91Ó°ÊÓ

Productivity growth, the Phillips curve, and the natural rate. (Braun, 1984 ; Ball and Moffitt, 2001 .) Let \(g_{t}\) be growth of output per worker in period \(t, \pi_{t}\) inflation, and \(\pi_{t}^{W}\) wage inflation. Suppose that initially \(g\) is constant and equal to \(g^{L}\) and that unemployment is at the level that causes inflation to be constant. \(g\) then rises permanently to \(g^{H}>g^{L}\). Describe the path of \(u_{r}\) that would keep price inflation constant for each of the following assumptions about the behavior of price and wage inflation. Assume \(\phi>0\) in all cases. (a) (The price-price Phillips curve.) \(\pi_{t}=\pi_{t-1}-\phi\left(u_{t}-\vec{u}\right), \pi_{t}^{w}=\pi_{t}+g_{t}\) (b) (The wage-wage Phillips curve.) \(\pi_{t}^{w}=\pi_{t-1}^{w}-\phi\left(u_{t}-\bar{u}\right), \pi_{t}=\pi_{t}^{w}-g_{t}\) (c) (The pure wage-price Phillips curve.) \(\pi_{t}^{w}=\pi_{t-1}-\phi\left(u_{t}-\bar{u}\right), \pi_{t}=\pi_{t}^{w}-g_{t}\) (d) (The wage-price Phillips curve with an adjustment for normal productivity growth.) \(\pi_{t}^{w}=\pi_{t-1}+\hat{g}_{t}-\phi\left(u_{t}-\vec{u}\right), \hat{g}_{t}=\rho \hat{g}_{t-1}+(1-\rho) g_{t}, \pi_{t}=\pi_{t}^{w}-g_{t} .\) Assume that \(0<\rho<1\) and that initially \(\hat{g}=g^{L}\)

Step by step solution

01

Understand the Initial Setup

We have initially constant growth of output per worker, \( g = g^{L} \), and unemployment, \( u \), is at a level where inflation is constant. We need to determine how \( u_{r} \) changes to maintain price inflation constant when \( g \) increases permanently to \( g^{H} > g^{L} \). The value \( \phi > 0 \) is a parameter indicating the responsiveness of inflation to unemployment.

02

Case (a): Analyzing the Price-Price Phillips Curve

The equation for price-price Phillips curve is given by \( \pi_{t} = \pi_{t-1} - \phi(u_{t} - \vec{u}) \) and \( \pi_{t}^{w} = \pi_{t} + g_{t} \). To keep \( \pi_{t} \) constant, \( u_{t} \) must stay equal to \( \vec{u} \), as any deviation will alter \( \pi_{t} \). Thus, \( u_{r} \) remains constant against the rise in \( g \).

03

Case (b): Analyzing the Wage-Wage Phillips Curve

Here, \( \pi_{t}^{w} = \pi_{t-1}^{w} - \phi(u_{t} - \bar{u}) \) and \( \pi_{t} = \pi_{t}^{w} - g_{t} \). To hold \( \pi_{t} \) constant as \( g_{t} \) increases, \( \pi_{t}^{w} \) must rise equivalently. Hence, \( u_{t} \) must decrease below \( \bar{u} \) to increase \( \pi_{t}^{w} \). This implies \( u_{r} \) must decrease.

04

Case (c): Analyzing the Pure Wage-Price Phillips Curve

For the pure wage-price Phillips curve, \( \pi_{t}^{w} = \pi_{t-1} - \phi(u_{t} - \bar{u}) \) and \( \pi_{t} = \pi_{t}^{w} - g_{t} \). To maintain constant price inflation as \( g_{t} \) increases, \( \pi_{t}^{w} \) needs to rise, which implies \( u_{t} \) must fall below \( \bar{u} \). Therefore, \( u_{r} \) decreases.

05

Case (d): Analyzing the Wage-Price Phillips Curve with Adjustment

In this scenario, we have \( \pi_{t}^{w} = \pi_{t-1} + \hat{g}_{t} - \phi(u_{t} - \vec{u}) \) with \( \hat{g}_{t} = \rho \hat{g}_{t-1} + (1 - \rho) g_{t} \), and \( \pi_{t} = \pi_{t}^{w} - g_{t} \). Initially, \( \hat{g} = g^{L} \). As \( g \) increases, \( \hat{g}_{t} \) becomes a weighted average. We need \( \pi_{t}^{w} \) to increase enough to counter \( g_{t} \); \( u_{t} \) must decrease to raise \( \pi_{t}^{w} \), leading to a decrease in \( u_{r} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Phillips Curve

The Phillips curve is a key concept in macroeconomics that illustrates the inverse relationship between unemployment and inflation. Developed by A.W. Phillips in the late 1950s, the curve suggests that with lower unemployment, inflation tends to be higher, and vice versa.
The idea behind this curve is relatively straightforward:

• As unemployment decreases, more people have jobs.
• This leads to higher demand for goods and services.
• Consequently, businesses could raise prices, leading to inflation.

However, the Phillips curve is not a simple, fixed rule. It has faced criticism and has been modified over time to incorporate factors such as expectations of future inflation. Despite these critiques, it's still a fundamental tool in understanding macroeconomic policy decisions and labor markets.

Productivity Growth

Productivity growth refers to the increase in the output produced per worker over time. It is a vital indicator of economic health because it leads to growth in the standard of living.
When productivity grows, it means:

• More goods and services are produced without increasing the number of workers.
• The economy can grow sustainably.
• Incomes can rise without causing inflationary pressure.

In the context of the exercise, when productivity growth increases permanently, it poses challenges to maintaining stable inflation. With more output per worker, wage and price adjustments must be made carefully to keep inflation stable. A steady increase in productivity can lower the natural rate of unemployment without sparking inflation if managed well.

Natural Rate of Unemployment

The natural rate of unemployment is a concept denoting the level of unemployment that exists even when the economy is at full potential. It's the sum of frictional and structural unemployment, excluding cyclical factors.
This concept is important because:

• It explains why zero unemployment is practically impossible.
• It helps policymakers set realistic employment and economic goals.
• It's used as a benchmark to evaluate labor market policies.

In the exercises concerning Phillips curves, the natural rate shifts based on changes in productivity and other factors. For instance, if productivity improves, the natural rate can decrease, allowing for more employment without triggering inflation. This dynamic adjustment aids in stabilizing the economy effectively.

Inflation

Inflation is the rate at which the general price level of goods and services rises, eroding purchasing power over time. It's a crucial economic indicator that affects both consumers and producers.
There are various causes of inflation:

• Demand-pull inflation where high demand drives overall prices up.
• Cost-push inflation where rising production costs lead to higher prices.
• Built-in inflation stemming from adaptive expectations.

Maintaining stable inflation is a major goal of central banks. By doing so, they aim to promote economic stability and predictability. In the context of the provided exercise, the adjustments to unemployment in the Phillips curve aim to counter the changes in productivity to keep inflation constant.

Wage Inflation

Wage inflation refers to the general rise in wages across an economy. It's crucial as it influences consumer purchasing power and overall economic inflation. Wage inflation can be both a cause and a consequence of general inflation.
Key aspects of wage inflation include:

• Rising wages increase consumer spending, potentially driving demand-led inflation.
• It can lead to a cost-push effect if wages rise faster than productivity.
• It's often tied closely to the labor market's tightness, reflecting how competitive or slack it is.

In the textbook exercise, wage inflation must be carefully balanced, particularly when productivity shifts. If wage increases do not align properly with productivity gains, it can challenge efforts to keep price inflation stable. This delicate balance is a hallmark of effective economic management.