Abstract
We study the time path of inflation and unemployment using the Blanchard treatment of the relationship between the two and taking the monetary policy condition into account. We solve the model both in continuous and discrete time and compare the results. The economic dynamics of inflation and unemployment shows that they fluctuate around their intertemporal equilibria, inflation around the growth rate of nominal money supply, respectively, and unemployment around the natural rate of unemployment. However, while the continuous-time case shows uniform and smooth fluctuation for both economic variables, in discrete time their time path is explosive and nonoscillatory. The hysteresis case shows dynamic stability and convergence for inflation and unemployment to their intertemporal equilibria both in discrete and continuous time. When inflation affects unemployment adversely the time paths of the two, both in discrete and continuous time, are dynamically unstable.
Highlights
The relationship between inflation and unemployment illustrated by the so called Phillips curve was first discussed by Phillips [1] in a path-breaking paper titled “The Relationship between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957”
The economic dynamics of inflation and unemployment shows that they fluctuate around their intertemporal equilibria, inflation around the growth rate of nominal money supply, respectively, and unemployment around the natural rate of unemployment
There he introduces the concept of the natural rate of unemployment and argues that labor market equilibrium is independent of the rate of inflation
Summary
The relationship between inflation and unemployment illustrated by the so called Phillips curve was first discussed by Phillips [1] in a path-breaking paper titled “The Relationship between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957”. In an influential 1968 paper titled “MoneyWage Dynamics and Labor Market Equilibrium” Phelps [4] studies the role of adaptive expectations in setting wages and prices There he introduces the concept of the natural rate of unemployment and argues that labor market equilibrium is independent of the rate of inflation. In his book Macroeconomics Blanchard [5] offers an alternative treatment of the relationship between inflation and unemployment He incorporates in the model the natural rate of unemployment Un at which the actual and the expected inflation rates are equal. The rate of change of the inflation rate p is proportional to the difference between the actual unemployment rate U and the natural rate of unemployment Un. The purpose of our paper is to study the economic dynamics and time path of inflation and unemployment from the perspective of Blanchard’s equation of the relationship between inflation and unemployment.
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