EC6012 Homework 2

1 Why must the Vertical Columns sum to zero?

First, it is very important to understand that the agent buying a service is engaged in a completely different activity from that performed by the seller of that service and the motivation behind the two types of activity is completely different. Then, the reason that the Vertical Columns must sum to zero is that the change in the amount of money held must always be equal to the difference between households’ receipts and payments, however these are determined. Similarly the change in the amount of money created must always, by the laws and logic, be equal to the difference between the government receipts and outlays. Moreover, as they are assumed to hold no cash, producers’ receipts from sale must equal their outlays on wages.

2 Why must the Horizontal Row sum to zero?

The following equations equalize demands and supplies.
Cs = Cd (1)
Gs = Gd (2)
Ts = Td (3)
Ns = Nd (4)

These four equations imply that whatever is demanded (services, taxes and labour) is always supplied within the period. These (apart possibly from (3)) are strong assumptions implying, obviously enough, that we are describing an economy that has no supply constraints of any kind. In particular, equation (4) implies that there is reserve army of unemployed workers, all eager to work at the going wage, whenever their labour services are being demanded.

Furthermore, Cs and Gs represent the sales of consumption and government services, Cs and Gs carry a positive sign in production column of the matrix. They thus represent sources of income-revenues that collected by the production sector. Similarly, Cd and Gd represent the purchase of consumption goods and government services. Of course, we know that the sales have to equal purchase.

In general, ‘everything comes from somewhere and everything goes somewhere’ (Godley & Lavoie, pg. 6). Every component in the matrix must have an equivalent component elsewhere. Therefore flows must always equal zero.

Row 1 Consumption:
In each period households consume their disposable income (YD) and the wealth they have accumulated in previous periods, H(t-1),H(t-2),etc. Households buy goods with this income, -Cd and producers supply these goods and receive +Cs for them. Therefore, -Cd+Cd=0.

Row 2 Govt Expenditure:
Governments demand goods and services similar to households. Government’s purchase these products –Gd and similarly producers supply these goods and services and receive +Gs. Hence, -Gd+Gs=0.

Row 3 Output:
Y, total production can be defined as the sum of all expenditures on goods and services or as the sum of all payments of factor income in an economy. In this matrix, Y is not a transaction between two sectors and hence only appears once.
Y=C+G.

Row 4 Factor Income:
The income received by a household for supplying labour, is denoted as a wage rate (W) times employment (N). It is an asset for the household and is a liability for the production firm as they must pay money out. The s and d denote supply and demand. The household earns income (+W.Ns) while the production firm pays employees (-W.Nd).Both amounts are equal therefore they sum to zero.

Row 5 Taxes:
When Households earn income they are subject to tax on their wages. This is a liability for the household and is denoted as (-Td). The amount paid by the households is received by the government, it is therefore an asset for the government and is denoted by (+Td).Both amounts are equal which means this row will sum to zero.

Row 6 Changes in Money stock:
Over time the household accumulates excess stocks of money, as income may exceed the demand for goods or services. When this occurs households can use their excess income is to purchase financial assets, it is denoted by –ΔHh as it is an outflow. In the model the government is the supplier of the financial asset therefore they receive additional income which is denoted by +ΔHs.

References:
Godley, W., and M. Lavoie (2007) Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, Palgrave Macmillan.