Microeconomia Corso E

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MicroeconomiaCorso E

• John Hey

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Chapter 7 what do we know?

• Individual with given preferences and income m
  faces prices p1 and p2 for two goods1 and 2.
• He or she is going to allocate his or her income
  buying quantities q1 and q2 of the two goods.
• What he or she buys/demands depends on her
  preferences.
• The relationship between q1 and q2 (the
  endogenous variables) and m, p1 and p2 (the
  exogenous variables) is called the demand
  function.

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Chapter 7 what do we know?

• Cobb-Douglas with parameter a
• q1 am/p1 and q2 (1-a)m/p2
• Perfect Substitutes 1a
• if p1/p2 lt a then q1 m/p1 q2 0
• if p1/p2 a then....
• if p1/p2 gta then q1 0 q2 m/p2
• Perfect Complements 1 with a
• q1m/(p1 ap2) and q2 am/(p1 ap2)
• These formulas are in the promemoria.

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The optimal point

• With indifference curves that are smoothly
  convex...
• ... the optimal point is the point of tangency
  between the budget line and the highest possible
  indifference curve...
• ...at which the relative price (the slope of the
  budget line) is equal to the marginal rate of
  substitution (the slope of the indifference
  curve).

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Are we economists or not?

• Economists are ...
• ... lazy ...
• ... efficient.
• In Chapter 7 income is in the form of money m. In
  Chapter 6, income is in the form of endowments of
  the two goods e1 and e2.
• What is the money value of this endowment? Call
  it m.
• We have m p1e1 p2e2.
• Let us just replace m with p1e1 p2e2
  everywhere!

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From Chapter 7 we have

• Cobb-Douglas with parameter a
• q1 a( m )/p1 and
• q2 (1-a)( m )/p2
• Perfect Substitutes 1a
• if p1/p2 lt a then q1 ( m )/p1
  and q2 0
• if p1/p2 a then....
• if p1/p2 gta then q1 0 and q2 ( m
  )/p2
• Perfect Complements 1 with a
• q1 ( m )/(p1 ap2) and
• q2 a( m )/(p1 ap2)

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Hence for Chapter 6

• Cobb-Douglas with parameter a
• q1 a(p1e1 p2e2)/p1 and
• q2 (1-a)(p1e1 p2e2)/p2
• Perfect Substitutes 1a
• if p1/p2 lt a then q1 (p1e1 p2e2)/p1 and
  q2 0
• if p1/p2 a then....
• if p1/p2 gta then q1 0 and q2 (p1e1
  p2e2)/p2
• Perfect Complements 1 with a
• q1 (p1e1 p2e2)/(p1 ap2) and
• q2 a(p1e1 p2e2)/(p1 ap2)

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Chapter 6

• Finished!

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Chapter 6

• We consider an individual who starts with an
  endowment of the two goods.
• We find his gross demands for the two goods.
• We analyse how these demands change when the
  prices and his income change. (These variables
  are exogenous for the individual).
• These are called comparative static exercises.

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Chapter 6

• We start with an individual with Cobb-Douglas
  preferences with parameter a 0.5.
• The Maple/html file contains other examples
• Cobb-Douglas with parameter a 0.3
• Stone-Geary
• Perfect Substitutes
• Perfect Complements.
• The shape of the demand curve depends upon the
  preferences.

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Chapters 6 and 7

• We use two spaces
• The first to show the preferences of the
  individual and the budget line
• q1 on the horizontal axis and q2 on the vertical
  axis.
• The second to show the effect of changes in an
  exogenous variable on the demand
• q1 (and q2 ) on the horizontal axis and the
  exogenous variable on the vertical axis.

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Chapter 6

• The indifference curves are given by the
  preferences.
• The budget constraint is given by the
  individuals income and the prices of the two
  goods.
• We denote by (e1, e2) the endowment and by (q1,
  q2) the quantities chosen to consume. The budget
  line is given by the equation
• p1q1 p2 q2 p1e1 p2e2
• This is a line with slope
• - p1/ p2
• which passes through the endowment point.

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q2
the budget line p1 q1 p2 q2 p1 e1 p2 e2
(p1 e1 p2 e2)/p2
has slope -p1/p2
and passes through (e1,e2)
e2
X
(p1 e1 p2 e2 )/p1
q1
e1
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Cobb-Douglas with parameter a 0.5 U(q1, q2)
q10.5q20.5
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Chapter 6 results

• Cobb-Douglas with parameter a
• q1 a(p1e1p2e2)/p1 e q2
  (1-a)(p1e1p2e2)/ /p2
• Perfect substitutes 1a
• if p1/p2 lt a then q1 (p1e1p2e2)/p1 q2 0
• if p1/p2 a then....
• if p1/p2 gta then q1 0 q2 (p1e1p2e2)/p2
• Perfetti complements 1 with a
• q1 (p1e1p2e2)/(p1 ap2) e
• q2 a(p1e1p2e2)/(p1 ap2)

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Chapter 6

• Goodbye!

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