【文章內(nèi)容簡介】 is is the set { (x1,…,x n) | x1 ? 0, …, x n ??? and p1x1 + … + p nxn = m }. 78 Budget Constraints ?The consumer‘s budget set (預(yù)算集）is the set of all affordable bundles。 B(p1, … , p n, m) = { (x1, … , x n) | x1 ? 0, … , x n ??0 and p1x1 + … + p nxn ? m } ?The budget constraint is the upper boundary of the budget set. 79 Budget Set and Constraint for Two Commodities x2 x1 Budget constraint is p1x1 + p2x2 = m. m /p1 m /p2 80 Budget Set and Constraint for Two Commodities x2 x1 Budget constraint is p1x1 + p2x2 = m. m /p2 m /p1 81 Budget Set and Constraint for Two Commodities x2 x1 Budget constraint is p1x1 + p2x2 = m. m /p1 Just affordable m /p2 82 Budget Set and Constraint for Two Commodities x2 x1 Budget constraint is p1x1 + p2x2 = m. m /p1 Just affordable Not affordable m /p2 83 Budget Set and Constraint for Two Commodities x2 x1 Budget constraint is p1x1 + p2x2 = m. m /p1 Affordable Just affordable Not affordable m /p2 84 Budget Set and Constraint for Two Commodities x2 x1 p1x1 + p2x2 = m is x2 = (p1/p2)x1 + m/p2 so slope is p1/p2. m /p1 Budget Set m /p2 85 Budget Constraints x2 x1 +1 p1/p2 Opp. cost of an extra unit of modity 1 is p1/p2 units foregone of modity 2. 86 Budget Constraints x2 x1 Opp. cost of an extra unit of modity 1 is p1/p2 units foregone of modity 2. And the opp. cost of an extra unit of modity 2 is p2/p1 units foregone of modity 1. p2/p1 +1 87 預(yù)算集特點 –在價格、收入給定的條件下，要增加 1單位 x1的消費就必須減少 p1/p2的消費。 –因此它還表示兩種商品之間的 市場替代比率 或者說是相互之間的 機會成本。 88 ?影響預(yù)算集的因素： Ine and Price 89 Higher ine gives more choice Original budget set New affordable consumption choices x2 x1 Original and new budget constraints are parallel (same slope). 90 How do the budget set and budget constraint change as ine m decreases? Original budget set x2 x1 91 How do the budget set and budget constraint change as ine m decreases? x2 x1 New, smaller budget set Consumption bundles that are no longer affordable. Old and new constraints are parallel. 92 Budget Constraints Price Changes ?What happens if just one price decreases? ?Suppose p1 decreases. 93 How do the budget set and budget constraint change as p1 decreases from p1’ to p1”? Original budget set x2 x1 m/p2 m/p1‘ m/p1‖ p1‘/p2 94 How do the budget set and budget constraint change as p1 decreases from p1’ to p1”? Original budget set x2 x1 m/p2 m/p1‘ m/p1‖ New affordable choices p1‘/p2 95 How do the budget set and budget constraint change as p1 decreases from p1’ to p1”? Original budget set x2 x1 m/p2 m/p1‘ m/p1‖ New affordable choices Budget constraint pivots。 slope flattens from p1‘/p2 to p1‖/p2 p1‘/p2 p1‖/p2 96 97 Relative Prices（計價物） ?The budget line p1x1 + p2x2 = m ?Can be equivalently expressed as ? p1/p2 x1 + x2 = m/p2 ?p2=1: numeraire price(基準價格 ), it defines all prices relative to p2． ?x2 is posite good, which is measured in dollars to be spent on goods other than good 1. 98 政府政策如何影響消費者預(yù)算約束？ 99 Uniform Ad Valorem Sales Taxes ?An ad valorem sales tax levied at a rate of t ?increases all prices by tp from p to (1+t)p. 100 Uniform Ad Valorem Sales Taxes ?A uniform sales tax levied at rate t changes the constraint from p1x1 + p2x2 = m to (1+t)p1x1 + (1+t)p2x2 = m 101 Uniform Ad Valorem Sales Taxes ?A uniform sales tax levied at rate t changes the constraint from p1x1 + p2x2 = m to (1+t)p1x1 + (1+t)p2x2 = m . p1x1 + p2x2 = m/(1+t). 102 Uniform Ad Valorem Sales Taxes x2 x1 mp2mp1p1x1 + p2x2 = m 103 Uniform Ad Valorem Sales Taxes x2 x1 mp2mp1p1x1 + p2x2 = m p1x1 + p2x2 = m/(1+t) mt p( )1 1?mt p( )1 2?104 Uniform Ad Valorem Sales Taxes x2 x1 mt p( )1 2?mp2mt p( )1 1?mp1Equivalent ine loss is m m t t t m? ? = ?1 1105 Uniform Ad Valorem Sales Taxes x2 x1 mt p( )1 2?mp2mt p( )1 1?mp1A uniform ad valorem sales tax levied at rate t is equivalent to an ine tax levied at rate tt1? .106 The Food Stamp Program ?Food stamps are coupons that can be legally exchanged only for food. 107 The Food Stamp Program ?Suppose m = $100, pF = $1 and the price of ―other goods‖ is pG = $1. ?The budget constraint is then F + G =100. 108 The Food Stamp Program G F 100 100 F + G = 100。 before stamps. 109 The Food Stamp Program G F 100 100 F + G = 100: before stamps. 110 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 40 111 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 The family‘s budget set is enlarged. 40 112 The Food Stamp Program ?What if food stamps can be traded on a black market for $ each? 113 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued. 140 120 Budget constraint with black market trading. 40 114 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget constraint after 40 food stamps issued. 140 120 Black market trading makes the budget set larger again. 40 115 Shapes of Budget Constraints ?Q: What makes a budget constraint a straight line? 116 ?A: A straight