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Effect of the policy and consumption delay on the amplitude and length of business cycle.

In this paper, the amplitude and the length of the business cycle are investigated. It is the first time the length of the business cycle based on the Goodwin model (one classical business cycle model) is discussed. The effect of the time delay of the economic policy and consumption on the amplitude and the length of the business cycle is studied. Meanwhile, the memory property of making economic policy is also considered. The theoretical amplitude of the business cycle is obtained by multiple-scale methods. The transitions of the amplitude induced by memory property and time delay are analyzed. How the economic parameter and random excitation affect the length of the business cycle is proposed. Based on the results, we can find that the time delay of both economic policy and consumption can induce the transitions. Moreover, the memory property of economic policy will change the critical value of the parameters when the transitions occur. In one typical induced investment function, the length of the business cycle is determined only by the autonomous investment and consumption. However, the length of the business cycle is not mainly affected by the autonomous investment and consumption in some other typical induced investment function. This states that the type of induced investment function has a very important role in determining the length of the business cycle.