Chapter four introduces the Model PC. This model of portfolio choice is presented because of the choice faced by agents between different possible portfolios of money and other different financial assets.

The Model PC

The Model PC goes further than SIM and introduces government bills, interest payments and a central bank. Treasury bills do not change in value throughout their lifetime. Therefore there are no capital gains from price fluctuations in financial assets.

The first column of the Balance sheet of Model PC highlights that the two assets held by households are either bills H or money Bh and that combined they add up to the households’ private wealth V.

There is no production sector in this balance sheet because of the supposition that it is a pure service economy. There is neither circulating nor fixed capital resulting in both household and private sector wealth being the same. From Model PC it is clear that private wealth is the sum of both cash money and bills held by households.

The outstanding bills B issued by the government, to households and the central bank are combined, equal the net worth of public debt.

The central bank is now considered a separate institution that buys bills from the government, resulting in additions to its own stock of assets (Bcb). Its liability side is comprised of money in form of cash or deposits. It is assumed that the central bank has a net worth of zero. This infers that if a profit is made, from Bills it owns over any liabilities, that it is automatically distributed.

Interest payments now arise on government debt. They are outlays by the government but do not form part of GDP, as is standard practice in national accounting. National income is composed of sales from households to the government only.

Assumptions:

Firms sell all goods and services demanded by consumers and government.

Households supply any and all labour demaned by firms.

Households also correctly foretell their incomes.

Households decide how much of their income to save, then where to allocate this wealth.

Money balances are elastic in a monetary system and change accordingly to shocks in flows of funds.

Hh = V - Bh (4.6)
Hh = (1-λ0) - λ1.r+λ2.(YD) (4.6a)
V V
Bh = λ0 + λ1.r - λ2.(YD) (4.7)
V V

Equations 4.6A and 4.7 demonstrate the proportions in which households hold their wealth. That held, as money is inversely proportionate to interest rates and positively related to disposable income resulting from the transaction demand for money.

ΔBs = Bs – Bs-1 = (G+r-1.Bs-1) – (T + r-1.Bcb-1) (4.8)

ΔHs = Hs – Hs-1 = ΔBcb (4.9)

Bcb = Bs - Bh (4.10)

Equation (4.8) shows how the government finances its deficit by issuing new bills, over and above those renewed at maturity.

The increase in the money supply ΔHs is the same as increase in demand by central bank, ΔBcb.

The above equations demonstrate how households demand to hold some part of their personal wealth in the form of cash; this leads to the leftover government bills being purchased by the central bank. In this way they provide cash on demand to households. The amount of cash held is endogenous and driven by requirements of household sector.

Bh = Bd (4.15)

If there are surprise savings, they will take the form of additional cash money balances. In this way they act as a cushion against wrong expectations. Ergo households at the end of the period hold the amount of bills demanded by them at the start of period. Meanwhile their cash balances will dictate corrective measures to modify their spending in the next period.


The Steady State

In Model PC the unlikely situation arises that interest rate increases cause an increase in economic activity. A rise leads to an increase in disposable income and consumption not just in the short run but also in the new stationary state.

Y* = G + r.Bh*.(1-θ) = GNT (4.18)
θ
C*= YD* = (G + r.Bh*). (1- θ) (4.19)
θ

Both formulas show that in the full stationary state, the aggregate income flow and disposable income flow are both increase as a result of interest rates.

Fiscal stance determines the level of GDP in the steady state, regardless of the average rate of interest payable on total government liabilities and the target wealth to disposable income ratio, depending on the G/θ ratio.

Results of Model

There are a number of results in the Model PC worth our attention. If the permanent level of government expenditures G increases this leads to an increase in the stationary level of disposable income and income. An increase in the stationary level of income and disposable income can be achieved by a permanent reduction in the overall tax rate θ.

Increases in the rate of interest or average interest rate due on total government liabilities results in an increase in the steady state level of disposable income. These increased rates cause the government sector to pay more to service its debt, this is followed by increased spending by the household sector. Higher returns on government bills also increases demand for them and entice households to hold more of them.

Reductions in liquidity preference causes an increase in national income.

Increases in the wealth to disposable income ratio, α3, ultimately precedes a growth in stationary income or disposable income. This arises as a diminished propensity to consume, augments the steady state levels of income and disposable income, in contradiction to the paradox of thrift.

Week 6 In-Class Problem

We had to solve the transactions matrix given changes in Theta:


Period 2
Given: G = 20, Y=38.5
T = (Theta) * Y = .2*38.5 = 7.7
YD = Y – T = 38.5 – 7.7 = 30.8
C = (Alpha1) * YD + (Alpha2) * (H-1) = (.6 * 30.8) + (.4 * 0) = 18.5
(ChgHs) = G – T = 20 – 7.7 = 12.3
(ChgHh) = YD – C = 30.8 – 18.5 = 12.3
H = (ChgH) + (H-1) = 0 + 12.3 = 12.3

(Theta) Changes to .3
Period 2:
G = 20
Y = G/(1-(Alpha1)+(Alpha1 * Theta) = 20/(1-.6+[.6*.3]) = 34.5
T = (Theta) * Y = 10.35
YD = (Y-T) = 24.15
C = (Alpha1) * YD + (Alpha2) * (H-1) = 14.5
(ChgHs) = G – T = 9.65
(ChgHh) = YD – C = 9.65
H = (ChgH) + (H-1) = 9.65

Period 3:
G = 20
Y = Y2 + (Alpha2)*H-1 = 34.5+(.4)*(9.65) = 38.36
T = (Theta) * Y = 11.51
YD = (Y-T) = 26.85
C = (Alpha1) * YD + (Alpha2) * (H-1) = 19.97
(ChgHs) = G – T = 8.49
(ChgHh) = YD – C = 6.88
H = (ChgH) + (H-1) = 8.49 + 9.65 = 18.14

Chapter 3 Summary

Outside money specifically refers to Government money. It is issued by public institutions. Inside money refers to Institutions outside the government realm relating to lending activities. The construction of a monetary economy makes some simplifying assumptions. It postulates that private money does not exist; purely for illustration purposes. Model SIM tests the affects of changing exogenous variables affect the endogenous variables.


Model SIM makes the following assumptions about the economy;


Closed economy.


No imports or exports.


Producers of services have no cost of production & no equipment. Production only carried out by labour.


Inventories do not exist.


No banks, firms or profits.


Government issues money which is legal tender. Used for exchange of good and services in the economy.


Government fixes price of labour per hours.


Unlimited supply of labour.


Demand led economy.


The Model SIM balance sheet has one item, money (H). Household (+) and government (-). Producers do not hold cash. Inflows (+) and outflows (-) cancel each other, therefore summing to zero. Wages are sole source of income for household; can be used for 1) taxes (T) 2) consumer services(C) 3) financial assets (∆ H)


Total production (Y) is expressed as Y== C+G=WB (sum of all expenditure)


There are a number of equations that underpin model SIM. They look to explain how both supply and demand react. Equations are offered to explain how price increases causes a decrease in demand. Firms have an excess of stock to meet demand that may arise. Keynesian approach assumes that supply reacts instantly to demand and completes the order instantly. It is also assumed that Investment must be exactly equal to saving.


The pitfalls of the traditional view of the multiplier effect are outlined. It deals with how flows were considered but not the reaction to stocks from these flows. It is a short run phenomenon and cannot be considered to exist in the long run.


The steady state assumes that flows and stocks are in a continuous rate of change. Either in stationary state, recession or growth the variables remain constant. Model SIM assumes the stationary state. It assumes that consumption must be the same as the available disposable income. The consumption function is adjusted tobe interpreted as a wealth accumulation function.


The model SIM uses the assumption that consumers have perfect foresight regarding their income. It assumes that households make some estimate on their income. Demand is added to the equation as households decide at the beginning of a period how much money they desire to have at the end of the period.


∆Hd = Hd – Hh-1 = YDe - Cd


If realised income is greater than that expected then household will hold the difference in larger cash money balances. The amount of cash held will be similar to that planned but will be modified by an error in their expectations. The difference between desired and realised holdings of money is equal to the expected and realised disposable income. Over time people change their consumption decisions due to unexpected changes in their wealth stock. The fact that expected income is used by the equation rather than realised income means that the system is recursive. If income is continually higher than expected then wealth will in turn be higher than expected causing consumption to grow.


Current income is established by the amount of money that was held in the previous period thus giving credence to Keynes’s argument that money is the link between each period and the next.
A rise in the tendency to consume from current income causes an initial rise in national income due to an increase in consumption expenditure. This will be cancelled out by a decline in accumulated money balances and therefore reduce consumption expenditure out of wealth.


It is sometimes assumed that the process of economic adjustments inevitably lead to an equilibrium. Stability analysis tests whether equilibrium can be attained.


As the SIM model is so simple it is possible to provide a more conventional graphical representation requiring four quadrants fully closed.

Week 5 Homework: Problem Set 4 Problem 2

The assignment was to explain/justify the lines within the SIM Behavioral Transactions Matrix:

Consumption Line: Households have a need or want (demand) for products and services within the economy. Consumers are willing to purchase these products using their own income (-Cd) if someone is willing to produce them. Producers fulfil the role of producing what is demanded from Households, and in return generate income (+Cs) from engaging in this activity.

Government Line: Governments and Producers have a similar relationship to that of Households and Producers. The government demands and spends its income on products and services for it's own purposes and public works (-Gd). In turn, producers supply these items as a means for generating their own income (+Gs).

Output Line: Output in the matrix is neither an income nor expenditure. Hence, its single “appearance” does not violate the macro-equilibrium concept. Its existence represents the income/expenditure (assuming income = expenditure) within the economy. Income = output = consumption from households + Government expenditure.

Factor Income Line: This line represents the influence of labour in the economy. Households provide their labour to production firms in order to earn an income (+W.Ns). They must earn this income in order to purchase the goods and services they demand. From a production firm's perspective, labour is required in order for them to produce goods and services which earn them income. The act of hiring this labour force is an expenditure to the production firm (-W.Ns).

Taxes Line: Governments must earn an income in order to provide public goods and services. To “earn” this income, the Government will collect tax income from households which benefit from these services (+Td). Households are taxed in various ways such as on income earned for their labour, which is viewed as an expenditure (-Ts).

Changes in Money Stock Line: It is assumed that over time, households will accumulate excess stocks of money, as their income may exceed the demand for goods and services (this can also be considered savings). If households have an excess amount of money, they can use it to purchase financial assets (-Chg Hh). It is assumed in the simplified transactions matrix that the sole-supplier of these financial assets is the Government. By issuing these assets, the Government can raise income to fund their public works.

Week 5 In-Class Work

Briefly, here are out notes for Problem 4 Pt 1 which was done in class last Monday:

Recorder of the day: Barry

Presenter of the day: Rory

Workers: Tom, John, Rob, Hugh

1.1
The amount of any given expenditures has to balance with incomes/inflows. Put simply, there must be “macro-balance” in each sector.

1.2
For every component in the table there must be an opposite component. There must be an equivalent or a sum of equivalent components. This is because we need to equalise supply and demand and find equilibrium.

Why?

We are aiming to achieve the steady state economy (Pg.63). All consumption required is demanded. Everything taxed is also “returned” with public goods. Using notation from our table:

Cs = Cd Ns-> Nd

Gs = Gd

Ts = Td

Which refer to the following topics in Chapter 3:

Investment function

Consumption Function (3.5, 3.7)

Taxation (3.11)

Chapter 7

Chapter 7


This chapter focuses on the meaning of the terms “saving” and “investment” and their relation to one another, in particular to when there is an excess of saving over investment. The excess here is said to be similar to that of an un-designed increment in the stock of unsold goods. Mr. Hawtrey does not agree, regarding the daily decisions of entrepreneurs concerning their scale of output as being varied from the scale of the previous day by reference to changes in their stock of unsold goods.

“Normal Profit” of entrepreneurs also declines with an excess of savings over investment. Furthermore, a continually increasing excess of savings shows a decline in actual profits.

An entrepreneur fixes the volume of employment to maximise present and prospective profits. The volume of employment is determined by the estimates of effective demand made by the entrepreneurs, an expected increase of investment relative to saving being a criterion of an increase in effective demand.

With Mr. D. H. Robertson’s definition of “today’s income”, saving can exceed investment by the excess of yesterday’s income over today’s income. Therefore if current expectations were always determined by yesterday’s realised results, today’s effective demand would be equal to yesterday’s income.

“Forced Saving” is then highlighted here. This has no definite relation to the difference between investment and saving. “Forced Saving” results from, and is measured by, changes in the quantity of money or bank-credit. A change in the volume of output and employment will cause a change in income which in turn redistributes income between borrowers and lenders. A change in aggregate income measured in money creates a change in the amount saved. These are not “forced savings”. A highly contrived definition of “forced savings”, resulting from a meaning for “savings” in a state of full employment, may be: “Forced saving is the excess of actual saving over what would be saved if there were full employment in a position of long-period equilibrium”.

Jeremy Bentham looked at the consequences of an increase in money in circumstances of full employment and pointed out that real income cannot be increased, and, consequently, additional investment involves forced frugality “at the expense of national comfort and national justice”.

No-one can save without acquiring an asset and no-one can acquire an asset which he did not previously possess, unless either an asset of equal value is newly produced or someone else parts with an asset of that value which he previously had. Therefore, the loss of wealth must be due to his consumption exceeding his income. The aggregate saving must be equal to the amount of the current new investment.

Bank credit that allows for the addition to current investment, will increase income and at a rate which will normally exceed the rate of increased investment. This brings an increase in real income. Money corresponding to the bank credit can be held rather than holding some other form of wealth. Bank credit has tendencies which may affect the distribution of real income between groups. This is avoidable only by passing up any course of action capable of improving employment.

The affect of consumption on the incomes of others make it impossible for all individuals to save any given sums simultaneously. The community as a whole cannot save less than the amount of current investment, as this will raise incomes to a level at which the sums at which individuals choose to save add up to a figure exactly equal to the amount of investment. Incomes and prices change until the aggregate of the amounts of money which individuals choose to hold at the new level of incomes and prices thus brought about has come to equality with the amount of money created by the banking system

Chapter 6 Summary

Chapter 6

Income

Keynes defines income and the factors which determine income. These determinants include sale of output, purchase of output, capital equipment (inventory, working capital, goods in production).

This lead Keynes to the equation of

A+G-A1

Where A is equal to sale of finished output to consumers etc.

G is equal to the working capital,

And A1 equals the cost of the inputs.

Keynes states that in order to define income a deduction must occur. This deduction is for the cost of having and maintaining capital equipment. This deduction is for the income that is not attributable to the present period, but from having a value inherited from previous periods. Keynes has come up with 2 methods for calculating the deduction; these 2 methods are based on production and the other on consumption. This figure can be either connected to voluntary activities or involuntary conditions.

In the deduction method dealing with production, Keynes refers to this as a voluntary activity. He argues that the value of G at the end of the period is determined by the maintenance and possible improvement that was done during the year; however there may be a decrease due to over use. He therefore comes up with the equation

(G’ – B’) – (G – A1)

Where B’ is the value of the maintenance, improvements during the year. G’ the value at the end of the period. (G – A1) is the value of the sacrifice to produce A. this is called the User Cost and is referred to U. The amount paid out for services of production is called the Factor cost. The User Cost + Factor Cost = Prime Cost of Output production.

In defining the deduction for consumption or as Keynes refers to as the involuntary conditions. These include changes in market values, obsolescence, time decay, and catastrophe. These may be unavoidable but they are not necessarily unexpected. These costs he describes as supplementary costs. These costs affect everyone. Keynes defines income like Marshall, as the excess value of finished output sold in the period over the prime cost.

Saving & Investment

Keynes states that savings is an agreed definition. This is the excess of income over expenditure on consumption. Any doubts must be on expenditure or consumption. This must mean the value of goods to consumers during that period, this leads to the problem of defining a consumer, such as consumer – purchaser or investor - purchaser. Keynes comes up with the equation A1 – U, for savings. For net saving for excess net income equals A1 – U – V.

This leads on to the definition of current investment. Keynes states that this is equal to the definition of savings. This is due to the current addition to the value of the capital equipment.

This can be seen through this

Income = value of Output = consumption + investment

Saving = Income – Consumption

Therefore Saving = Investment.