Homework 4

Question 1

Summary of Godley and Lavoie, chapter 4, pages 99-107, while answering the following questions:

1. Why is the interest rate on bills, B, fixed such that r = ȓ? What would it mean for the model if r could vary?
2. How does the household make its decisions with regard to cash balances?
3. How is PC different from SIM?

Chapter 4 introduces the stock approach to the circular flow of money approach from the model SIM to create the model PC. In the stock approach households have to decide how much of their stock of wealth is held in money and in other assets. This is dependent on the rate of interest that can be earned on the other assets. The households therefore have to make a portfolio choice, hence the model PC.

The model PC is different to model SIM as it separates the central bank from the government and introduces interest payments and government bills into the transactions-flow matrix. The price of the bills remains constant as it the interest rates do not change from t_-1 to t. The model PC assumes the principal and interest of the bills is paid at maturity (This is not like the real world where government bills often have periodic coupon payments during the life of the bill). The payoff from holding the bills at t is dependent on the interest rate at t_-1.

The disposable income and tax equations change from the model SIM versions to account for the interest received from holding bills as part of the households’ wealth.

• · YD = Y – T + r_-1 . B_h-1 (4.2)

• · T = Θ . (Y + r_-1 . B_h-1) (4.3)

The interest received from the bills is added to the households’ disposable income (4.2) and the government taxes the interest received as it is added to the income of the household. (4.3)

The households have to make a portfolio choice decision. Firstly, they must decide how much income to consume and save. From SIM, the households’ propensity to consume could be used to measure this. Then they must decide to allocate their savings to bills or cash holdings.

• · V = V_-1 + (YD – C) (4.4)

• · C = α₁ . YD + α₂ . V_-1 0 < α₂ < α₁ < style=""> (4.5)

In the model PC the wealth of households is a function of their wealth in the previous period plus disposable income (minus consumption). (4.4) SIM, wealth of households was just their stock of money. This can also true for the consumption function. (4.5)

Households hold a proportion of their wealth in money (1 – λ₀) and a proportion of their wealth in bills (λ₀). These sum to unity, therefore the amount of bills purchased by the household, will define the exact amount of wealth the household will retain in the form of money.

• · H_h/V = (1 – λ₀) – λ₁ . r + λ₂ . (YD/V) (4.6A)
• · B_h/V = λ₀ + λ₁ . r - λ₂ . (YD/V) (4.7)

Disposable income is positively related to money and negatively related to bills. Interest rates are positively related to bills and negatively related to money as interest is not paid on money held at the central bank.

Equation 4.6A is dropped for equation 4.6 which defines the money held by the household as the wealth not spent on bills. This means the households’ treat money as a residual.

• · H_h = V - B_h (4.6)
• · ∆B_s = B_s – B_s-1 = (G + r_-1 . B_s-1) – (T + r_-1 . B_cb-1) (4.8)
• · ∆H_s = H_s – H_s-1 = ∆B_cb (4.9)
• · B_cb = B_s - B_h (4.10)
• · r = ȓ (4.11)

Equation 4.8 describes the government budget constraint.

Equation 4.9 describes the capital account of the central bank.

Equations 4.10 and 4.11 explain how the demand for bills by the central bank is determined. The central bank purchases the government bills not bought by the households at the given interest rate. The interest rate must be fixed to stop the bills changing value during time periods to prevent capital gains which are not accounted for in the model PC. If the interest rate varies over time, it would no longer be treated as an exogenous variable. The demand for bills by the central bank would be treated as exogenous instead.

Question 2

1. How does Keynes define liquidity preference?

“... [liquidity preference] is given by a schedule of the amounts of his resources, valued in terms of money or of wage units, which he will wish to retain in the form of money in different sets of circumstances”

In this case when with regard to liquidity preference, Keynes is trying to determine whether or not the individual will retain money for future consumption by holding that money in cash and risk-free form or is the individual willing to give up that current liquidity and invest in illiquid assets in order to earn a given interest rate r. The interest rate r is the compensation received by the investor for parting with that immediate liquidity and holding less of his/her stock of wealth in cash form.

Keynes' stated that the public holds money for three distinct purposes:

1. Transaction motive: people have a need for cash for current transactions. This may be for personal or business transactions.
2. Precautionary motive: this is the desire for security and the holding of cash for extraordinary situations e.g. Sickness.
3. Speculative motive: this is the opportunity to take advantage of a profit making opportunity.

2. Is PC a faithful representation of Keynes’ original vision of household decision-making? If so, why? If not, why not?

It would seem that the PC model is a faithful representation of Keynes’ original vision of household decision making. This is true for a number of reasons:

• · The PC model encompasses the 3 divisions of liquidity preference that Keynes discusses, namely; the transactions motive, the precautionary motive and the speculative motive.

• · Further to this, the PC decision has two steps:

1. Households make a decision regarding their propensity to consume, i.e. they decide what proportion of their disposable income they will consume.

2. The remainder of the disposable income that is not spent is allocated to savings. Therefore a decision is made whether or not to keep these savings in cash form or alternative assets. Keynes’ also discusses the allocation of savings (see Question 2.1).

• · The PC model distinguishes between disposable income and consumption. This idea is also inherent in Keynes’ writings.

• · In both models, the rate of interest is the equilibrium in the desire to hold wealth in cash form and the availability of cash.

• · Also in both models, the quantity of money held depends on the rate of interest that can be obtained on other assets.

Furthermore, the PC model assumes that the money supply is endogenous and demand-led with the interest rate r being exogenous