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Consumer Theory: Objectives

Consumer Theory: Objectives. Derive and understand: How Rational People make Choices 2. How this should Guide our own Decisions. Consumer Behavior. We are now studying the foundations of demand theory. - Why do demand curves slope downward?

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Consumer Theory: Objectives

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  1. Consumer Theory: Objectives Derive and understand: • How Rational People make Choices 2. How this should Guide our own Decisions

  2. 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 arecomplete 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).

  4. 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.

  5. 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) > u(x') if and only if x > x'.

  6. Properties of Consumer Preferences • Complete • Transitive • More is better (non-satiation) • Continuity (technical assumption) • Strict Convexity (technical assumption: prefer averages to extremes: if a>c and b>c, then wa+(1-w)b>c for 0<w<1).

  7. Preference Maps

  8. Indifference Curves

  9. 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.

  10. Properties of Indifference Curves

  11. 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/dF|U = a constant [MRSFC is the amount of Clothing Emily is willing to give up for one addition unit of food, holding utility constant]

  12. • 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/dF|U = constant = MRSFC • For U = FC: UF = C, UC = F -> 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

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