Ricardian Models: Profits

Notes on The Principles of Political Economy and Taxation

10 Jul 2019
modified: 28 Sep 2019

Under Ricardo’s economic framework, income is the component of valuation remaining after rent, wages and any other consumed capital is deducted from revenue. In considering the distribution of a wealth over the participants in a nation’s economy, profits constitute that portion of production retained by capitalists and entrepreneurs.

Context and assumptions

Ricardo assumes simple relationships between the amount of food produced, the labor required to produce that food, and the price of food.

Define the following terms:

  • $Q_F^{*}$ : quantity of food or raw produce generated with a fixed quantity of capital and labor.
  • $Q_L^{*}$ : quantity of labor required to generate a fixed quantity of food on land that pays no rent
  • $v_p$ : price for a fixed quantity of food or raw produce

Then Ricardo maintains that the price of a fixed basket of necessaries/provisions at the margin is proportional to the quantity of labor required to produce it; and inversely related the amount of food produce with a fixed quantity of labor:

\[\begin{eqnarray} v_p &\propto& Q_L^{*} \\[2em] v_p &\propto& \frac{1}{Q_F^{*}} \end{eqnarray}\]

For Ricardo, a worker’s annual wage will depend on the price of necessaries modified by two additional factors:

  1. a factor $k$ scales the price of food to a level sufficient to sustain a laborer and family over the course of an annual period.
  2. a premium or decrement that accounts for fluctuations in supply and demand of labor $f\left(\frac{c_L}{P} \right)$, where $c_L$ is the capital allocated to labor and $P$ is the population.

worker wages

\[w = kv_p + f\left(\frac{c_L}{P} \right)\]

The total annual wages paid for production simply scales with the number of workers employed during production of commodities:

total wages

\[\begin{eqnarray} W &=& w \times Q_L \\ &=& \left(kv_p + f\left(\frac{c_L}{P} \right) \right) \times Q_L \end{eqnarray}\]

Then the annual income achieved amounts to the value of the commodity produced with a given quantity of labor scaled by the total labor utilized during production.


\[M = Q_F \times v - W\]

And the annual rate of profits is the income less any additional consumption of capital divided by the sum of wages and additional capital consumption.


\[r = \frac{Q_F \times v_p - W - c}{W + c}\]