Expectation Formation and Endogenous Fluctuations in Aggregate Demand

again affects the profitability, and so on. This process continues and results in
an equilibrium change in the aggregate output.²

3.3 Intertemporal Allocation

The ultimate goal of this paper is to show that macroeconomic cycles can con-
stitute an equilibrium outcome. It is widely known, Grandmont [20], that the
Diamond OLG model, used as the benchmark in this paper, itself is capable of
generating endogenous cycles. Therefore, it is imperative to show that the exis-
tence of cycles in the model presented in the paper is due to expectation selection
rather than being due to the fact that the Diamond OLG model is a key build-
ing block of the model. Accordingly, the paper assumes first perfect foresight
and shows that the economy does not exhibit endogenous fluctuations and then
assumes that information gathering and processing are costly and solves for the
equilibrium allowing agents to select amongst different expectation formation
technologies.

Let x_t+1 denote the present value of future profit income, i.e., let

The equilibrium outcomes in period t not only depend on the values of macro-
economic variables in period t, but also depend on values of variables in period
t + 1. In particular, the amount saved at time t, as equation (9) indicates, de-
pends on x_t+ι. Therefore, the value of capital stock in period t + 1, which is
itself determined in period t, depends on the way economic agents form expec-
tations at time t regarding the value of x_t+ι. Thus, agents’ expectations at time
t regarding period t + 1 influence economic activity in period t.

Let Ω_t be the information set of a young agent born at time. Her problem
given the information set Ω_t is to maximize

U (cι_ιt,C2_ιt+ι) = log(c∙ι,t) + ^t(log(c2,t+ι) ∣Ωt)

subject to her budget constraints. Under the assumption of perfect foresight
the information set Ω_t contains the values of all current and future variables, in
particular, the information set at time t contains the value of x_t+ι, i.e.,

^χt+ι ∈ Ω_t.

Therefore, young agents at time t are fully aware of the precise value of x_t+ι
and accordingly the amount that they save is equal to, see equation (9),

⅛t₊ι = 2 ^{(1 - x}t+i⁾ ■                            ⁽²²⁾

²The fact that the production functions in the final consumption good sector and the
investment good sector differ additionally contributes this result.

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