1、Chapter Two,Budget Constraint预算约束,Structure,Describe budget constraintAlgebraGraphDescribe changes in budget constraintGovernment programs and budget constraintsNon-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
2、consumer.,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 daySubsistence needE
3、tc.,Budget Constraint,What constrains consumption choice?Budgetarytime other resource limitations.,Budget Constraints,Commodity prices are p1,p2,pn.Q:When is a bundle(x1,xn)affordable at prices p1,pn?A:When p1x1+pnxn mwhere m is the consumers(disposable)income.,Budget Constraints,The bundles that ar
4、e only just affordable form the consumers budget constraint.This is the set(x1,xn)|x1 0,xn 0 and p1x1+pnxn=m.,Budget Constraints,The consumers 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 se
5、t.,Budget Set and Constraint for Two Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p1,m/p2,Budget Set and Constraint for Two Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p2,m/p1,Budget Set and Constraint for Two Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p1,Just affordable,m
6、/p2,Budget Set and Constraint for Two Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p1,Just affordable,Not affordable,m/p2,Budget Set and Constraint for Two Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p1,Affordable,Just affordable,Not affordable,m/p2,Budget Set and Constraint for Two
7、 Commodities,x2,x1,Budget constraint isp1x1+p2x2=m.,m/p1,BudgetSet,the collection of all affordable bundles.,m/p2,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,BudgetSet,m/p2,Meaning of the Slope,Increasing x1 by 1 must reduce x2 by p1/
8、p2.Opportunity cost of consuming x1Or,the rate of exchange that market allows.,Budget Constraints,x2,x1,Slope is-p1/p2,+1,-p1/p2,Budget Constraints,x2,x1,+1,-p1/p2,Opp.cost of an extra unit of commodity 1 is p1/p2 units foregone of commodity 2.,Budget Constraints,x2,x1,Opp.cost of an extra unit of c
9、ommodity 1 is p1/p2 units foregone of commodity 2.Opp.cost of an extra unit of commodity 2 is p2/p1 units foregone of commodity 1.,-p2/p1,+1,Budget Sets 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 bud
10、get set and budget constraint change as income m increases?,Originalbudget set,x2,x1,Higher income gives more choice,Originalbudget set,New affordable consumptionchoices,x2,x1,Original andnew budgetconstraints areparallel(sameslope).,How do the budget set and budget constraint change as income m dec
11、reases?,Originalbudget set,x2,x1,How do the budget set and budget constraint change as income m decreases?,x2,x1,New,smallerbudget set,Consumption bundlesthat are no longeraffordable.,Old and newconstraintsare parallel.,Budget Constraints-Income Changes,Increases in income m shift the constraint out
12、ward 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 inc
13、ome 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 p
14、1 to p1”?,Originalbudget set,x2,x1,m/p2,m/p1,m/p1”,-p1/p2,How do the budget set and budget constraint change as p1 decreases from p1 to p1”?,Originalbudget set,x2,x1,m/p2,m/p1,m/p1”,New affordable choices,-p1/p2,How do the budget set and budget constraint change as p1 decreases from p1 to p1”?,Originalbudget set,x2,x1,m/p2,
