12  Equilibrium

For more information on these topics, see Varian Chapter 16: Equilibrium.

12.1 Objective

In this chapter, I will provide examples of equilibrium analysis, demonstrating how prices adjust to align demand and supply decisions. I will introduce supply curves, market equilibrium, and the effects of shifts in supply or demand curves.

12.2 Market Equilibrium

So far, we’ve focused exclusively on demand, and after this section, we will delve into supply. But to preview equilibrium: while the demand curve shows how many units consumers are willing to buy at different price levels, the supply curve shows how many units producers are willing to sell at various price levels. The supply curve typically slopes upward because initial units are produced at a lower cost using the most suitable, least expensive resources. However, as production increases, costs rise as less suitable, more expensive resources must be used.

We’ll assume markets are competitive (each consumer and producer are small relative to the market size, so they are price-takers, not price-makers). Buyers who are unwilling to pay the market price for the good won’t buy it; sellers who are unwilling to sell at the market price won’t make sales.

Even though individual buyers and sellers don’t influence the market price, the combined actions of all agents determine it. In equilibrium, the market price adjusts so that the quantity demanded equals the quantity supplied. Geometrically, this is where the supply and demand curves intersect. At any other price level, there is either excess supply or excess demand, which exerts downward or upward pressure on price:

Practice Question: At a price that is higher than the equilibrium price, there is:






12.3 Demand and Supply Determinants

Demand Determinants

In sections 3-11 of this workbook, we built up the full theory of consumer demand. So what does market demand depend on?

  • Consumer budget constraints
  • Consumer indifference curves

Budget constraints are determined by the price of the good in question, along with the prices of any other good the consumer might buy, and consumer incomes. Indifference curves are determined by consumer preferences.

So if consumer incomes increase, we should expect that the demand curves for all normal goods shifts to the right: for any given price, consumers will be willing to buy more. (And demand curves for all inferior goods shift to the left.)

If there’s a viral advertising campaign that makes a lot of people want a certain good more, that affects peoples indifference curves and we’d expect that the market demand curve for that good to shift to the right.

Supply Determinants

We’ll spend the next section on Producer Theory to build up a theory of supply, but for now, think of supply determinants as anything influencing the cost of production. If wage rates increase for example, producers will need more money to supply the same amount of a good (the supply curve shifts up or to the left).

12.4 Comparative Statics

If the demand curve shifts to the right (consumers are willing to purchase more than before at every price level), then equilibrium price and quantity exchanged will both increase:

And considering the reverse, if the demand curve shifts to the left (consumers are no longer willing to purchase as many units at any given price level), then the equilibrium price and quantity exchanged will both decrease.

If the supply curve shifts to the right (producers are willing to sell more units than before at any given price level), then the equilibrium price falls and the quantity exchanged rises.

Considering the reverse, if the supply curve shifts to the left, the equilibrium price will rise and the quantity exchanged will fall.

Practice Question: What will happen to the equilibrium price and quantity exchanged when both the supply and demand curves shift to the right?






12.5 Classwork 12 Preqrequisites

Math prerequisites for question 1:

  1. Slope-intercept form: The equation \(y = mx + b\) is in slope-intercept form. The slope is given by (choose one: y, m, x, b, mx). The y-intercept is given by (choose one: y, m, x, b, mx).
  2. Finding the point where two lines intersect is the same as solving a system of linear equations. For what values of \(x\) and \(y\) do the lines \(y = x\) and \(y = 10 - x\) cross?


12.6 Classwork 12: Equlibrium

  1. Equilibrium with algebra:

    1. Suppose the demand curve is given by \(q = a - bp\) and the supply curve is given by \(q = c + dp\). However, we usually think of price being on the y-axis. What are the slopes and y-intercepts of the demand curve as functions of a, b, c, and d?

    2. At equilibrium, supply and demand intersect. Show that the equilibrium price is \(p^* = \frac{a - c}{d + b}\) and the equilibrium quantity exchanged is \(q^* = \frac{ad + bc}{b + d}\). Include your steps.

    3. Suppose demand shifts to the right by 2 units: that is, for any given price, people are willing to buy two more units than they were previously. So now we have that demand is given by \(q = a - bp + 2\). What is the change to equilibrium price and quantity exchanged? Will price and quantity exchanged increase?

  2. Perfect elasticity and inelasticity: Remember that elasticity is escape. If you have elastic demand for a good, that means you can easily escape into another market when the price increases (and easily come back when the price falls). But if you have inelastic demand, you can’t escape the market when the price increases: you’re stuck paying higher amounts. The same idea holds for elastic supply: if producers have elastic supply for a good, they can easily escape into other markets when the price is too low (they can plant soybeans instead of corn if the price of corn is low). If producers have inelastic supply, they can’t easily escape into other markets, and are stuck having to accept low prices for their goods.

    1. Which of the following two goods is more likely to be elastically demanded? That is, for which good would it be easier for consumers to escape? Demand for tangerines, or demand for fruit?

    2. Which of the following two goods is more likely to be elastically demanded? Demand for exxon gasoline at the corner of 7th and Grand, or demand for gasoline in the entire city?

    3. After more employers allow employees to telecommute, will the demand curve for cars be more elastic or more inelastic?

    4. Let \(p\) be on the y-axis and suppose one side of the market (we’ll call it side A) is perfectly inelastic, or close to it. That means side A is (choose one: horizontal/vertical). Then side A would solely determine equilibrium (choose one: price/quantity) and the other side of the market would solely determine equilibrium (choose one: price/quantity). Intuitively, this is what’s going on: if there’s a fixed supply of houses, (choose one: supply/demand) is perfectly inelastic, and there will never be more houses exchanged in equilibrium. The willingness of (consumers to pay/suppliers to sell) completely determines the market price of housing. This is realistic in the short run.

    5. Let \(p\) be on the y-axis and suppose one side of the market (we’ll call it side B) is perfectly elastic, or close to it. That means side B is (choose one: horizontal/vertical). Then side B would solely determine equilibrium (choose one: price/quantity) and the other side of the market would solely determine equilibrium (choose one: price/quantity). Intuitively, this is what’s going on: suppose paperclip suppliers can make any amount of paperclips at a total cost of just 1 cent per paperclip. If they can sell paperclips at 2 cents a piece, they are basically willing to supply infinity. But if they sell paperclips at anything under 1 cent a piece, they won’t be willing to supply any. Then supply for paperclips is perfectly (choose one: elastic/inelastic). Any equilibrium will have paperclips being sold at 1 cent a piece, and the quantity of paperclips exchanged will completely depend on how many units (choose one: sellers are willing to sell/buyers are willing to buy) at that price.

    6. Going back to problem 1, if the demand curve is perfectly inelastic and the supply curve is perfectly elastic, what are \(b\) and \(d\)? Using your answer to 1c, how much will equilibrium price and quantity exchanged increase if the demand curve shifts to the right by 2?