British economist David Ricardo’s Law of Rent comes from his 1809 work On the Principles of Political Economy and Taxation. The term rent here, or economic rent, doesn’t refer to the usual meaning of the payment a tenant makes to a landlord for use of land, but refers to something that is closer to producer surplus (i.e. producer’s profit, simply the producer’s revenue minus cost).
Ricardo’s motivation to explore the nature of economic rent was due to rising grain and land prices during his time. He wanted to explore the question of whether rising land prices caused grain prices to rise or whether rising grain prices caused land prices to rise. In Ricardo’s simplified model, there is land, quality of land, and grain to produce and sell. The grain market is assumed to be a competitive market. Thus, grain producers are price-takers. The only use for land is assumed to be for growing grain. However, the quality of land is different for different land. Higher quality land takes less cost to produce a unit of grain compared to lower quality grain. Thus, we can imagine the quality of land to be composed of things like fertility of land, the transportation distance and thus transportation cost from the land to the grain market, etc.
When the only use for land is for growing grain, that means the supply of land and thus the supply of grain is inelastic (a vertical line). This means that all revenue made by the producer is profit and producer surplus/economic rent. If there are other possible uses for land that can generate revenue, that other use will compete for land space with grain growing. In this case, the supply of grain will not be inelastic (a slanted supply line). In this case, the area under the supply line is transfer earnings – the opportunity cost of not producing non-grain products or the minimum money that must be paid to keep product (grain) produced – and the area between the price and the supply line is producer surplus or economic rent. With an elastic supply, as the price goes down, the product (grain) supplied goes down due to it not being worth producing product at these lower prices. In other words, the transfer earnings for those units of product are not being met and thus these units of product are not being produced. Instead, the productive capacity i.e. extra land in this case may be being used to produce other products.
Going back to the Ricardian example where the only use of land is to produce grain and so the supply of grain is inelastic. If the supply of land and grain is inelastic and the price of land rises exogenously but the only use of land is to grow grain, as price-takers, producers still have no way to influence the price of grain. If the price of land rises, the only way a land owner can benefit from that is to sell that land, but what will the new owner do with that land other than grow grain or sell to another owner? If the land is used to grow grain, the productive capacity of the land hasn’t changed compared to before the land price increase, and since the grain market is competitive, all producers are price-takers. Thus, if the price of land increases, the price of grain should be unchanged.
Now we explore the case where the price of grain increases exogenously in the mode of Ricardo. So we have high quality land where a unit of grain is produced at a lower cost than low quality land where a unit of grain is produced at a higher cost. At the end of the low cost spectrum is free land with no landlord where labor can go and produce grain on their own, which is labeled as marginal land. Note again that the grain market is assumed to be competitive and thus all producers are price-takers.
Note that it’s possible for marginal land to make a profit as well if the price is high enough and the quality of marginal land is high enough. In the example above, we assume that marginal land ekes out a zero profit.
Note how the above figure illustrates a competitive market. If producers try to raise the price — even if it’s many producers raising the price — theoretically many new producers will enter the market (assuming there is enough land that that is as fertile as the original marginal land) and will be able to out-compete the producers that tried to raise the price. The price will thus be competed down to the original price, where the original producers will be selling at the old original price and the new producers are all left with zero profit. Going back to the original situation, theoretically a producer already making a profit might lower the price to try to out-compete others. In this situation, the producers are making a profit and thus it isn’t a true competitive market. This means that a producer can afford to lower the price, which perhaps means that that producer’s product is sold first. However, there are still enough buyers where after the products at the cheaper product are sold out, products at the higher original price will be bought. Thus, there is no real point for a producer to lower their price. Thus, the equilibrium product price in this model is the price at which new market entrants obtain zero profit, which is equivalent to Marginal Revenue = Marginal Product, what we expect from a competitive market. The cost to produce one unit of product on marginal rent-free land (Marginal Cost) is the equilibrium product price (Marginal Revenue) in this competitive market.
Going back to the figure above, what we have is that owners of high quality land make a high profit and owners of lower quality land make lower profit, until at some point, the quality of land is such that the profit is zero. Now let’s see what happens when the price of grain exogenously rises.
We see that low quality land that previously was too low quality to be affordable as grain-producing land is now feasible due to the new higher price of grain. Thus, land that used to be free now has positive value and would develop a market of land buyers and sellers. Furthermore, previously owned higher quality land is even more valuable now since these units of land can produce higher profit than before.
Thus, in this Ricardian model, we see that exogenously higher grain prices lead to higher land prices.
Note that the labor in producing grain is done not by owners but by workers hired or paid for by the owners. The work done by the laborers is assumed to be the same – i.e. we assume that from a worker’s perspective they are indifferent to working on high quality land or low quality land. We also assume that it is the workers who go to the market and sell grain for revenue. Thus, what happens in our model is that the land owner charges rent so that the worker is left with a subsistence-level wage. On high quality land, the owner charges a large rent; on low quality land, the owner charges less rent; on the lowest quality land that can earn profit equal to a subsistence-level wage, the owner charges no rent. Thus, the lowest quality land that can still earn profit equal to a subsistence-level wage is marginal rent-free land.
In Wikipedia’s wording, Ricardo’s Law of Rent is:
The law of rent states that the rent of a land site is equal to the economic advantage obtained by using the site in its most productive use, relative to the advantage obtained by using marginal (i.e., the best rent-free) land for the same purpose, given the same inputs of labor and capital.
So the economic rent of a site of land is how much more profit that land can produce relative to the profit that the best marginal, i.e. rent-free land can produce.
The definition above takes care to mention other productive uses and purposes, and inputs of labor and capital.
Along that line, we can extend the concept of the Law of Rent beyond land as a factor and just one product. Turn land into any scarce factor or factors that the owner has exclusive rights or ownership to and let there be many possible products to produce. The profit that the owner makes due to their exclusive ownership of scarce factors (e.g. that allow the owner to produce products at a lower cost) over the profit that another owner would make without ownership of those scarce factors (since it will cost that owner more to produce the same product) is the economic rent of that first owner that comes from exclusively owning those scarce factors for a certain product. Thus, for every product, if there is a scarce factor that makes producing that product cheaper or more efficient, the profit that an owner of that scarce factor would make over the profit of an owner without that factor is the economic rent gained due to owning that factor.
This concept is extended to the concept of economic rent-seeking, where companies pursue, maintain, and protect exclusive rights or ownership of factors of production that give them an advantage in production. These factors may be things like monopoly over resources; government licenses, subsidies, tariff protections; patents, etc. In these cases, society may judge that they are paying a cost when purchasing the product that is too high compared to the benefits (if there are any) of giving the company the exclusive rights or ownership.