Expectation Formation and Endogenous Fluctuations in Aggregate Demand

2.2 Goods

There are two classes of final goods in this economy and a class of intermediate
goods. There is a single final consumption good. There are a continuum of
measure one of intermediate goods, which are used as inputs in the production
process of the final consumption good. In addition, there is physical capital,
which plays both the role of an investment good, used as a form of saving, and
of a productive input.

2.3 Production

The final consumption good is produced from intermediate goods via the fol-
lowing CES production function

^ct = 9o ^cγ,tdi^ 1 ’                               ⁽²⁾

where Cj_jt denotes the input of the intermediate good i. The market for the
consumption good is perfectly competitive.

The intermediate goods are produced using a Cobb-Douglas technology

Cj,t = kξ_t Ij-^α,                                   (3)

where kj_jt denotes the amount of capital and lj_jt denotes the amount of labor
used in the process of production of good i. The markets for the intermediate
goods are monopolistic. The demand for good i takes the form

Pt = Dl^- p c⅛¹,                      (4)

where D_t denotes the level of demand for the final consumption good and p^j_t
and p_t denote the price of the intermediate good i and the consumption good,
respectively.

Physical capital is produced using a linear technology

Qk = ι_t*,                                    (5)

out of labor, where denotes the amount of labor used in the production of
physical capital. In addition, it is assumed that the market for physical capital
is perfectly competitive.¹

The input output matrix is presented in figure (1.)

2.4 Income

There are several sources of income in this economy. First of all, factors of
production receive rental fees. Secondly, imperfect competition in the inter-
mediate goods sectors allows profits to arise in equilibrium. It assumed that

¹ The fact that labor is the only input in the production of physical capital allows for a
complete analytic tractability of the model. However, the results do not depend on this specific
assumption.

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