Bending Over Backwards

I’m constantly bending over backwards explaining to the Keynesians how clueless they are but a particular fallacy that spans beyond Keynesianism is the backward bending supply curve of labor. Conventional economics states that in most industries as the price goes up the quantity supplied increases and therefore there is a, typically linear, upward sloping supply curve. Of course, there is one exception in the case of labor. When wages(the price of labor) increase, initially, the supply of labor increases because people substitute better paying labor for leisure. If wages continue to rise, then incomes rise so people choose to enjoy more leisure, and therefore less labor so the quantity supplied decreases, hence backward bending.

The backward bending supply curve of labor is fallacious because the concept implies that labor is unique because of the supposed “substitution” and “income” effect. In reality, every good has a backward bending supply curve. The law of diminishing marginal utility perfectly explains why every supply curve is backward bending. Furthermore, every supply curve increases at an exponential rate.

First, I’ll explain how diminishing marginal utility explains the backward bending supply curve of labor, as opposed to the traditional “substitution” and “income” effect. The graph always represents the trade-off between the price received(vertical axis) and the quantity supplied(horizontal axis). As the price received(income) increases the value of the marginal dollars decreases, hence diminishing marginal utility. As the quantity supplied increases the suppliers have less and less product which means the remaining supply, after marginal units are exchanged, becomes more and more valuable. Initially, on the supply curve, the dollars received are worth more than the supply being exchanged. However, eventually an inflection point is reached where the suppliers have received many dollars and have given up a lot of their supply. They now value the product, that they supply, more highly than the dollars that they receive, and so the supply curve bends the other way.

Most economists attribute the backward bending supply curve of labor to the “income effect”. However, it’s only true that incomes rise because the y-axis is measuring price/income. If workers were being paid for their labor with cupcakes then it is more evident that there is no income effect. The law of diminishing marginal utility is taking effect. Initially the marginal value of cupcakes is high relative to labor. As leisure is being given up, it becomes more valuable relative to the marginal cupcakes being accumulated.

Leisure is a good, like any other. As wages rise it eventually leads to the leisure becoming more valuable because the marginal dollar is worth less and less. If I’m a supplier of labor, a worker, then I’d rather work for one hour and be paid 1 million dollars for it, then work 10,000 hours and be paid $1000 per hour. Even though I will receive more money in the latter scenario, the marginal dollar after 1 million dollars is valued less highly than the leisure.

Now, let’s consider and examine the supply curve of different industries. Imagine you are a supplier of land. Suppose you own 10 units of land. In order to have a place to live you must keep at least 1 unit of land. Therefore, it is clear that the marginal value of the initial unit of land is extremely high. You would be more comfortable if you had a beach house(another unit of land) as well, but it’s not absolutely essential. And keeping additional units of land will benefit you but not very much. So, how would your supply curve look? Well, the first 8 units of land could be sold at a fairly low price. However, after those units are sold you end up with a lot of money, which means that the marginal value of money decreases, and only 2 units of land are remaining which means the marginal value of land increases. In order for you to give up your beach house, you must be paid exponentially more for this unit of land than the previous units. The last unit of land is where the inflection point is reached on the backward bending supply curve because you will not sell it at any price. If a price above the inflection point is offered you will not sell the land because the value of the marginal dollars are not high enough to compensate for the highly valued marginal unit of land. In fact, as more dollars are offered they become less and less valuable and so the supplier of land would choose to keep his more highly valued land. This example clearly shows how there is a backward bending supply curve of everything, and that it is certainly not unique to the labor market.

The extent regarding how quickly the supply curve bends backwards depends on whether the total supply is fixed or whether it can be increased easily by producing less of something else. Labour, land, gold, houses, etc. are all inelastic assets and so the shape of their supply curve will tend to bend backward very quickly. Other products, like wheat or manufactured goods may increase for a while before they begin to bend backwards. If the price of wheat doubles then more wheat will be produced as farmers produce less of other crops. However, if the price of wheat goes to one million dollars per bushel, then it is clear that super-rich farmers would just begin to consume their own wheat instead of selling it for the less-highly valued marginal dollars.

The fact that every product has a backward bending supply curve may seem like a problem because it creates the possibility for 2 points of equilibrium. Although, if there is a free market, with a lot of competition, then the multiple equilibriums are not a problem because the highest quantity will be produced at the lowest price.

The government loves to espouse the concept of the backward bending supply curve of labor because it allows them to justify all the government intervention within the labor market. The fact is that every supply curve is backward bending and so there is no excuse for the government to interfere. Of course, if anything the government will view this as a justification to manage and regulate every industry, as opposed to de-regulating the labor market.