Buying and Selling

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Buying and Selling
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• It is often the case that the consumers income
  is not some fixed amount but is given by the
  value of what he has to sell.
• This is typically the case for farmers who
  produce food but wish to consume not only food
  but also non-food products. Their income is given
  by the value of the food they produce.

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Net and gross demands

• Suppose the consumer starts with endowments,
  noted (?1, ?2).
• The gross demand for good 1 is how much the
  consumer will end up consuming.
• The net demand is hpw much he will have to buy or
  sell, given his initial endowments, to actually
  consume his gross demand.
• If (x1, x2) are the gross demands, (x1-?1, x2-?2)
  are the net demands.

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The budget constraint with endowments

• The consumers budget is given by the value of
  his endowment
• If (x1-?1) is positive, the consumer is a net
  buyer, or a net demander of good 1. if it is
  negative, hes a net seller or net supplier.

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• Insert graph.

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Changing the endowment

• If the endowment changes so that the value of the
  endowment changes, prices being constant, the
  budget constraint shift accordingly.
• A higher value endowment will always be
  preferred.
• If (?1, ?2) is such that p1?1, p2?2gt p1?1,
  p2?2, then the new budget set contains the old
  one.

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• Insert figure

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Price changes, for given endowment.
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Gross demand net demand and net supply

• Insert figure 9.6

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Slutsky revisited

• In this case, income is not fixed anymore. A
  change in price will directly affect the value of
  the endowment, so that the total effect of a
  change in price on the demand of a good will be
  as before the sum of a substitution effect and an
  income effect reflecting the change in purchasing
  power, an income effect reflecting the change
  in the value of the endowment.

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• We have
• Endowment income effect change in demand when
  income changes x change in income (value of
  endowment) when prices changes.

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• In total
• Even for a normal good, the sign of the income
  effect is not necessarily negative anymore. It
  depends whether the consumer is net buyer or net
  seller of the good.

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Labour supply

• If the consumer has a fixed non labour income M
  and earns wage w for each hour worked.
• His budget constraint can be written
• Where C upper bar and L upper bar can be seen as
  endowment in consumption and time.

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Wage increase

• Assuming leisure is a normal good. A wage
  increase does two things it increases the
  opportunity cost of leisure and the returns to
  working increase.
• The increase in the cost of leisure provokes the
  usual substitution effect against leisure the
  usual income effect such that leisure demand will
  decrease, hence labour supply should increase.
  Nevertheless, the increase in wage also increases
  the income and hence increase the demand for all
  normal goods, including leisure.
• What is the net effect?

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• The Slutsky equation would look like this
• The substitution effect is negative, but the
  total income effect is positive. Hence total
  effect is ambiguous.

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• Insert curve.

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