Microeconomics Corso E

1
MicroeconomicsCorso E

• John Hey

2
Chapter 5

• We know that the indifference curves of an
  individual are given by the preferences of that
  individual.
• We know that the demand and supply curves depend
  upon the preferences.
• Up till now we have assumed a particular kind of
  preferences quasi-linear where the
  indifference curves are vertically parallel.

3
Chapter 5

• Today we study other types of preference.
• Economists have made a catalogue of the types
  that we observe in reality.
• We cannot study all these types.
• We make an important selection Perfect
  Substitutes, Perfect Complements, Cobb-Douglas,
  Stone-Geary.
• The important thing demand and supply depend on
  the preferences.

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Chapter 5

• We first make a small generalisation we work
  with two goods (instead of one good and money)
  the quantity of good 1 on the horizontal axis and
  the quantity of good 2 on the vertical axis.
• Of course, a special case is when good 2 is money
  (and then its price is 1).

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Chapter 5

• Representation of preferences with utility
  functions.
• Suppose indifference curves are given by g(q1,q2)
  constant
• where the higher the constant the happier the
  individual. Then we can represent these
  preferences by the utility function
• U(q1,q2) g(q1,q2)
  or by
• U(q1,q2) fg(q1,q2) for any increasing
  function f..
• Note that this utility function is not unique.

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Chapter 5

• Perfect substitutes 11
• An indifference curve is given by
• q1 q2 constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) q1 q2
• Or
• U(q1 , q2) f(q1 q2) for any f(.)

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Chapter 5

• Perfect substitutes 12
• An indifference curve is given by
• q1 q2/2 constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) q1 q2/2
• Or
• U(q1 , q2) f(q1 q2/2) for any f(.)

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Chapter 5

• Perfect substitutes 1a
• An indifference curve is given by
• q1 q2/a constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) q1 q2/a
• Or
• U(q1 , q2) f(q1 q2/a) for any f(.)

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Chapter 5

• Perfect complements 1 with 1
• An indifference curve is given by
• min(q1, q2) constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) min(q1, q2)
• Or
• U(q1 , q2) fmin(q1, q2) for any f(.)

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Chapter 5

• Perfect complements 1 with 2
• An indifference curve is given by
• min(q1, q2/2) constant
• Hence a utility function which represents these
  preferences is
• U(q1, q2) min(q1, q2/2)
• Or
• U(q1, q2) fmin(q1, q2/2) for any f(.)

11
Chapter 5

• Perfect complements1 with a
• An indifference curve is given by
• min(q1, q2/a) constant
• Hence a utility function which represents these
  preferences is
• U(q1, q2) min(q1, q2/a)
• Or
• U(q1, q2) fmin(q1, q2/a) for any f(.)

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Chapter 5

• Cobb-Douglas with parameter a
• An indifference curve is given by
• q1a q2(1-a) constant
• Or by
• a ln(q1 ) (1-a) ln(q2 ) constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) q1a q2(1-a)
• or
• U(q1 , q2) a ln(q1 ) (1-a) ln(q2 )
• or
• U(q1 , q2) f(q1a q2(1-a)) for any f(.)

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Chapter 5

• Stone-Geary with parameters a, s1 and s2
• An indifference curve is given by
• (q1-s1)a(q2 s2)(1-a) constant
• Or by
• a ln(q1s1) (1-a) ln(q2 s2) constant
• Hence a utility function which represents these
  preferences is
• U(q1 , q2) (q1s1)a (q2 s2 )(1-a)
• or
• U(q1 , q2) a ln(q1s1) (1-a) ln(q2 )
• or
• U(q1 , q2) f(q1s1)a (q2s2)(1-a) for any f(.)

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Chapter 5

• In the book you can find all the formula.
• It is not necessary to remember the formulas
• in the exams there will be an Aide-Memoire.
• Note the important result
• Preferences can be represented by a utility
  function but this is not unique.

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Exam 3 of 8 september 2008

• Consider a market for a hypothetical good in
  which there are a number of buyers and sellers,
  each of which wants to buy or sell one unit of
  the good. Assume that a buyer who is indifferent
  about buying always buys and a seller who is
  indifferent about selling always sells. The
  reservation prices are given below, first for the
  buyers and then for the sellers.
• Buyers 10, 10, 8, 5, 4. Sellers 4, 5, 5, 7, 2,
  4.
• Question 1 What is the competitive equilibrium
  price (specify a range if more than one
  equilibrium price)?
• Question 2 What is the quantity exchanged in the
  competitive equilibrium?
• Question 3 What is the maximum total surplus
  generated in the market?
• Question 4 What is the maximum number of trades
  (not necessarily with the same price)?

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Exam 3 of 8 september 2008

• Consider a market for a hypothetical good in
  which there are a number of buyers and sellers,
  each of which wants to buy or sell one unit of
  the good. Assume that a buyer who is indifferent
  about buying always buys and a seller who is
  indifferent about selling always sells. The
  reservation prices are given below, first for the
  buyers and then for the sellers.
• Buyers 10, 10, 8, 5, 4. Sellers 4, 5, 5, 7, 2,
  4.
• Question 1 What is the competitive equilibrium
  price (specify a range if more than one
  equilibrium price)? Answer 5.
• Question 2 What is the quantity exchanged in the
  competitive equilibrium? Answer 4.
• Question 3 What is the maximum total surplus
  generated in the market? Answer 18.
• Question 4 What is the maximum number of trades
  (not necessarily with the same price)? Answer 5.

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Chapter 5

• Goodbye!!