Chapter 16 Equilibrium Defer the discussion of the market supply curve to later chapters and only denote it by S(p): at any given price p, how many units the suppliers are willing to supply. We have the market demand D(p) and the market supply S(p). Basically the market curve is the horizontal sum of the individual curves. Now we can determine the market equilibrium.

Solve D(p*)=S(p*). Then at p* (taking price as given), consumers choose the best they can afford (utility maximization) and this results the quantity demanded by all consumers D(p*). Similarly, at p* (taking price as given), producers choose the best they can produce (profit maximization) and this results the quantity supplied by all suppliers S(p*).

Furthermore, D(p*)=S(p*) implies that market clears. So we have an equilibrium.

The idea is, at the equilibrium price, consumers max utilities, producers max profits, and the market clears. The equilibrium price is determined by all, yet any individual is small so that when making a choice, he takes the price as given. When p S(p), some suppliers realize that they can sell at a higher price to satisfy disappointed consumers. This results a price increase pressure.

When p> p*, typically D(p)<S(p), some suppliers are unable to sell and they try to undercut the current price. This results a price decrease pressure. The comparative statics is to see how the equilibrium changes when the demand or the supply changes. Look at an example: a quantity tax on a good. A quantity tax is a tax levied per unit of quantity bought or sold.

As it suggests, either suppliers or consumers are supposed to pay the tax t. So whether the tax incidence (who gets to pay and how much) will be the same in the two cases? Consider the case where the supplier has to pay. Suppose at p, before the tax, suppliers supply x. After the tax, if the suppliers supply x, the price must be p+t since what matters is the price that the suppliers can put into their pockets.

Alternatively, suppose consumers have to pay the price. Suppose at p, before the tax, consumers consume x. After the tax, if consumers still consume x, the price must be p-t since what matters is the price that the consumers have to take out of their pockets. The two cases give you same results?

Fig. 16.3

Fig. 16.4

We can also talk about the tax incidence a bit. Imagine two extreme cases. One where the supply is perfectly inelastic, the other where it is perfectly elastic. Suppose before the tax the equilibrium price is p. In the former case, no way you can get consumers to take more than p out of pockets. So producers pay all the tax. In the latter case, no way you can make producers to take in less than p, so consumers pay all the tax.

Fig. 16.5

These two extreme cases suggest that the tax incidence has a lot to do with the elasticities of demand and supply. When it is more like the former, producers pay most of the tax. When it is more like the latter, consumers pay most of the tax.

Fig. 16.6

Can also talk about the welfare loss of a tax. A quantity tax t makes the marginal willingness to pay higher than the marginal willingness to supply by t. So for all units where MWP>MWS, there is a deadweight loss (should be produced, but are not produced).

Alternatively, can calculates the change of consumers’ surplus and producers’ surplus to reach the same conclusion. So why on earth is the market equilibrium so efficient (Pareto efficient)? Think about what Pareto efficiency means. If MWP  MWS, it is not efficient because say if MWP>MWS, at least a consumer and a producer can strike a price inbetween to produce an additional unit and the consumer is better off while the producer is making more profit.

Fig. 16.7

It is clear that market equilibrium makes MWP=MWS. What about looking at consumers only? If MWP 1 >MWP 2 (say 5>4), then consumer 1 can buy a unit of good in concern from consumer 2 at the price of 4.5. This will make both 1 and 2 better off. Market equilibrium achieves MWP 1 =MWP 2 because MWP 1 =p=MWP 2.

Look at producers only, if MWS 1 >MWS 2 (say 5>4), then producer 2 can produce a unit of good in concern more and this increases 2’s cost by 4. Producer 1 can reduce its production by a unit and this decreases 1’s cost by 5. So in total, a cost of 1 dollar is saved and this saved cost (saved resource) can be used to produce. Market achieves MWS 1 =MWS 2 because MWS 1 =p=MWS 2.