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, P e. Wage demands will be lower the higher is the rate of unemployment, u.

Wage setting continued Wage-setting relation is then W = P e 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 Oru = 1 – Y/ L Our wage-setting relation becomes: W = P e F(1 – Y/L, z)

Bringing it all together We have two equations W = P e 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 (P e, L, z, μ). Although you should immediately see that there should be a relationship between P and P e, but we will deal with this later.

Natural rate of unemployment If our expectations about prices are correct, then P e = 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”, u n (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 IS- LM 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 P e F(u, z) = P / (1 + μ ) Unemployment is related to how prices behave relative to expected prices.