Two Types of Currency

Laborers can anchor their own labor and issue time currency as labor options. In addition, merchants can anchor their goods and issue commodity currency as commodity options.

This leads to a question: Will commodity currency squeeze out time currency, thereby harming the interests of laborers and rendering exploitation ineffective?

Stability Analysis

First, the main function of currency is circulation, and liquidity is not much related to the value of the currency itself, but rather to the stability of its value. So, how stable are the values of time currency and commodity currency?

The value stability \(v_{goods}\) of commodity currency issued by merchants depends on each production stage:

\[v_{goods} = \sum_{i=1}^{n} v_i\]

where \(v_i\) is the value of the \(i\)-th production stage, including the output of workers and managers.

In the time economy, enterprises need to purchase the currency of laborers at each stage for production, so the output of the producer equals the value of the currency they issue: \(v_i = m_i\).

Now, let's analyze the stability (variance) of \(v_{goods}\):

\[Var(v_{goods}) = Var\left(\sum_{i=1}^{n} m_i\right) = \sum_{i=1}^{n} Var(m_i) + 2\sum_{i<j} Cov(m_i, m_j)\]

Assuming the currency issuance of laborers at each stage is independent, \(Cov(m_i, m_j) = 0\), thus:

\[Var(v_{goods}) = \sum_{i=1}^{n} Var(m_i)\]

Therefore, the stability of commodity currency is greater than or equal to that of time currency, which means the liquidity of time currency is greater than or equal to that of commodity currency.

Limitations

Of course, the above analysis is based on the assumption that the currency issuance of laborers at each stage is independent. In reality, there may be correlations, which will affect the stability of commodity currency.

Sources of such correlations include the influence of internal strategies of organizations such as unions and enterprises, as well as changes in the market environment.