Chapter TwoConsumption Choice SetsBudget ConstraintsSlide 4Slide 5Slide 6Slide 7Budget Set and Constraint for Two CommoditiesSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Budget Constraint for Three CommoditiesBudget Set for Three CommoditiesSlide 18Slide 19Slide 20Slide 21Slide 22Budget Sets & Constraints; Income and Price ChangesHow do the budget set and budget constraint change as income m increases?Higher income gives more choiceHow do the budget set and budget constraint change as income m decreases?Slide 27Budget Constraints - Income ChangesSlide 29Slide 30Budget Constraints - Price ChangesHow do the budget set and budget constraint change as p1 decreases from p1’ to p1”?Slide 33Slide 34Slide 35Slide 36Uniform Ad Valorem Sales TaxesSlide 38Slide 39Slide 40Slide 41Slide 42Slide 43The Food Stamp ProgramSlide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Budget Constraints - Relative PricesSlide 54Slide 55Slide 56Slide 57Shapes of Budget ConstraintsSlide 59Shapes of Budget Constraints - Quantity DiscountsSlide 61Shapes of Budget Constraints with a Quantity DiscountSlide 63Slide 64Shapes of Budget Constraints with a Quantity PenaltyShapes of Budget Constraints - One Price NegativeSlide 67Slide 68More General Choice SetsSlide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Chapter TwoBudgetary and Other Constraints on ChoiceConsumption Choice SetsA consumption choice set is the collection of all consumption choices available to the consumer.What constrains consumption choice?–Budgetary, time and other resource limitations.Budget ConstraintsA consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, … , xn).Commodity prices are p1, p2, … , pn.Budget ConstraintsQ: When is a consumption bundle (x1, … , xn) affordable at given prices p1, … , pn?Budget ConstraintsQ: When is a bundle (x1, … , xn) affordable at prices p1, … , pn?A: When p1x1 + … + pnxn  mwhere m is the consumer’s (disposable) income.Budget ConstraintsThe bundles that are only just affordable form the consumer’s budget constraint. This is the set{ (x1,…,xn) | x1  0, …, xn  and p1x1 + … + pnxn  m }.Budget ConstraintsThe consumer’s budget set is the set of all affordable bundles;B(p1, … , pn, m) ={ (x1, … , xn) | x1  0, … , xn 0 and p1x1 + … + pnxn  m }The budget constraint is the upper boundary of the budget set.Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m. m /p1m /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p2m /p1Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1Just affordablem /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1Just affordableNot affordablem /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1AffordableJust affordableNot affordablem /p2Budget Set and Constraint for Two Commoditiesx2x1Budget constraint isp1x1 + p2x2 = m.m /p1BudgetSet the collection of all affordable bundles.m /p2Budget Set and Constraint for Two Commoditiesx2x1p1x1 + p2x2 = m is x2 = -(p1/p2)x1 + m/p2 so slope is -p1/p2.m /p1BudgetSetm /p2Budget ConstraintsIf n = 3 what do the budget constraint and the budget set look like?Budget Constraint for Three Commoditiesx2x1x3m /p2m /p1m /p3p1x1 + p2x2 + p3x3 = mBudget Set for Three Commoditiesx2x1x3m /p2m /p1m /p3{ (x1,x2,x3) | x1  0, x2  0, x3 0 and p1x1 + p2x2 + p3x3  m}Budget ConstraintsFor n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean?xppxmp21212 Budget ConstraintsFor n = 2 and x1 on the horizontal axis, the constraint’s slope is -p1/p2. What does it mean?Increasing x1 by 1 must reduce x2 by p1/p2.xppxmp21212 Budget Constraintsx2x1Slope is -p1/p2+1-p1/p2Budget Constraintsx2x1+1-p1/p2Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.Budget Constraintsx2x1Opp. cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p2/p1 units foregone of commodity 1. -p2/p1+1Budget Sets & Constraints; Income and Price ChangesThe budget constraint and budget set depend upon prices and income. What happens as prices or income change?How do the budget set and budget constraint change as income m increases?Originalbudget setx2x1Higher income gives more choiceOriginalbudget setNew affordable consumptionchoicesx2x1Original andnew budgetconstraints areparallel (sameslope).How do the budget set and budget constraint change as income m decreases?Originalbudget setx2x1How do the budget set and budget constraint change as income m decreases?x2x1New, smallerbudget setConsumption bundlesthat are no longeraffordable.Old and newconstraintsare parallel.Budget Constraints - Income ChangesIncreases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.Budget Constraints - Income ChangesIncreases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.Decreases in income m shift the constraint inward in a parallel manner, thereby shrinking the budget set and reducing choice.Budget Constraints - Income ChangesNo original choice is lost and new choices are added when income increases, so higher income cannot make a consumer worse off.An income decrease may (typically will) make the consumer worse off.Budget Constraints - Price ChangesWhat happens if just one price decreases?Suppose p1 decreases.How do the budget set and budget constraint change as p1 decreases from p1’ to p1”?Originalbudget setx2x1m/p2m/p1’m/p1”-p1’/p2How do the budget set and budget constraint change as p1 decreases from p1’ to p1”?Originalbudget setx2x1m/p2m/p1’m/p1”New affordable choices-p1’/p2How do the budget set and budget constraint change as p1 decreases from p1’ to p1”?Originalbudget setx2x1m/p2m/p1’m/p1”New affordable choicesBudget constraint pivots; slope flattens from -p1’/p2 to -p1”/p2-p1’/p2-p1”/p2Budget Constraints -