# Monetary Circuit Model/Profits

In this lesson, we will derive the income of capitalists - profits - in our simple economy. We do this by assuming a constant wage share of surplus. In more advanced models, this assumption is relaxed and wage share can vary cyclically.

(My knowledge of this topic is somewhat shaky. Steve Keen's papers omit a lot of explanation of this area, so my interpretation may not be 100% correct. Corrections are welcome.)

Surplus here is in the Sraffian sense of revenues minus direct costs (not including labour) for each individual firm.

The "wage rate", fwr, paid by firms depends on two factors. First is the wage share received by workers, 1 - σ, where σ (sigma) is the share of surplus going to capitalists. Second is the turnover period, τ (tau), the length of time it takes for the firm to recoup its initial investment in production. The initial investment is the stock of firm deposits, fd. If we take the inverse of the turnover period, 1/τ, we have the number of times the firm recoups on its initial investment in a year. Multiplying this by the initial investment, fd, gives the firm revenue over the course of a year and multiplying this again by the wage share, 1- σ, gives the wage bill. Since the wage bill is also given by fwr*fd, we can derive τ from fwr and an assumed wage share:

$fwr={\frac {1-\sigma }{\tau }}$ Given our fwr parameter of 2 and an assumed wage share (1 - σ) of 60%, we can calculate τ to be 0.3. Since all firm revenue that does not go to wages is distributed as profit (Π), we can now determine it using τ (turnover period) and σ (profit share):

$\Pi ={\frac {\sigma }{\tau }}F_{d}$ The result (plus interest earned on deposits and banker income) is this:

All classes are able to earn a continuous positive income despite a fixed initial stock of money. This is because that initial stock is recycled over and over in the economy - one person's expenditure is another's income.

In the next lesson, we will look at what happens when we apply a shock to the model in the form of a credit crunch.