Homework 5

Homework 5
Modify the PC model to allow for a simulation of a stagflation type episode in the economy

Y = G + C
Government expenditure should be held constant. It has been demonstrated that efforts of fiscal policy, i.e. increasing taxes and/or reducing expenditure only exacerbates inflationary problems. Substitute G for G*
Because of increased inflation, an individuals’ purchasing power will be reduced meaning that while his/her income has not changed he/she will not be able to purchase the same amount as previous time periods. As a result their consumption patterns and expenditure decisions will become more disciplined and will depend on the prices of goods i.e. the inflation rate π. Substitute C for C(π)
Adjusted equation: Y = G* + C(π) (1)

YD = Y – T + r-1.Bh-1

An individuals’ disposable income will remain dependent on their income adjusted for taxes and on the interest received from government debts that they hold. However, this amount should be subjected to a MPS parameter, i.e. (1-MPC) or (1- α1) because during times of recession, people are uncertain about the future and therefore, should consider saving portions of their present income.
It is important to note that while their income will not change during periods of stagflation, the yield that they receive on their investments will be below their expectations since it is usual for interest rates to fall during recessions.
Adjusted equation: YD = (1 - α1).(Y – T + r-1.Bh-1) (2)

T = θ.(Y + r-1.Bh-1)
Taxable income will remain as before – tax will be paid on income and interest received from government bills. As mentioned before, efforts of fiscal policy do not work during a recession and therefore, tax rates should remain constant. Replace θ with θ*.
Adjusted equation: T = θ*.(Y + r-1.Bh-1) (3)

V = V-1 + [YD – C(π)] (4)

An individuals’ stock of wealth will stay as per the PC model, with consumption adjusted for inflation rates.

C = α1.YD + α2.V-1
An individuals’ behavioural decisions to consume should be modified to consider savings as per the equation for disposable income.
Adjusted equation: C = (1- α1).(α1.YD + α2.V-1) (5)

Hh = (1 – λ0) – λ1.r + λ2.(YD)
V (V)
Bh = λ0 + λ1.r - λ2.(YD)
V (V)
The portfolio allocation decision of households depends on the level of interest on bills and the level of disposable income relative to wealth. During a recessionary period, interest rates are inclined to decline (see below that interest rates are not fixed). While yields will be lower than usual, individuals should realise that bonds are a good bet for investors seeking safety, flexibility and inflation protection. In an uncertain environment investors need to make careful investment decisions. Therefore, the extent to which individuals should allocate their wealth between bills and cash should take investors’ tolerance for risk into account. The inclusion of a risk tolerance parameter, R, is seen in the adjusted equations:

Hh = R.(1 – λ0) – λ1.r + λ2.(YD) (6)
V (V)
And, Bh = R.λ0 + λ1.r - λ2.(YD) (7)
V (V)

The money held by the household still equals to the wealth of the household minus the money held in bills.
Hh = V – Bh (8)

Balancing equations are also as per PC model:
ΔBs = Bs – Bs-1 = (G + r-1.Bs-1) – (T + r-1.Bcb-1) (9)
ΔHs = Hs – Hs-1 = ΔBcb (10)
Bcb = Bs – Bh (11)

r = r*
In this model, interest rates should not be held constant. As demonstrated by Paul Volcker, Federal Reserve chairman during the 1970s period of stagflation, increased interest rates will reduce money supply and incur “disinflationary” measures. In addition, theory goes that higher interest rates should depress growth in demand which should lead to lower prices. Adjust r* for rnf, indicating non fixed interest rates.
Adjusted equation: r = rnf (12)