EC6012 – Monday Week 5 – Chapter 3 "The Simplest Model with Government Money" Summary

Firstly, we define two methods of money creation: “Outside” (i.e. Government) and “Inside” (i.e. Private) money. The former is created when a government makes payments and the opposite is when the said government receives taxes. The latter is created by banks via loans and its’ opposite is the repayment of said loans. We initially postulate a simple model, SIM, and build from there. SIM assumes:
1. A closed economy.
2. All transactions occur in government money, i.e. no private banks.
3. Demand-led, i.e. unlimited labour force.

SIM has 6 items, e.g. Money (H) which is a source for households, therefore, positive and negative for government (as it’s debt, therefore a use). From this, for Households, Production and Government we build a behavioural matrix describing inter-transactional relations (except Output, which only appears once) between these sectors such that all columns and rows in this matrix sum to zero. It’s entities are:

1. Households 2. Production 3. Govt
1. Consumption -Cd +Cs
2. Govt. Expenditure +Gs -Gd
3. Output [Y]
4. Wages +W.Ns -W.Nd
5. Taxes -Ts +Td
6. Change in money stock -Hh +Hh

(Where s, d, h, w and N equate to supply, demand, household, cash, wages and employment respectively)

From this we start to build our equations:
3.1. Cs = Cd
3.2. Gs = Gd
3.3. Ts = Td
3.4. Ns = Nd
…where state demand equals supply.

How can we ensure equality between sales and purchases, given production might differ from supply, and supply from demand?
We employ the Keynesian/Kaleckian quantity adjustment mechanism. By this, producers produce exactly what is demanded, i.e. no inventories. Also firms sell whatever is demanded, i.e. no rationing.
We add to SIM by defining Disposable income (i.e. household wages minus tax) as:

3.5. YD = W*Ns - Ts

Further we define Tax rate on taxable income (q) as:

3.6. Td = q*W*Ns and Consumption (being dependent on YD and past wealth accumulated H-1) as:

3.7. Cd = a*YD+a2*Hh-1

Government spending, not covered by taxes is met via issuing of debt (i.e. cash money), so

3.8. Hs = DHs - Hs-1 = Gd - Td

Household wealth is the excess of income over expenditure. We say Hh represents household cash, so:

3.9. DHh = Hh - Hh -1 = YD – Cd

Finally, we define national income identity thusly:

3.10. Y = Cs + Gs

…from income perspective is:

3.10. Nd = Y/W

…this completes SIM. Wages are assumed fully exogenous.

The Walrasian principle dictates the removal of one redundant equation to avoid over-determination. Said equation is:

3.12. DHh = DHs

…because savings must equal investment.

Previous equations yield Y* (equilibrium) as:

3.13. Y* = G/ 1 - a1*(1 - q)

..but this is only short-run/temporary equilibrium, i.e. not steady-state. We use 3.7. to solve for long-term. It says that consumers spend current income PLUS savings, hence income level rises despite fixed government expenditure.

We define steady-state as state whereby stock and flows (i.e. key variables) remain in constant relationship to each other. If variable levels are constant, as per SIM, the steady-state is stationary i.e. no government surplus or deficit. Hence:

3.14. Y* = G/q

…G/q is called fiscal stance. Stationary dictates consumption must equal disposable income. Previous equations yield:

3.15. YD* = C* = G*(1 - q)/ q

Finally we define stationary value of household wealth as:

3.16. H* = [(1 - a1)/a2] * YD* = a3*YD* = a3*G*[(1 - q) /q] where a3= (1 - a1)/ a2

The a3 coefficient is the stock-flow norm of households. Combined with Modigliani’s consumption function, it means when households earn more than expected, more is saved. This assumes consumption depends on lagged wealth besides current disposable income.

Uncertainty is brought into SIM by making consumption depend on expected (e), not actual, income. Ergo, households can only guess expected disposable income: Hd. So

3.17. DHd = Hd - Hh-1 = YDe - Cd

Since end of period money stock must differ from that initially demanded we say:

3.18. Hh - Hd = YD - Yde

Thus money acts as a buffer in that it allows people to transact without knowing exactly what their income and expenditure levels will be.

SIM is now more recursive in that expected, not realized, income is used. If we assume expected income equals that realized previously:

3.19. Yde = YD - 1

..which builds SIMEX. People here amend consumption based on wealth and future income changes.

We solve Y for intermediate situations thusly:

3.20. Y = (G + a2)*(H-1)/(1 - a1)*(1 - q)

…so proving Keynes claim that money links each period with the next. The intermediate stock of money is:

3.21. Hh = (1 - a1)*(1 - q)*Y + (1 - a2)*H-1

…the last two intermediate equations are out-of-equilibrium, but temporary since they’re the values that would be achieved in each period.