What is supply?
What is a supply curve? What is a price elasticity?
[This essay is intended for students in my law and economics and my microeconomics class (for law students), but you may also find it useful. Read this essay one time through, ignoring the queries that are interspersed. Go back to the queries after you feel you have understood the essay. The queries test whether you have understood enough to develop a richer understanding of the topic of the essay (supply). These instructions will also apply to future essays.
I have bolded certain words. These are terms that you should know going forward. If you do not understand them, ask your favorite foundational AI model about them.
I will post the python notebook that generates all the figures in this essay in case you are interested in reproducing them.]
Not only do incentives matter for people who buy and consume goods, they matter for firms that make and sell the goods that people consume. Just as people view money as a reward (because it indirectly represents consumption, which people directly value), firms view money as a reward (because it can be given as income to a firm’s owners, who also value consumption).
We define a firm as an individual or a group of individuals who produce something. The firm can have an informal structure, not registered under formal law with or given any formal legal rights. Or it can be formal, such as a sole proprietorship (an individual), a partnership, a corporation, etc.1 A firm can even be a government!
We will often speak of consumers as individuals, and producers as firms. But firms can be consumers too. For example, a company that produces electric vehicles will demand batteries from firms that produce batteries. Indeed, each firm is both a consumer in markets for inputs into the goods it produces, and a supplier in markets for the goods that it outputs.2
Producing goods costs firms money. Firms have to buy some inputs (labor and physical capital), and then use those inputs to make some outputs. For example, a bakery will combine flour, sugar and eggs, along with some labor from employees, to produce bread or cakes. The firm has to pay for its inputs, and cover that expense with sales of its output. If the price a bakery gets from selling a cake is smaller than the cost of inputs required to produce the cake, the bakery will lose money. It will either choose never to produce a cake, or will go out of business if it already started making cakes. However, if the price of a cake is greater than the cost of inputs into the cake, the bakery will make a profit. The profit can be given to the firm’s owners, who value consumption. This is an incentive for the bakery owners to form a bakery and make cakes!
One challenge with production is that, as a firm makes more output, at some point its cost per unit of output rises. Increasing the number of cakes produced per week requires not just proportionally more kitchen appliances and employees, but also more layers of management or the fixed costs of a new store. Eventually, these extra costs rise faster than output, so that the cost of each cake increases. If the price of cakes is fixed, maybe the firm makes some profit producing a small amount of cakes; but as output increases, the cost of producing cakes exceeds the price of cakes. Since the bakery will only produce an additional cake if its price can cover the marginal cost of that cake, it will stop producing when the price of cakes equals the marginal cost of cakes. However, if the price of cakes rises, the firm will produce some more cakes, because a few more cakes will be profitable. This generates what is called an individual firm’s supply curve: an upward-sloping line that indicates how much quantity (on the x-axis) a firm produces as price (y-axis) rises.
(Query: Private firms make revenue by selling goods. Their expenses are the cost of their inputs, including labor and capital. Suppose we treat the government as a public firm. How do its revenues differ from those of a private firm?)
(Query: Why didn’t I say that if a firm makes a profit, it can raise wages? Hint 1: Employees are an input. What happens to profit when wages rise? When answering, remember that you are not making a value judgment; you are just doing some accounting. I have not said whether higher wages or higher distributions to owners is morally superior.)
Just as we added up individual demand curves to obtain an aggregate demand curve, we can add up individual supply curves of individual firms to obtain an aggregate supply curve (see figure below) across all firms in an industry or sector that supplies a good. If the supply curve were drawn such that quantity were on the y-axis, we would simply add individual firms’ supply functions on top of each other. But the supply curve, like the demand curve, is drawn with quantity on the x-axis. So, to get an aggregate supply, you have to horizontally add up different firms’ supply curves.
(Query: In the essay on demand, we distinguished between shifts along the demand curve and shifts in the demand curve. We can analogously distinguish between shifts along the supply curve and shifts in the supply curve. Can you give examples of changes that would be represented by each? To the point, what might cause shifts in the supply curve, holding selling price constant?)
The slope of a demand curve is the rate at which an increase in selling price of a good increases how much the industry is willing to supply the good. For example, if the price of a coffee increases from $3 to $4, how many more coffees will all coffee shops in Chicago be willing to supply? (This does not mean people will consume all those extra coffees. We’ll get to how much they consume later.) We can ask the same thing about, say, donuts: how many extra donuts would bakeries supply if the price of a donut increased from $10/dozen to $11/dozen.
But comparing slopes of supply curves for coffee and donuts is complicated. One is denominated in coffee and one in donuts. The solution is to change units. Instead of talking about coffee and donuts, we can talk about the percentage increase in coffee or the percentage change in donuts. To be symmetric, we can talk about change in price in percentage terms too. When we measure the slope of a supply curve in percentage change in output rather than direct units of the output (e.g., cups of coffee), we call a supply curve’s slope the “price elasticity of supply”: price elasticity of supply = percentage change in quantity of output for a 1% increase in price.
(Query: Indeed, one can define the price elasticity of demand in an analogous fashion. Can you write down that definition?)
To compute this, we just divide the numerator of the slope of supply by the quantity of the good before the price change and the denominator of the slope by the price of the good before the price change:
Slope = (Quantity at price B - Quantity at price A) / (Price B - Price A)
Elasticity = [(Quantity at price B - Quantity at price A)/Quantity at price A] / [(Price B - Price A)/Price A]
A key insight from the discussion above is that supply curves are upward sloping because costs increase with scale: as a firm or an industry of firms produces more, their cost per unit rises, so that they produce more only if they are paid more per unit. While this statement is true, it deserves an important qualifier.
An important qualifier to this statement is that, in the long run, supply curves become more flat. If we think in terms of percentage changes, the claim is that in the long run supply is very elastic. If price rises, in time more firms enter the market and people come up with innovations to reduce costs. We can see evidence for this everywhere. In 2010, cellular data was expensive. That signalled demand for more speed. Now we all get 5G speeds on mobile data for pretty cheap. In 2010, the green transition was daunting because solar cells were expensive. The high price signalled demand, and technology drove down costs tremendously. Humans are remarkable, and one place we see it is supply elasticity. So, as Tyler Cowen says, never underestimate supply elasticity.
There is one type of firm that is especially important: the individual. Individuals typically generate income by exchanging their labor for money. They sell this labor to firms, which use the work as an input into the production of their outputs. Thus individuals supply labor, and firms demand labor. Individuals then use the income from selling their labor to demand goods that the firms produce. This is a circle that completes an economy. Just as a firm’s supply of a good increases in the price of that good, an employee’s supply of labor increases in the wages she receives for that work. I.e., labor supply is upward sloping.3
(Query: What other sources of income does an individual have? What is the individual supplying in return for receiving capital income? How does this relate to saving and borrowing?)
If you want more explanation of a supply curve, I encourage you to watch the demand curve video at Marginal Revolution University: https://mru.org/courses/principles-economics-microeconomics/supply-curve-definition-example.
A firm typically has four elements. (1) It has some owners, who can be individuals or other firms. (2) It has employees or contractors, who supply labor to a firm, i.e., do things for the firm. (Contractors can be other firms, though employees are all individuals under US law.) (3) It has physical capital (like a building or equipment), or rights to physical capital (like a lease or rental agreement). (4) It has financial capital. The financial capital can be thought of as an account. The account could be net positive (representing cash on hand that is unencumbered). It could be net negative (representing debt). You don’t have to worry about many of these details about a firm until you get to the economics of legal fields such as corporate law, tax, and bankruptcy. For now, just think of a firm as a black box that supplies products and services.
People often refer to final goods markets—markets for goods sold to individuals to consume for their own utility and not to use as inputs into products that will be resold—as markets for retail goods. By contrast, markets for inputs into other goods or markets for completed goods that are sold to distributors who sell the goods to final consumers as wholesale markets.
A final product uses inputs, and those inputs in turn use other inputs, and so on. For example, the electric vehicle company will use batteries from a battery company, and the battery will use lithium from a lithium mining company. So there is in some sense a chain of companies—and product markets they participate in—behind each final product that you or I consume for our personal use. Firms that are further away from the final product are upstream producers, and those closer to the final product are downstream producers. Firms that produce their own inputs are said to be “vertically integrated”; the opposite is vertical disintegration. Finally, this all relates to the idea of “privity” in products liability law: the firm that directly contracts with a consumer is in privity with the consumer. The firm that sells inputs to the firm that is in privity with the consumer but does not itself contract with the consumer is not in privity with the consumer.
It makes sense to separate labor markets from other goods markets, even though nearly all goods are made with labor. If there were only 1 firm and 1 product in the economy, we could do away with money and just have people exchange labor for goods. But in a realistic economy I may work for firm A, you may work for firm B, our friend may work for C, and so on. Moreover, we all buy goods from firms A, B, C, etc. Firm B does not care for my labor—they have yours; so they are unlikely to trade their goods directly for my labor. Same for all firms other than A. Since there are many firms other than my employer, and because most of my consumption will be bought from those other firms, it is best to think of markets for labor as distinct from markets for other products.)