北京大学：《微观经济学》Chapter Two Budget Constraint 预算约束

Chapter Two Budget Constraint 预算约束

Chapter Two Budget Constraint 预算约束

Structure Describe budget constraint -Algebra Graph Describe changes in budget constraint Government programs and budget constraints Non-linear budget lines

Structure Describe budget constraint –Algebra –Graph Describe changes in budget constraint Government programs and budget constraints Non-linear budget lines

Consumption sets A consumption set(消费集) is the collection of all physically possible consumption bundles(消费束)to the consumer

Consumption Sets A consumption set （消费集）is the collection of all physically possible consumption bundles （消费束）to the consumer

Consumption bundle A consumption bundle containing x, units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector x,, x23

Consumption Bundle 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 )

Physical constraints Non-negative: Consumption set X={(X1…,Xn)x1≥0,…,Xn≥0} You only have 24 hours a day Subsistence need Etc

Physical Constraints Non-negative: Consumption set: X={ (x1 , … , xn ) | x1  0, … , xn  0 } You only have 24 hours a day Subsistence need Etc

Budget Constraint What constrains consumption choice? Budgetary time other resource limitations

Budget Constraint What constrains consumption choice? –Budgetary – time –other resource limitations

Budget Constraints Commodity prices are p1, p23., pn Q: When is a bundle(X1……,xn affordable at prices p,,...,pn? A When p11+∴+pnXn≤m where m is the consumers (disposable income

Budget Constraints Commodity prices are p1 , p2 , … , pn . Q: When is a bundle (x1 , … , xn ) affordable at prices p1 , … , pn? A: When p1x1 + … + pnxn  m where m is the consumer’s (disposable) income

Budget Constraints The bundles that are only just affordable form the consumers budget constraint. This is the set {(X13…xn)|X1≥0,…,xn≥0and p1X1+…+pnXn=m}

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(预算集 is the set of all affordable bundles B(p1…,pnm) (X1,…Xn)|X1≥0,……,xn≥0and p1x1+…+pnXn≤m} The budget constraint is the upper boundary of the budget set

Budget Constraints The consumer’s budget set （预算集 ）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 Commodities m|2 Budget constraint is P1X1+ p2X 2=m m/p

Budget Set and Constraint for Two Commodities x 2 x1 Budget constraint is p1x1 + p2x2 = m. m /p1 m /p2