Monetary Policy, Inflation, and the Business Cycle Chapter 2 A ...

While the previous framework does not explicitly introduce a motive for
holding money balances, in some cases it will be convenient to postulate a
demand for real balances with a log-linear form given by (up to an additive
constant):
m t p t = y t i t (10)
where 0 denotes the interest semi-elasticity of money demand.
A money demand equation similar to (10) can be derived under a variety
of assumptions. For instance, in section 5 below we derive it as an optimality
condition for the household when money balances yield utility.
2 Firms
We assume a representative …rm whose technology is described by a production
function given by
Y t = A t Nt 1
(11)
where A t represents the level of technology. We assume a t log A t evolves
exogenously according to some stochastic process.
Each period the …rm maximizes pro…ts
P t Y t W t N t (12)
subject to (11), and taking the price and wage as given.
Maximization of (12) subject to (11) yields the optimality condition
W t
P t
= (1 ) A t N
t (13)
i.e. the …rm hires labor up to the point where its marginal product equals
W
the real wage. Equivalently, the marginal cost,
t
, must be equated
(1 )A t Nt
to the price, P t .
In log-linear terms, we have
w t p t = a t n t + log(1 ) (14)
which can be interpreted as labor demand schedule, mapping the real wage
into the quantity of labor demanded, given the level of technology.
5