Chapter 16 Equilibrium

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• 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.

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• 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).

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

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• 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 plt p, typically D(p)gtS(p), some suppliers
  realize that they can sell at a higher price to
  satisfy disappointed consumers. This results a
  price increase pressure.

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• When pgt p, typically D(p)ltS(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 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.

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• 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 pt since what matters is the price
  that the suppliers can put into their pockets.

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• 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?

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Fig. 16.3
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Fig. 16.4
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• 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.

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Fig. 16.5
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• 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.

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Fig. 16.6
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• 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 MWPgtMWS,
  there is a deadweight loss (should be produced,
  but are not produced).

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• 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 MWPgtMWS, 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.

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Fig. 16.7
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• It is clear that market equilibrium makes
  MWPMWS.
• What about looking at consumers only? If
  MWP1gtMWP2 (say 5gt4), 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 MWP1MWP2 because
  MWP1pMWP2.

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• Look at producers only, if MWS1gtMWS2 (say 5gt4),
  then producer 2 can produce a unit of good in
  concern more and this increases 2s cost by 4.
  Producer 1 can reduce its production by a unit
  and this decreases 1s 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 MWS1MWS2 because MWS1pMWS2.