Expectation Formation and Endogenous Fluctuations in Aggregate Demand

The Evolution of GDP under Perfect Foresight

0            10           20           30           40

50            60           70           80            90           100

time

Figure 2: The Evolution of Ouptuput under Perfect Foresight.

Furthermore, equation (17) indicates that x_t = 2ψk_t, where ψ = ∙-^γ. Iteration
by one period implies that x_t+∙ = 2ψk_t+∙. Thus, the level of investment at time

t is given by

^kt+1   2(1 + ψ ∙

Therefore,Vt∙ι , t2 : k_tl = k_t2 ∙ Naturally, under the assumption of perfect fore-
sight the level of investment and the level of physical capital are constant
and independent of time. Moreover, recall that in equilibrium the marginal
propensity to save equals to the level of investment equation (10.) Therefore, it
turns out that in equilibrium the average propensity to save is a constant, i.e.,
Vt1,t2 : β_tl = β_t2 ∙ Consequently aggregate output, as given by formula (21), is
constant. Figure (2) presents sample dynamics of output.

Clearly, the assumption of perfect foresight leads to a stable equilibrium in
which all variables are constant and, in particular, in which aggregate output
does not fluctuate. Therefore, should there any oscillations occur if the assump-
tion of perfect foresight is relaxed the oscillations will not be due to the fact
that the Diamond OLG model is used as the benchmark.

The assumption of perfect foresight leads to an uninteresting equilibrium
dynamics. The situation is different if one allows for alternative expectation
formation technologies. Recall that x_t+∙ determines the amount saved by young
agents at time t. Therefore, economic agents must form expectations with the
regard to x_{t +} 1. In particular, if agents decide to expect x≡₊₁ at time t then the
level of investment and, hence, the marginal propensity to save take the form

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