EC6012 GROUP 5 BLOG: April 2007

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.

EC6012 GROUP 5 BLOG

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