Working Paper No 879



practice to start the analysis with a macro model and then introduce sectors. The results of the

macro analysis are obviously modified when the sectoral analysis is taken into account. However,

the complications that arise at the lower levels of abstraction do not make the abstract model any

more or less useful.

This point is also important for the discussion below and a more-detailed example is in order here.

Think of the simple Keynesian multiplier model:


Y = C + I + G + X − M


C = ¯C + c ·Y d


I = Ī

Government Expenditure: G = Ḡ − g ·Y


X = ¯X

Imports: M = ¯M − m ·Y

Disposable Income: Y d = Y − T


T = t ∗Y

The equilibrium level of income is Y ∗ = µ · [ ¯C + Ī + Ḡ + ¯X − ¯M], where the multiplier is

µ = 1/[1 − c(1 −t) + g + m]. Based on this very simple model at this very high level of

abstraction one can talk about several interesting things, like the fiscal expenditure multiplier

(∂Y ∗ /∂Ḡ), the effects of austerity, etc.

However, one could argue that there are many different kinds of government expenditure that can

have a differential impact on the several components of demand. For example, public investment

in R&D can arguably have a secondary positive spillover effect on investment that government

consumption does not have. On the other hand, some other kinds of government expenditure

might even have a negative impact through distortion of incentives, increasing bureaucracy, etc. At

this lower level of abstraction, let’s assume that we decompose overall autonomous government

expenditure into n kinds, so that Ḡ = G(ḡ 1 ,ḡ 2 ...ḡ n ). These different kinds of government


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