Does the economy oscillate
People who know say there is a seven year trade cycle, with boom years followed by slump then another boom. The overall trend is up.
In an economy there are some factors I identify here which clearly show the relationship to a physical system.
1. Positive Feedback (Profit means money to invest)
2. Inertia (Capital investments in the means of production takes time to change)
3. Friction (Money tends to lose its value)
These features make the components of an oscillator.
To reduce the tendency to oscillate, negative feedback needs to be applied.
A business often borrows money to invest in the means of production and there is a lag before profits are made to repay the loan. This debt is a restoring force. This makes for oscillations in profit. A numerical analysis is not attempted here.
As borrowing increases the economy goes negative and this tends to put a break on further borrowing, this reduces profit, thus reduces investment, so there is less employment. This trend continues until there is a recession. Once the debts are paid the economy recovers. People start buying, businesses invest, employment increases and so trade increases.
This cycle repeats with a predictable period. This period may be found by solving a differential equation thus:
A*D2(activity)+ B*D(activity) + C=0 where D is a differential with respect to time and A,B,C are constants determined by the inertia of capital, inflation and the amount of feedback.
The force moving the investment of capital is the K1*rate of
change of investment So
force=K1*Dinvestement + friction - feedback
Profit is the return on investment, so profit=K2*investment
the positive feedback is the fraction of profit invested= K3*profit.
Friction is the rate at which money looses its value = K4*profit
So
force = K1*D(profit)/K2 +K4*profit - K3*profit
but force = K5*D2(investment)
So D2(profit) - K1/K5*K2*D(profit) + (K3-K4)*(profit)=0
This is the equation of simple harmonic oscillator. It has a well know solution.
Chris 16-7-2002