Homework 2

Fill in the blanks.

1.1 Why must the vertical columns sum to zero?
The difference between the inflows of income and outflows of expenditure for each sector must match the sum of the transactions in stocks and financial assets.

For each sector the change in the amount of money held must equal the difference between the sector’s receipts and payments. For households, the change in their end of period holdings of cash must equal their wages minus taxes minus consumption. Similarly, government expenditure should equal the taxation supplied by households plus their end of period holdings of high powered money. It is assumed that producers hold no cash and therefore receipts from sales must equal their outlays on wages. This results in a zero sum rule for each column.

[Reference] Chapter 3, Monetary Economics, Godley & Lavoie

1.2 Why must the horizontal columns sum to zero?
In order to ensure that the horizontal rows sum to zero, the equalizing mechanisms must be specified. The fundamental economic principles of supply and demand help describe the behaviour of agents at the time of the transactions. In order for the horizontal rows to sum to zero four equations must be specified that imply whatever will be demanded will always be supplied in that period.

Cs = Cd Sales of consumption services will equal purchases of consumption services.

Gs = Gd Sales of government services will equal purchases of government services.

Ts = Td Taxes supplied will equal the taxes demanded.

Ns = Nd There is a reserve of unemployed workers willing to work at the going wage.

For sales to equal purchases we use the Keynesian quantity adjustment mechanism which states that production is flexible and producers produce what is demanded. This is the most suitable approach for a demand led economy without any supply constraints and will ensure all rows sum to zero.

For row 6 ∆Hh = ∆Hs

Under Keynesian economics investment = saving. In model SIM there is no investment therefore the saving of the overall economy equals zero. ∆Hs is the government’s fiscal deficit. The two terms are equal in order for overall saving to equal zero.

Total production is not a transaction between two sectors and therefore does not sum to zero. It is used in national accounts to denote the sum of expenditure on goods and services. Y = C + G

The equations have now been satisfied so that all rows, except output, sum to zero.

[Reference] Chapter 3, Monetary Economics, Godley & Lavoie

2.1. Consumption
Within the behavioural transaction matrix, consumption represents the purchase of goods by the household. The source of funds can come from current disposable income, YD, and from savings H[t-1]. Using the Keynesian quantity adjustment mechanism, the production sector will have a consumption of Cd which is exactly equal to Cs :

Cd = Cs

Note: the level of consumption demand has a direct link to the source of government revenue from the production sector and the level of employment.


2.2. Government Expenditure
This relates to the purchase of goods and services, Gd, and is used to provide essential facilities to the nation i.e. roads & schools. The source, Gs, of income is from "revenues collected by the production sector."[1]

Gd = Gs

[1] p.63 Monetary Economics, Godley & Lavoie

2.3. Output
Output is used to describe the end result in the production sector for the given period.
This can be used to measure the productivity of the nation. The measurement can be taken in the form of "the sum of all expenditure on goods and services (C + G)or, as the sum of all payments of factor income (WB)."[1]


[1] p.61 Monetary Economics, Godley & Lavoie

2.4. Factor Income
This refers to the flow of wages for services provided by the household for the production sector.
W.Ns = wage rate times the employment supplied by the household.
W.Nd = wage rate times the employment demanded by the production sector.

W.Ns = W.Nd; factor income rises and falls as the demand/supply for labour rises or falls in the production sector.

2.5. Taxes
A government use taxes as a source of money supply, Td, to enable it to influence the direction of the economy. In order to maintain a relatively steady flow of money, a “fixed proportion of money income”[1], θ, is levied as taxes. In the behavioural transaction matrix, the supply must equal demand;

Ts = Td.

Td = θ. W.Ns θ<1

[1] p.66 Monetary Economics, Godley & Lavoie




2.6. Change in Money Stock
The change in money stock relates to the supply that the government has as a result of income and expenditure. In real terms, this is usually a surplus or deficit. A deficit may occur due to the income from taxes, Td, not meeting the required government expenditure, Gd. This would lead to the government issuing debt in the form of treasury bonds to cover the excess.

In the behavioural transaction matrix, this deficit can be explained by households saving a proportion of their income to accumulate wealth. In theory, these savings should match the deficit.

Hh = Hs

Hh = YD - Cd

Hs = Gd - Td

Key to equations

Cs :Consumption supply
Cd :Consumption demand
Gs :Government supply
Gd :Government demand
Ts :Tax supply
Td :Tax demand
W.Ns :Wage rate times employment supply
W.Nd :Wage rate times employment demand
∆Hh :Change in cash held by households
∆Hs :Change in the supply of money
H[t-1] :Cash held from the previous period
Y :Total production
YD :Disposable income