Chapter nine Buying and Selling
Chapter Nine Buying and Selling
What Are We doing in this Chapter We expand our basic consumer choice framework to include the possibility that consumers can sel something to generate income. Again in terms of theoretical framework nothing is new
What Are We Doing in this Chapter? We expand our basic consumer choice framework to include the possibility that consumers can sell something to generate income. Again, in terms of theoretical framework, nothing is new
Endowments禀赋 The list of resource units with which a consumer starts is his endowment A consumers endowment wil be denoted by the vector a(omega)
Endowments 禀赋 The list of resource units with which a consumer starts is his endowment. A consumer’s endowment will be denoted by the vector (omega).
Endowments Eg.O=(01,O2)=(10,2) states that the consumer is endowed with 10 units of good 1 and 2 units of good 2 What is the endowments value? For which consumption bundles may it be exchanged?
Endowments E.g. states that the consumer is endowed with 10 units of good 1 and 2 units of good 2. What is the endowment’s value? For which consumption bundles may it be exchanged? = ( , ) = ( , ) 1 2 10 2
Budget Constraints revisited So, given p, and p2, the budget constraint for a consumer with an endowment(@1,O2)is p1X1+p2X2=p11+p202 The budget set is {(x1,x2)P1X1+P2X2≤P101+p22, X1≥0,x2≥0
Budget Constraints Revisited So, given p1 and p2 , the budget constraint for a consumer with an endowment is The budget set is ( , ) 1 2 p1 x1 + p2 x2 = p1 1 + p2 2 . ( , ) , , . x x p x p x p p x x 1 2 1 1 2 2 1 1 2 2 1 0 2 0 + +
Budget Constraints revisited x2 p1X1+p2X2=p1+p202 Budget set {(x1,x2)P1x1+p2X2sP11+p202, X1≥0,X≥0
Budget Constraints Revisited x2 1 x1 2 p1 x1 + p2 x2 = p11 + p22 Budget set ( , ) , , x x p x p x p p x x 1 2 1 1 2 2 1 1 2 2 1 0 2 0 + +
Budget Constraints revisited x2 p1X1+p2X2=p1+p202 Budget set p1x1+p2X2=p101+p202
Budget Constraints Revisited x2 1 x1 2 p1 x1 + p2 x2 = p11 + p22 p1 x1 p2 x2 p1 1 p2 2 ' ' ' ' + = + Budget set
Budget Constraints revisited The endowment point is always on x2 the budget constraint p1X1+p2X2=p1+p202 So price changes pivot the constraint about the endowment point p1x1+p2X2=p101+p202
Budget Constraints Revisited x2 1 x1 2 p1 x1 + p2 x2 = p11 + p22 The endowment point is always on the budget constraint. p1 x1 p2 x2 p1 1 p2 2 ' ' ' ' + = + So price changes pivot the constraint about the endowment point
Budget Constraints revisited The constraint p1X1+p2x2=p101+p22 s p1(X1-1)+p2(X2-2)=0 That is the sum of the values of a consumer's net demands is zero
Budget Constraints Revisited The constraint is That is, the sum of the values of a consumer’s net demands is zero. p1 (x1 −1 ) + p2 (x2 −2 ) = 0. p1 x1 + p2 x2 = p11 + p22
Net Demands x2 p1(X1-01)+p2(x2-02)=0 At prices(p,p2) the consumer sells units of good 1 to acquire more units of good 2
Net Demands x2 1 x1 2 p1 (x1 −1 ) + p2 (x2 −2 ) = 0 x2 * x1 * At prices (p1 ,p2 ) the consumer sells units of good 1 to acquire more units of good 2