Question

Define the natural rate of unemployment in terms of wage-setting and price-setting relations. Write the equation that expresses the natural rate of unemployment in terms of these relations.  Using an appropriate diagram, explain the effect of a decrease in unemployment benefits on the natural rate of unemployment.

Answer 1

before defining the natural rate of unemployment, we will define what the wage setting and price setting relations are and then deduce the definition of natural rate of unemployment from there,

In the market space, we have the firms and the laborers, the firms decide the price of the product according to the following

PRICE SETTING RELATION :- the firms decide the price by using a markup value say "c"

P_s = (1+c)W where, W = nominal wage rate in the market

If the firms operate in competitive market , then the value of c = 0 and we have our prices = nominal wage rate (W )

But, if we assume our firms have some market power, like a monopoly then c > 0 because the firm can now earn some proft.

P_s = (1+c)W => P/W = (1+c)

W/P = 1/ (1+c) -------------------------------- Price setting relation (1)

WAGE SETTING RELATION :- in the wage setting relation we have

W = Pf(u,z) ------------------------------------------------ (2)

which says that nominal wages are dependent on 3 factors, prices, unemployment (u) and a variable (z) to capture the factors that affect wage setting ( for example unemployment insurance)

Now, you must understand that the relationship of u with W will be negative because as unemployment rises, the bargaining power of the laborers fall and the nominal wage rate falls and vice versa. similarly z has a positive impact on the wage rate, as the level of unemployment insurance increases, the nominal wage rate also increases.

Now the natural rate of unemployment is that rate of unemployment which makes our wage setting and price setting relations equal to each other. It is that level of unemployment where (1) = (2), You will have a better understanding with the diagram I'm attaching below. Please note that the price setting relation is drawn as a horizontal line because it is independent of the rate of unemployment ( W/P = 1/1+c) and the wage setting relation is drawn as downward sloping because as we have already established, with an increase in the rate on unemployment, the wage rate falls, so there is a negative relationship between the two.

As, you can see, the intersection of the two curves is at the unemployment level u_n which is the natural rate of unemployment.

b) a decrease in unemployment benefits, is captured by the variable z, and as we established it has a direct relationship with the wage rate, so a decrease in the unemployment benefits lead to a lower real wage, W/P therefore, our wage setting curve will shift leftwards leading to a fall in the natural rate of unemployment. from u_n to u_n"

Hope this helps. Please feel free to ask any doubts or give feedback in the comments section. PLEASE DON'T FORGET TO UPVOTE !