A quick introduction into the mathematics behind the model
We first start by looking a little bit more at the rabbits and foxes model. This model works as follows. First assume we start with a fixed number of rabbits and foxes. Then, if there is an excess amount of rabbits, the foxes have more than enough to eat and the number of foxes will increase. Because of the growing number of foxes more and more rabbits get eaten and the number of rabbits dwindles down. From this the number of foxes also starts to decrease due to a fall in food supply. Then finally the number of rabbits can start to increase again and we arrive back in the situation where we started. Hence this model describes a cyclical process. This cyclical process can also mathematically be explained. So let us now look at the mathematics. The Lotka-Volterra model consists of a system of the following 2 differential equations:

The Goodwin model
Now that we are a little bit more familiar with this system of differential equations, we will take a look at an economic application of this model. Richard Goodwin was one of the first people to come up with such an application. Goodwin thought he could model the Marxist class struggle between the bourgeoisie and the proletariat. Here we have that the bourgeoisie controls all the capital and means of production and the proletariat forms the labour force and hence provides the labour. If we try thinking about why this specific proposition would go well with the Lotka-Volterra equations, it becomes apparent that we are dealing with so-called business cycles. The similarity here with the rabbits and foxes model stems from the fact that we are dealing with two groups in both cases. The assumption that every person falls into one of two groups is of course not very realistic, but models are often not realistic and never have the goal of perfectly explaining reality. Thus we can still use this assumption. As we saw, the Lotka-Volterra model also provides us with this cyclical behavior. So now let’s see what this cycle entails. Goodwin looked at the cyclical relation between the employment rate and the wage share in a working class economy. The macroeconomic effects that Goodwin modelled are explained by the circular flow chart below.