Expectation Formation and Endogenous Fluctuations in Aggregate Demand

the form of physical capital. Therefore, the level of investment, newly installed
capital, at time t is given by

kt+1 = β_t.                                     (10)

Moreover, the form of the production function implies that the level employment
in the investment good sector by l_t is given by lt = β_t. The market clearing
condition implies that the level of employment in the intermediate good sectors
is given by

l≡^t = 1 - βt.                                 (11)

The market for the final consumption good is perfectly competitive. The
production function is of a standard CES form. Therefore, the price of a unit
of the final consumption good is equal to the marginal costs and is given by

Pt =

(12)

where pt denotes the price of intermediate good i. Markets for intermediate
goods are monopolistic. The demand for a given good is given by equation 4.
The price of intermediate good i, note assumption of a CES production function,
is equal to a markup over marginal costs

---i— r^aw^1-a.

γα^a (1 - α)^1-α

Monopolistic competition in the intermediate goods sectors together with
the assumption of the CES production function allow to establish that the level
of profits generated in the economy is given by

∏t = (1 - γ) Dt,

and the total wage bill in the intermediate goods sectors assumes the form

"W∕l^tl1 = (1 — α)γDt,

and the factor payment to physical capital can be expressed ad

rtkⁱj^nt = αγDt.

Note that in equilibrium the level of physical capital engagement in the interme-
diate goods sector k^l_t^nt is equal to the supply of capital k_t, recall that only labor
is used in the process of production of the investment good (physical capital),
whereas the level of employment in the intermediate goods sectors lf^nt is given
by equation (11). Furthermore, it is straightforward to establish that

∏t _ 1 - γ
rt     αγ

r_t       α   lf^nt

w_t   1 - α k_t

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