producers are assumed not to hold cash. . The wage bill is the only source of income for household; can be used to pay tax, buy services or buy financial assets. A crucial element of the matrix is total production which is an exception as it is not a transaction between sectors. It is equal to the sum of all spent on goods/services.

3.3
The accounting matrices cannot show how the system works. Therefore, we need to introduce behavioral transactions matrix in order to understand the system as a whole. In the matrix, the vertical columns must sum to zero because the change in the amount of money held must be the same as the households’ income minus their payments. It is similar for government.
There are several mechanisms to insure the supply and demand in the behavioral matrix equal.
1. Neoclassical theory
Higher prices caused by excess demand reduce the excess demand.
2. Rationing theory
Imposing rigid price, this theory believe that the adjustment is done on the short side of the market when supply and demand are not equal.
3. Inventories theory
The theory indicates that there are always enough inventories to absorb the difference between supply and demand.
4. Keynesian quantity adjustment mechanism
Keynesian mechanism base on the premise that production is the flexible element and there are no inventories. The equality between demand and supply is achieved by the quantity adjustment.
Equations of model SIM:
1. YD = W • Ns – Ts
Disposable income equal to wages of households less taxes paid.
2. Td = θ · W · Ns θ< 1
Taxes are deduced from income on the tax rate.
3. Cd = a1 · YD + a2 · Hh-1 0 < a2 < a1 <1
Consumption equals to some proportion of disposable income and some smaller proportion of reserved income.
4. ΔHs = Hs – Hs-1 = Gd – Td
The change in the stock of money of government is the same as the difference between government receipts and outlays in the same period.
5. ΔHn = Hh- Hh-1 = YD – Cd
The accumulated wealth of households equals to disposable income less expenditure.
The following equations illustrate the determination of output and empolyment
6. Y = Cs + Gs
6. Y = W · Nd
7. Nd = Y / W
8. ΔHh = ΔHs
Thus, including the 4 basic equations the SIM model has 11 equations and 11 unknown parameters.

3.4
A numerical example and the standard Keynesian multiplier
This chapter focuses on “the standard Keynesian multiplier”, and the numerical example shows how this model evolves through time, starting with the beginning of the world. This chapter considers whether the multiplier should be interpreted as a logical relationship, occurring within the period, as has been done here, or as a dynamic relationship, occurring over several periods, possibly using trial and error. On the other hand, the drawbacks are also mentioned. First, the view of the multiplier process lacks coherence. Second, the model SIM deals with flows, while not take into account the impact of flows on stocks and the subsequent impact of stocks on flows.


3.5

The model assumes a steady state which means that both flows and stocks change at the same rate and are in a constant relationship to each other .As we omit growth we assume a stationary steady state in which government expenditure equals tax receipts so that no surplus/deficit exists and hence a zero change in the stock of money. It also assumes that consumption must be the same as disposable income and the stock of past accumulated wealth.

3. 6
Another interpretation of the consumption function is offered in terms of a wealth accumulation function

Consumption is disposable income minus the household savings of the period. Households have a defined level of wealth they want. If the target level is below the actual level households will save in order to achieve their target thus consumption will always be below disposable income until the target is reached. Once the target has been passed no more saving will occur and the stationary state is reached.
3.7

The government expenditure is equal to tax receipts in both these two sections. The relationship between income and government expenditure can be descried as
Y*=G/θ
The G/θ ratio means when the income increases and the government expenditure is steady, then the average tax rate will be reduced. This result can be called fiscal stance.
There is two fundamental property of the steady-state such as
(1) As the average tax rate is constant, the aggregate income will increases at the same level when the government expenditure increases.
(2) In a stationary state, there is no savings because of there is no change in financial stocks. So, YD*=C*= G· (1-θ) /θ
This equation expresses the relationship between the disposable income and government expenditure that is the disposable income can be increased as the government increases its expenditure.
Also the equation shows us there is an equal relationship between the consumption with disposable income in the stationary state.

3.8
Stability analysis is important in the dynamic module and coefficient can be used to measure it. In form of equation H = A + BH -1, the B coefficient next to H-1 is always positive. This means the module towards stationary when it is out-of- equilibrium. Therefore, the change of money balances according to time increases in step until it


3.9

The author uses a graphical to illustrate the model of SIM. Especially, the author tries to use two kinds of way to answer the question which are “given the various household consumption parameters and fiscal policy parameters set by government, what is the level of production compatible with aggregate demand?” The short-run answer used different periods of cash money balances to calculate. On the other hand, the long-run answer thought the level of wealth is an endogenous variable.

Excel Spreadsheet Q in class

An the excel spreadsheet was given , in which a level of income was given, and from this income some is saved . This is the withdrawal row. In a closed economy, injections always equal withdrawals. There also was a randomly allocated investment. It was required that we balanced the system, so we set the withdrawal level to make the level of income equal to the level of aggregate expenditure, which is just a sum of the other rows. To do this we had to work out the marginal propensity to consume, this is calculated by dividing the change in consumption by the change in income and if it was say, 0.8, then you'd set 30% of your income towards withdrawals to get the system close to equilibrium. Aggregate expenditure is the sum of income, consumption and injections, less withdrawals. To balance the system, one adjusts the withdrawals figure until income equals aggregate expenditure.

Q2

Q.2 Write out an explanation for each row.

Consumption – Consumers buy products with their income (-Cd) . Producers produce what is demanded and are paid (+Cs) for this.

Government Expenditure – The government buys goods/services (-Gd). Producers get the money in return for producing what is demanded (+Gd).

Output – This is all money spent on goods/services and is seen to be the total production of an economy.

Factor Income – Producers need a labour force to produce goods/services. This costs
(-W.Ns).The labour is provided by households who earn (+W.Ns).

Taxes – Households are charged taxes by the government (-Td) while the government receives this in order redistribute it for the public benefit.(+Td).

Change in money stock – Households will not always immediately spend but will save money which they may use to buy financial assets (- change Hh). . By the Government providing these financial assets they receive additional income to what to get in taxes. (+ change Hs)

Consumption Function

Definition:

Keynes devised this function to state consumer spending as one term. It is shown as a linear function and explains how consumption expenditure depends on the level of income. The consumption function shows that what people spend depends on their income, and that as income increases, so does consumption.

C = a + mpc * Y

Where
c = total consumption

a = autonomous consumption i.e. consumption when income is zero so therefore it is consumption which is not influenced by current income.

mpc = the marginal propensity to consume i.e. the rate at which consumption is changing when income changes.

Y=disposable income

Note also that mpc * Y is induced consumption , i.e. consumption influenced by the economy’s income level.

The concept revolves around the fact that a consumer’s expenditure depends on his or her disposable income. Real income is money income adjusted for inflation. It is a measure of the quantity of goods and services that consumers have buy with their income.
·There is normally a positive relationship between disposable income and consumer spending. This fraction of additional income that people spend is called the marginal propensity to consume. MPC = (change in consumption) divided by (change in income)The gradient of the consumption curve gives the marginal propensity to consume. As income rises, so does total consumer demand.
· A change in the marginal propensity to consume causes a pivotal change in the consumption function. In this case the marginal propensity to consume has fallen leading to a fall in consumption at each level of income.

The Keynesian consumption function is based on current income only and does not consider future income . Therefore extensions of this theory are Friedman's permanent income hypothesis and Modigliani's life cycle hypothesis.

Example:
An increase of disposable income could result in higher level of consumer expenditure. Also, the level of consumption depends on the change in MPC. As the MPC goes up, the consumption will increase.

References:
www.businessdictionary.com
www.tutor2u.net/economics/content
http://en.wikipedia.org/wiki/Consumption_function
http://www.ingrimayne.com/econ/Keynes/SimpleModel.html

Problem 1. Defining terms and characterising them as Income, Expenditure or Output

Wages – Periodic payments for labour
Employer’s view – expenditure
Employee’s view – Income

Consumption – household expenditure on goods and services for a specific period
Expenditure

Rent – periodic expenditure for the use of capital assets
Landlord/Asset owner – Income
Tenant/Lessee – expenditure

Government Expenditure – expenditure of a day-to-day nature by a Government
Expenditure

Manufacturing Output - the output from labour and capital
Output

Interest Payments – The cost of borrowing
Bank – Income
Borrower – Expenditure

Loans – a sum of money given or received at an agreed rate of interest
Issuer – Income
Borrower - Expenditure

Bank Deposits – cash savings held at a bank
Bank – Income

Bonds – A guaranteed loan made from a country or company with or without coupon payments.
Issuer – Expenditure
Borrower – Income

Equities – capital investment in companies
Issuer – Income
Borrower – Expenditure

Money Balance – How much money/wealth in the form of readily available purchasing power – consumers and firms actually hold at a given moment.
Output

Chapter 7. The Meaning of Saving & Investment Further Considered

I
Saving and Investment are defined as equal in amount. Investment, defined includes the increase of capital equipment, whether it consists of fixed capital, working capital or liquid capital.

II
Hawtrey suggests that an excess of saving over investment would be the same as an increase in liquid capital. Keynes prefers to emphasise the total change of effective demand and not just the changes in liquid capital i.e. unsold stocks in the previous period as Mr. Hawtrey does. Hawtrey’s method in the case of fixed capital ignores that changes in unused capacity corresponds to changes in unsold stocks, which effects decision to produce. Keynes makes reference to the vagueness of capital consumption and capital formation used by the Austrian School of Economists and says they are not identical to his definition of investment and disinvestment (disinvestment - sale of an investment as being negative investment).

III
Keynes acknowledges that his new argument is much better than his argument in Treatise on Money where he didn’t distinguish clearly between expected and realised results. Keynes new argument is that the expectation of an increased excess of investment over saving, given a volume of employment and output will lead entrepreneurs to increase the volume of employment and output. Any changes in the expected levels of investment over saving will motivate firms to raise the volume of employment and production. Therefore the volume of employment is determined by expected demand or an expected increase of investment over saving.

Robertson proposes an alternative attempt at defining saving and investment. From his definition an excess of saving is exactly equal to the decline of income in Keynes sense.

IV
The definition of “forced saving” is a measure of changes in the quantity of money or bank-credit and consequently it is found that “forced saving” has no distinct relationship to the difference between investment and saving. However it is difficult to distinguish between “forced saving” and any other changes in saving unless the amount saved in certain given conditions is given as a standard. “Forced saving” needs a specified standard rate of saving, for example - full employment.

V
Keynes emphasises that investment and saving are a two-sided transaction. People exercise their ‘free choice’ as to the proportion in which they divide their increase of income between saving and spending. The aggregate saving of an individual and of others taken together must be equal to the amount of current new investment.

Keynes elucidates three effects of credit:
1. increasing output.
2. marginal returns on that output increasing.
3. rising wages.
These may affect the distribution of real income between different groups.
Keynes concludes that the old-fashioned view that saving always involves investment is formally sounder that the view, that there can be saving without investment or investment without saving.

The mistake people make is thinking that when an individual saves, he will increase aggregate investment by an equal amount. It is true that when an individual saves he increases his own wealth but the conclusion that he also increases aggregate wealth fails to allow for the possibility that an act of individual saving may react on someone else’s saving and hence on someone’s else’s wealth.

Therefore incomes and prices change until the aggregate amount of money that individuals choose to hold at the new level of incomes and prices is equal to the amount of money created by the banking system.

This is the fundamental proposition of monetary theory. There cannot be a buyer without a seller or a seller without a buyer.

Summary of Chapter 6. The Definition of Income, Saving and Investment

I
Income is output sold to others for a certain sum A, which consists of an amount A1 (purchase of finished output from others) and G (working capital).

Keynes states it is not suffice to say income equals A+G-A1. Part of A + G - A1 is due to the capital equipment from the previous period. To determine income from the current period there are two possible methods identified, one in relation to production, the other in connection with consumption

1. If the capital equipment had never been used an amount would be spent on maintaining it (B1). G will now be worth G1. Therefore G1-B1 is the value saved had the equipment not been used to produce A. The excess of this value over G-A1 is what has been sacrificed to produce A. This is the user cost of A. This plus the amount paid out by the entrepreneur to other factors of production is the factor cost of A. The sum of both the factor cost and the user cost is the prime cost of A. Therefore income is the excess of the value of finished output over prime cost, which is equal to the quantity the entrepreneur attempts to maximise. Since the income of the rest of the community equals the entrepreneurs factor cost, aggregate income equals (A-U).

Keynes adds for the community as a whole, the aggregate consumption (C) of the period is equal to sum of (A – A1) and aggregate investment (I) is equal to sum of (A1 – U).

2. Secondly the involuntary loss or gain in the value of his capital equipment is examined. These losses often are unavoidable but possibly not unexpected. Keynes defines Supplementary Cost (V) is the excess of the expected depreciation over user cost (U). This cost is deducted from income and gross profit to calculate net income and net profit. However there is also the change in the value of the equipment due to unforeseen changes in market values or extraordinary events. It is called a ‘Windfall Loss’ which is ignored in calculating net income.

The amount of supplementary costs and the amount of windfall loss/gain made on the capital account affects net income. Estimating supplementary costs depends on the choice of accounting method. It can be fixed from the outset or it can be recalculated annually.
Keynes states net-income is not clear. He discards his definition of income in the Treatise on Money. The new definition of net income comes very close to Marshall’s definition of Income and it also corresponds to the money value of Pigou’s definition of the National Dividend.

II
Saving is the excess of income over consumption expenditure. (A1 – U) and net saving for the excess of net income over consumption is equal to A1 – U – V.

Keynes uses his definition of income to lead on to his definition of current investment. The part of income, which has not passed into consumption, is investment. During the same period finished output having a value of A – A1 will have passed into consumption and A1 – U is the addition to capital equipment as a result of the productive activities of the period and is therefore the investment of the period. Similarly A1 – U – V is the net investment of the period.

To summarise;
Income = Value of output = Consumption + Investment
Saving = Income – Consumption
Therefore Saving = Investment

Equilibrium in the market is decided by the free choice of individuals, as it is the amount saving individual decides to save which is equal to the aggregate amount which investing individuals decide to invest.

List of Group

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