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CHAPTER 2. WAGE-PRICE DYNAMICS
wage level of the s-sector needs to follow the same trend as e-sector wages. Third,
the development of the domestic price level will also be influenced by trend growth
in international prices and productivity trend. In this section we spell out the details
of the first proposition in detail. The two other hypothesis are briefly dealt with at
the end of the section.
We first need to establish some notation: Let Ye denote output (measured as
value added) in the tradeable or exposed sector, and let Qe represent the corresponding price (index). Moreover, let Le denote labour input (total number of
hours worked), and use We to represent the hourly wage. The wage share of value
added output is then
We
Ye
We Le
=
, where average labour productivity is given as Ae =
.
Qe Ye
Qe Ae
Le
Conversely, the rate of profit is
We
Qe Ye − We Le
=1−
.
Qe Ye
Qe Ae
It is reasonable to assume that in order to attract the investments needed to maintain
competitiveness and employment in the e-sector, a certain normal rate of profit has
to be met, at least in the long term. Since there is a one-to-one link between the
profit rate and the wage share, there is also a certain maintainable level of wageshare. Denote this long run wage-share Me , and assume that both the product price
and productivity are exogenous variables. We can then formulate what we might
call the main-course proposition:
We∗ = Me Qe Ae ,
(2.1)
where We∗ denotes the long-run equilibrium wage level consistent with the twin
assumptions of exogenous price and productivity trends and a constant normal wage
share. Using lower case letters to denote natural logarithms of a variable, i.e.,
for example we = log(We ) for the wage rate, we obtain the following, equivalent
formulation, which we will use in the following:
H1mc :
we∗ = qe + ae + me ,
(2.2)
The marker H1mc is used to indicates that this is the first hypothesis of the theory.
To make the theory operational, so that it can be applied to data, we identify the
long run equilibrium wage level, We∗ or (in log) we∗ , with the steady state wage level.
Equation (2.2) therefore captures conveniently that the long run elasticities of the
wage level with respect to productivity and price are both unity.
Equation (2.2) has a very important implication for actual data of wages, prices
and productivity in the e−sector: Since both qe and ae show trend-like growth
over time, actual time series data for the nominal wage, we,t , should also show clear
positive growth, and with limited fluctuation around trend defined by price and