Question One
The PC model extends SIM by introducing government bills, interest payments and a Central Bank. The bills have a value of one unit and at maturity bill holders receive the principal plus interest. The private wealth of households is given by the sum of money and government bills held. Like SIM this model assumes a pure service economy and this means there is no production sector. This implies that household net worth is equal to the net worth of the private sector. Public debt is equal to the value of bills outstanding issued by the government.
In PC the central bank is considered an independent institution with zero net worth. Its only assets are government bills and its liabilities consist of cash or deposits held at the central bank. In the transactions flow matrix for the PC model all rows and columns sum to zero to reflect all transactions. The matrix accounts for two financial assets (money and bills) but the equivalent matrix in SIM only includes money. PC also includes interest paid on government debt and these payments depend on both the stock of assets and the interest rate at the end of the previous period. These interest payments are transfer payments and are not included in national income.
The central bank is separated into two components: the current account and the capital account. The current account records current period inflows and outflows such as interest payments while the capital account records changes to the bank’s balance sheet. The central bank makes a profit as it pays no interest on cash money and earns interest on its bills. All profits are paid to the government and as a result interest payments by the government are only paid on the portion of public debt held by households.
PC also assumes that firms supply the goods/services demanded by households and the government and that households supply the labour demanded by firms. National income is again given by consumption plus government expenditure. Disposable income equals income minus taxes plus interest earned on government bills. The tax paid by households is given by the product of the personal tax rate and taxable income (income plus interest earned on bills). The identities are shown below.
Y = C + G
YD = Y – T + r-1Bh-1
T = Ѳ(Y + r-1.Bh-1)
It is assumed that households make a two stage decision. They first decide how much of their income they will save and they then decide how to allocate their wealth. The consumption decision determines the value of the end of period wealth and the portfolio decision determines the allocation of wealth. In the steady state the quantity of cash held by households is the same as the amount provided by the central bank.The difference between disposable income and consumption is given by the change in total wealth. The consumption function is also modified to include total wealth and not just the stock of money.
V = V-1 + (YD-C)
C = α1YD + α2V-1
Households will hold a certain proportion of wealth in bills and the rest in money. The proportion of wealth held as money is negatively related to the interest rate and positively related to disposable income because of the transactions demand for money. The relevant rate of interest used in determining such proportions is the interest rate that equates the demand and supply of bills at the end of the current period. The proportions of wealth held in bills and money must sum to unity and this is known as the wealth constraint.
The transactions demand for money declines as the ratio of consumption to income becomes normal. In the steady state the ratio V/YD represents a stock flow norm. If cash holdings are modelled as the residual equation then money holdings are equal to the difference between household wealth and the household demand for bills.
Hh = V - Bh
The government deficit is funded by issuing new bills. The central bank purchases all bills not bought by households. As the residual purchaser of bills it provides cash money on demand. Households wish to hold a proportion of their wealth in cash. Cash money is endogenous and the rate of interest is exogenous. The interest rate is fixed and it is the point of equilibrium of the demand and supply of government bills for the current period. The interest rate provides us with one of the parameters for government responses. If the interest rate could vary then there would be no symmetry in the allocation decision.
Question 2Liquidity Preference
Liquidity Preference is a tendency amongst individuals to fix the amount of money they have on hand for use in immediate consumption. Keynes notes that an individual’s liquidity preference is driven by three factors:
Transactions motive – the need to have a certain amount of cash on hand for personal and business transactions
Precautionary motive – the need for security of knowing your future cash amount
Speculative motive – It may be that the individual who wished to retain cash in a more liquid position believes that the rate of interest in the future may be higher than the existing on in the market
Different economic conditions drive these three factors. A relationship between the last two factors and the existence of an organized market can be seen. In the absence of an organized market, the precautionary motive would be more prevalent whereas the existence of one drives the speculative motive. A decrease in interest rates would cause an increase in national income and a proportional increase in the amount of money convenient to have on hand and so raise the transaction motive factor.
The Liquidity Preference Curve below shows the relationship between interest rate and liquidity preference
An individual’s liquidity preference can be seen as a propensity to hoard (in this case taken as the actual holding of cash) if the decision to hoard were reached with regard to the advantages available for parting with the liquidity. A “balancing of advantages”.
Keyne’s contests the notion that the rate of interest is a return for saving, as an individual hoarding cash will earn no interest. The rate of interest is instead a reward for parting with liquidity. The interest rate of the market can therefore be viewed as a measure for the liquidity preference of society.
M = L(r)
PC ModelThe Keynesian notion of household’s making a two step decision, the first being how much of their income they will save and the second being how they allocate this saved income, is incorporated into the same time frame within the PC model. Consumption decision determines size of saved income and portfolio decision determines allocation.
The PC model introduces the concept that the difference between disposable income and consumption is equal to the change in wealth and not just money as was the case in the SIM model.
V = V-1 +(YD-C)
The consumption function is also expressed in terms of total wealth instead of money
C = α1.YD +α2*V-1
Making money balances a proportion of total wealth incorporates Keyne’s notion of liquidity preference. The lower the liquidity preference, the lower the money to wealth ratio.
Hh/V = (1-λ0) – λ1*r+λ2.(YD/V)
The λ variables are proportions of wealth. 1-λ0 is the proportion of wealth held in the form of money and it is affected by changes in the rate of return on treasury bills and the level of disposable income relative to wealth. It is negatively affected by interest rate increase and positively affected by increase in disposable income.
A similar equation used by the model is shown below.
Hh = V – Bh where Bh = V*((λ0) + λ1*r-λ2.(YD/V))
It states that the money holdings are the difference between the total household wealth (V) and the demand for bills by the household (Bh).
In both models, the interest rate is the equilibrium in the desire to hold cash and the availability in cash.The quantity of money held depends on the rate of interest that can be obtained on other assets.
ReferencesThe General Theory, KeynesMonetary Economics, Godley and Lavoie
