Consumer Theory: Objectives

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Consumer Theory Objectives

• Derive and understand
• How Rational People make Choices
• 2. How this should Guide our own Decisions

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Consumer Behavior

• We are now studying the foundations of demand
  theory.
• - Why do demand curves slope downward?
• - Why do they shift with changes in prices for
  substitutes and complements?
• - Why do they shift with changes in income?
• - What normative significance can we give to
  demand based on underlying consumer preferences?

3
Preferences

• Preferences are complete if for any two
  consumption points x and x', either x x' (x is
  at least as good as x') or x' x (x' is at
  least as good as x), or both.
• Preferences are reflexive if for all x, x x (x
  is at least as good as itself).

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Preferences

• Preferences are transitive if x x' and x' x''
  implies that x x''.
• Preferences are strongly monotonic if for any two
  commodity points x (x1, x2) and x' (x'1, x'2)
  if x1 x'1, x2 x'2, and x ? x', then x' is
  preferred to x.
• Preferences are continuous if the set of all
  choices that are at least as good as a choice x'
  and the set of all choices that are no better
  than x' are both closed sets.

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From Preferences to Utility Function

• Representation Theorem
• If a consumer has a preference relation that is
  complete, reflexive, transitive, strongly
  monotonic, and continuous, then these preferences
  can be represented by a continuous utility
  function u(x) such that u(x) gt u(x') if and only
  if x gt x'.

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Properties of Consumer Preferences

• Complete
• Transitive
• More is better (non-satiation)
• Continuity (technical assumption)
• Strict Convexity (technical assumption prefer
  averages to extremes if agtc and bgtc, then
  wa(1-w)bgtc for 0ltwlt1).

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Preference Maps
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Indifference Curves
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Properties of Indifference Curves

• Bundles further from the origin are preferred to
  those closer to the origin.
• There is an indifference curve through every
  bundle.
• Indifference curves cannot cross.
• Indifference curves slope downward.
• Indifference curves cannot be thick.

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Properties of Indifference Curves
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• Consider the following (ordinal) utility function
  for Food (F) and Clothing ( C ) for Emily
• U(F,C) FC
• Each indifference curve gives the combinations of
  F and C that yield the same level of satisfaction
  to Emily (e.g. 25, 50, 100).
• Think of slicing the utility function at
  different levels and projecting into F,C space.
• Her marginal rate of substitution of Food for
  Clothing is given by the slope at any point on an
  indifference curve
• MRSFC - dC/dFU a constant
• MRSFC is the amount of Clothing Emily is
  willing to give up for one addition unit of food,
  holding utility constant

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Marginal rate of substitution of F for C is
equal to the marginal utility of F divided by the
marginal utility of C at a point on
an indifference curve, i.e holding utility
constant (dU 0) dU(F,C) UFdF UCdC
0 Where UF Marginal utility of F UC Marginal
utility of C UF/Uc -dC/dFU constant
MRSFC For U FC UF C, UC F -gt MRSFC
C/F Set U 25 C 5, F 5 MRSFC 5/5 1 C
2.5, F 10 MRSFC 2.5/10 0.25 Declining
MRS of F for C as F increases holding U
constant Declining marginal utility of Food as F
increases U constant