The labour market
• In this lecture, we will introduce the labour
market into our IS-LM framework.
• The variables we will want to talk about
are wages, prices, and unemployment.
Real wage
• Workers and firms are assumed to only
care about real wages or the buying power
of wages.
– The nominal wage (wage in cash) is W.
– The average price level is P.
Real wage = W / P
– Intuition: Workers care only about what wages
can buy. Firms care only about wages
relative to price of their output good.
Wage setting
• Wages are typically set in a contract in
advance of work done. Typical labour
contracts or awards may last 1-5 years.
• Wages are set in advance based on an
estimate of what prices will be in the
future, or “expectation” of prices, Pe.
• Wage demands will be lower the higher is
the rate of unemployment, u.
Wage setting continued
• Wage-setting relation is then
W = Pe F(u, z)
– Where z is the set of all other variables that
can influence wage demands, such as
unemployment compensation, labour market
reforms, etc.
– There is a negative correlation between W
and u, so higher u leads to lower W.
– The correlation between z and W depends on
the variable in z.
Price determination
• We assume that firms set prices based on a
mark-up of labour costs.
• If 1 worker produces A goods at a cost of W for
the worker, the cost to the firm per good is W / A.
The firm marks-up the price of the good to
P = (1 + μ ) W / A
• Then we can “normalize” our definition of a good
so that A = 1. We have
W / P = 1 / (1 + μ )
Normalizing
• Our “normalized” production function is (as each
worker produces 1 good):
Y=N
• Total labour supply is assumed constant at L.
• Unemployment is then
u = (L – N) / L = 1 – N / L
Or u = 1 – Y/ L
• Our wage-setting relation becomes:
W = Pe F(1 – Y/L, z)
Bringing it all together
• We have two equations
W = Pe F(1 - Y/L, z)
W = P / (1 + μ )
• These are our labour market equations.
• We have introduced into our system two new
endogenous variables (W, P) and four new
exogenous variables (Pe, L, z, μ).
• Although you should immediately see that there
should be a relationship between P and Pe, but
we will deal with this later.
Natural rate of unemployment
• If our expectations about prices are
correct, then Pe = P.
• Setting the two equations equal and
dropping W, we have
P F(u, z) = P / (1 + μ )
• Dropping P, we have a relationship
between u and features of the labour
market, z, and the mark-up behaviour of
firms, μ.
Natural rate continued
F(u, z) = 1 / (1 + μ )
• This can be solved for the equilibrium or “natural
rate of unemployment”, un (which is not zero).
• The natural rate of unemployment then is the
unemployment rate when prices are equal to
expected prices- or inflation is fully anticipated.
• The natural rate of unemployment depends on:
– Features of the labour market, z, such as
unemployment compensation
– Mark-up behaviour of firms, μ.
Where is this going?
• We can bring these equations into our ISLM framework.
• Once added, we can talk about (W/P, u) as
well as (Y, i) in our explanations.
• Expectations now become important, as
eliminating W, we have
Pe F(u, z) = P / (1 + μ )
• Unemployment is related to how prices
behave relative to expected prices.