The physics of business cycles and inflation

We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey and consumers as predators provides the required instability, but its natural damping is too high for spontaneous cycles. Extending the Lotka-Volterra equations with a small term for collective anticipation yields a second analytic solution without damping. It predicts the base period, phase shifts, and the sensitivity to shocks for all six cyclic variables correctly. Business cycles are more or less regular fluctuations of production, employment, consumption, growth, money supply, and inflation on the time scale of up to 7 years. They have nothing to do with long-term technical change or medium-term recovery of the technical infrastructure from wartime destruction. Their cause and control are central problems of economic policy [1], but their analytic understanding is still limited to accepting the oscillator [2] and Lotka-Volterra [3] equations without damping, or denying the existence of cycles because there seems to be no propagator [4]. Times of negative growth are treated with estimated money injections. Times of positive growth are approximated with the “Phillips Curve” for the relative change in % between annual inflation and employment [1]. Figure 1 shows the only existing “experiment” with 4 consecutive cycles. Its initial wing from 1961 to 1966 follows the Phillips Curve. Due to a temporary entente between the USA and the former USSR the first cycle was initially too flat and too long. Due to the Vietnam War it ended nearly rectangular. Figure 1: Four business cycles of the USA. The data are taken from [1]. The doubled changes of the inflation rate are due to 3 crude oil price shocks. Natural damping prohibits cycles (dashed envelope). The added ellipse shows the normal range of cycles. The original unemployment axis was reversed. The double lines show the increase of inflation due to the crude oil price shocks of the Jan Kippur Embargo and the Iranian Revolution, and its return to the normal range towards the end of the Cold War. The first price change happened in the calendar year 1974, the second in two years, the third in 4 years. The employment between 1981 and 1985 was a shock reaction caused by the banking system’s ! inflation p.a. ! employment 61 69 79