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Consumer Choice

Consumer Choice. Preferences, Budgets, and Optimization. The Consumer’s Problem. Preferences A consumer prefers one good (or bundle of goods) to another. Income or Budget Income (Budget) limits a consumer’s buying Consumers are Rational

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Consumer Choice

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  1. Consumer Choice Preferences, Budgets, and Optimization

  2. The Consumer’s Problem • Preferences • A consumer prefers one good (or bundle of goods) to another. • Income or Budget • Income (Budget) limits a consumer’s buying • Consumers are Rational • A consumer seeks the maximum satisfaction from consuming goods and services • Where consumption is limited by income

  3. Preferences • Completeness • All pairs of goods (bundles) are ranked • Transitivity • A > B and B > C, then A > C • Goods are “good” (not “bad”) • More is always preferred to less • Described by Indifference Curves • All combinations of goods that yield the same satisfaction (or “utility”)

  4. Shapes of Indifference Curves • Convex • Goods are gross substitutes (downward slope) • Diminishing marginal rate of substitution • Special cases • Perfect substitutes • Perfect Complements • Impossibilities • Intersecting indifference curves • Upward sloping (one “good” is a “bad”) • Circular (Bliss point)

  5. Budget Line • All income is spent on goods • PYY + PXX = I • All combinations of goods that a consumer can afford to buy • Equation for the budget line • Y = (I/PY) – (PX/PY)X • Shifts in the budget line • Changes in Prices • Changes in Income

  6. Solutions to the Consumer’s Problem • A combination of goods on the highest indifference curve the consumer can afford to reach • Budget line tangent to indifference curve • Slope of budget line = slope of indifference curve • -PX/PY = ΔY/ΔX = -MUX/MUY = -MRS • -PY/PX = -MUX/MUYimplies • PY/PX= MUX/MUY implies • MUX / PX = MUY / PY or • Marginal utility per dollar equal across goods

  7. Special Cases • Perfect substitutes • Corner solutions • Perfect complements • No response to price changes • Non-convexities • Gaps or jumps • Corner solutions

  8. Changes in Income and Prices • Income Changes • Budget line shifts out for increase in income • Budget line shifts in for decrease in income • Changes in the price of one good • Price decrease • Budget line shifts out along axis for that good • Price increase • Budget line shifts in along axis for that good • Substitution and Income effects • Revealed Preference

  9. Utility Functions • Suppose U = 2FC is a consumer’s utility function for food (F) and clothes (C) • Is this a proper utility function? • Increasing in F and C? • Indifference curves downward sloping? • Diminishing MRS? • Define an Indifference Curve: 2FC =100 • C = 100/F, ∆C/∆F = -100/F2 < 0 • MRS = 100/F2

  10. Example: Consumer Choice • Max U = 2FC • Subject to $500 = $5F + $10C • Find MUF/MUC = PF/PC • MUF/MUC = 2C/2F = C/F • C/F = $5/$10 = ½, or C = ½ F • Substitute into constraint • $500 = $5F + $10(½ F) = $10F • F = 50, C = ½ F = 25

  11. A Note on Derivatives • For any function U = DXaYb • MUX = ∂U/∂X = aDXa-1Yb • MUY= ∂U/∂Y = bDXaYb-1 • MUX/MUY = (a/b)(Y/X) • (aDXa-1Yb )/(bDXaYb-1) = (a/b)X-1Y1 • If a + b = 1, then U = XaY1- a • MUX/MUY = [(a/(1- a)](Y/X) • Known as the Cobb-Douglas functional form • Same solutions as lnU = lnD +alnX + blnY

  12. Exercise • U = F¼C¾ • PF = $2.00 PC = $3.00 • Income = $120.00 • Find the optimal quantities of food and clothes for this consumer • Graph the budget line • Illustrate your answer on this graph

  13. Substitution and Income Effects • Substitution Effect: ∂X/∂PX|U=U* • The change in the quantity demanded holding utility fixed • Income Effect: (∂X/∂I)(∂I/∂PX) • The change in the quantity demanded when utility changes, holding relative prices fixed • Slutsky Equation • dX/dPX = ∂X/∂PX|U=U* + (∂X/∂I)(∂I/∂PX) • From budget constraint (∂I/∂PX) = X • dX/dPX = ∂X/∂PX|U=U*- X(∂X/∂I)

  14. Deriving Demand Curves • Individual demand • Change prices and record quantites • Graph price quantity combinations • Market demand • Add individual demand curves horizontally • Total quantity demanded at each price

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