Question

a. We know that households (wage setters) set the wages as follows: W=Pe F(u, z). Firms (price setters), though, set the prices as P=W(1+m). Assume that F(u, z)=1+z-αut. Develop the inflation – unemployment relationship as done in class (it is known as Expectations Augmented Philips Curve, EAPC) b. Do what you need to do to the equation you developed on part a) to get to be a function of un. (Clue: what happens to inflation when economy is at natural rate of unemployment? Assume π e t = πt-1) c. Let’s country’s current u is 2.5%, and economics estimated the country’s un=3%. Given this information, what do you think should happen to the country’s inflation rate? Discuss what is going to happen to labor market, consider using the wage setters and price setters equations. Think about bargaining power. d. Consider the equation you developed in part b. Assume 45% of workers have wage indexation on their labor contract. What is the new EAPC equation? Finally, draw two Phillips curve you have developed in this question – one with indexed wade and another without. Discuss the slopes of the two curves.

Answer 1

a. Given that,

We know that, the Aggregate Supply (AS) relationship is given by the following expression

Substituting the value of F (u,z) in the above expression

Introducing subscript t for time period

Divide the above expression with Pt-1

Now, as inflation is defined as the quantitative rate at which the prices increase over time,

                  ⇒

                  ⇒

Substituting the values, we get

By using approximations, we get

⇒

The above expression gives the inflation – unemployment relationship known as Phillips Curve.

In order to arrive at the Expectations-augmented Phillips curve, it is assumed that

⇒

Where is the parameter which measured the effect of last year’s inflation on expected inflation.

Considering , we get

Thus, the above derived expression can now be written as

This expression is known as the Expectations Augmented Phillips Curve, which gives the relationship between change in inflation rate and inflation.

b. In previous part, we derived the following expression :

Natural Rate of Unemployment, u_n is defined as that rate at which the inflation rate is not changing and price is not accelerating.

⇒

Hence, u_n can be derived as follows

Using value of derived above in the following equation of modified Phillip’s curve,

Given that

This equation shows the relation of Phillip’s curve with the natural rate of unemployment. It gives the relation between inflation rate, unemployment rate and the natural rate of unemployment.

c. The equation derived above gives the relation between inflation rate, unemployment rate and the natural rate of unemployment.

Any deviation of the unemployment rate away from natural rate of unemployment causes a deviation in the inflation rate from expected rate of inflation.

From equation we can see that –

• If , then
• If , then
• If , then

Given in that current u = 2.5% and u_n= 3%, we have the case where u . Hence, the current inflation π will be greater than the inflation in the previous period, i.e., the country’s inflation rate increases.

Wage setting equation is:

Wages are inversely related to the unemployment rate in the economy.

The unemployment rate has decreased from the natural rate of unemployment, i.e., 3% to 2.5%.

This implies that the workers now have a higher collective bargaining power with the firms. So, the wages are bid up.

Price setting equation is:

Price does not depend on the unemployment rate and hence, remain unchanged.

Hence, the real wages increase in the labour market.