Price Rigidities and Unemployed Factor Fluctuations in the Adjustment Process : A Dynamic General Equilibrium Approach

Using a dynamic general equilibrium model with many goods and many factors, this paper studies the adjustment process in a transition from one equilibrium to another. Applying a search process, an adjustment technique is developed to link the product and factor markets. Then an optimal control problem is solved and the optimal price adjustment is shown to be periodical, which generates price rigidities and unemployed factor fluctuations. Therefore, this paper develops an exploratory business cycle model in which price rigidities and unemployed factor fluctuations are the properties of the adjustment process in a transition from one equilibrium to another. In contrast to many conventional macroeconomic models, the model studied in this paper has the following distinguishing characteristics: 1) The adjustment process from one equilibrium to another, not equilibrium itself is studied. As a result, price rigidities and unemployment fluctuations are consequences of adjustment to the change of equilibrium prices that results from change of economic environment. 2) A general equilibrium model with multiple sectors is used to analyze factor flows across different sectors in the adjustment process. With this setup, the change in equilibrium prices means the change of any component in the price vector, not just the change of price index as in the one good model. 3) Perfect information and perfect competition are assumed. 4) The consumer maximizes instantaneous utility subject to a current budget constraint and then a social planner chooses an optimal price adjustment path to maximize intertemporal social utility. Thus, we investigate the causes of price rigidities and unemployment fluctuations that are distinct from intertemporal substitution. 5) Adjustment cost is assumed to be zero. We assume that factor adjustments take time. Changes in economic environment require change of steady state equilibrium prices. Price adjustments then take place in a transition from one equilibrium to another. Price adjustment results in changes in factor demands among different sectors. The reductions (increases) of factors demanded result in unemployment (vacancy) immediately after the price adjustment. The unemployed factors then find new positions through a searching process. Price adjustment alone increases social welfare, however, unemployment resulting from price adjustment reduces social welfare. An optimal price adjustment is determined by the net dynamic gain of the adjustment. It is shown that the net dynamic gain of the price adjustment is the sum of the net intertemporal gain and its dynamic residual. The price adjustment takes place when the net dynamic gain equals zero. The amount of the price reduction is determined such that the net intertemporal gain of the price adjustment equals zero. The dynamic residual is negative when the stability conditions hold. Therefore, net dynamic gain becomes negative immediately after the price adjustment taking place. Negative net dynamic gain prevents any further price adjustment. As time goes on, unemployed factors find new positions and the net dynamic gain reaches zero; the next price adjustment then begins. Therefore, the optimal price adjustment path is periodical, which generates price rigidities and unemployed factor fluctuations in the economy