Markup Rule and Surplus Labour
I came across an interesting equation called the Markup Rule (see here: https://en.wikipedia.org/wiki/Markup_rule). This formula seems to be standard economic fare and relates the elasticity of a product with the possible amount of profit made. Similar formulas can be found elsewhere, but I like how things are framed here. This post will be about how this rule is applied to the labour market. This might be a trivial insight, but I do think it’s a nice way to introduce people to Marxian concepts.
The markup rule (as described in the link above) shows how economic profit is made in a product market. An enterprising individual comes to the market with their product and would like to know how to maximise their profit. They have with them two functions, P and C. Both functions take as input a quantity of product Q, and return an associated amount of money. So function C (the cost function) will return the cost (amount of money) required to create a given quantity of product. The function P (price function) will give you the price (amount of money) you can get per product if Q product is sold at the market. So the revenue is P(Q)•Q. The resulting equation is:
Where π is the profit. Do some calculus to maximise the profit and you’ll arrive at the equation relating the optimal price and price elasticity of demand.
Where MC is the derivative of C at the optimal Q, P is shorthand for P(Q), and η is the reciprocal of the price elasticity of demand (ϵ). (This elasticity is the degree to which the quantity demanded changes as price changes. A product has low elasticity if you can increase the price without much decrease in the quantity demanded. Note that ϵ and η are negative numbers)
The result is intuitive: the less elastic a product is, the higher the possible profit for the entrepreneur. Good real world examples are university costs and healthcare, if you’re in the US.
Next we apply this to the labour market, instead of the product market. This requires a slight change in perspective. Now, the entrepreneur comes to the market looking to sell money instead of product. In return, they receive labour for that money. It’s important to recognise that money is now the input to P and C, rather than the output. I’ll use the same function symbols P and C for consistency, but when writing equations I’ll add the ‘ₗ’ subscript (Pₗ/Cₗ) to signify that these are labour functions. Instead of Pₗ and Cₗ taking quantity of product Q as input, they take quantity of money M. Instead of Pₗ and Cₗ outputting amounts of money, they output amounts of labour. How you want to quantify amounts of labour is up to you, I just imagine them as labour hours for this post (similarly I’ll just say ‘dollars’ when referring to money units). I’ve made a table to clarify the changes:
Rewriting the profit equation (just swapping out symbols):
So now, instead of computing money profit, the equation computes surplus labour L⁺; the amount of labour the entrepreneur can obtain from the market with M dollars over the amount of labour that was required to generate M dollars. Quantities of products and money are physical quantities, so the markup rule for the product market is likely easier to visualise. But once you get used to thinking about quantities of labour (think labour time / labour hours), the rest lines up with the original markup rule.
All you need to do now is just follow the same line of reasoning as the original markup rule shown in the Wikipedia page. I’ll only write down the important equations, but the proof follows exactly as what’s that wiki page.
The price elasticity of demand shows up again, as well as its reciprocal:
Of course, now we are talking about Pₗ being the labour “price”, i.e. the amount of labour hours you’ll receive per dollar. So now we are talking about the labour elasticity of demand for money (ϵₗ). This elasticity corresponds to the degree to which the amount of money demanded will change as you change the labour price.
The final equation remains the same:
What’s the takeaway? The same logic as the product market. If employers find themselves able to reduce the amount of money given out as wages without an equivalent reduction in labour hours accrued, then they can make a profit (surplus labour). Of course, we live in a monetary economy and money is a necessity to live. So the demand for money is expected to have somewhat low elasticity, especially for workers living in precarity. The entrepreneur can thus generate surplus labour by solely relying on the above equation: by having money when others need money. It is important to recognise that the entrepreneur accrues the surplus labour not through any positive effect on the economy, it is accrued simply by virtue of having.
The analysis of surplus labour is a core component of the Marxist view of capitalist economies. Surplus labour, along with surplus value(profit, as given in the original markup rule), represent the driving forces of the economy. The existence of one naturally implies the existence of the other and these forces generate a process which Marx called capital accumulation. If left alone, these forces will propel themselves and conditions will worsen.
Institutions like the welfare state are crucial for handling this problem of surplus labour. If workers are not solely dependent on the labour market to survive, then employers have less power over workers. Increased competition in the labour market will also increase the elasticity of demand for money (similar to how competitive substitutions will increase the elasticity of demand for products in the product market). If the market is not competitive, the government could also create competitive firms (state owned enterprises), which also have the benefit of alleviating the elasticity problems in the product market. Plenty of other solutions have been used, but the main take away is that something must be done. Non-intervention under the guise of avoiding market distortions is basically adding fuel to the fire.