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
Endowments p1=2 and p2 =3 so the value of the endowment(@1,02)=(10, 2)is p1a+p2O2=2×10+3×2=26 Q: For which consumption bundles may the endowment be exchanged? A: For any bundle costing no more than the endowment's value
Endowments p1=2 and p2=3 so the value of the endowment is Q: For which consumption bundles may the endowment be exchanged? A: For any bundle costing no more than the endowment’s value. ( , ) ( , ) 1 2 = 10 2 p1 1 + p2 2 = 2 10 + 3 2 = 26
Budget Constraints revisited So, given p, and p2, the budget constraint for a consumer with an endowment (@1,@2)is p1X1+p2X2=p1a1+p202 The budget set is {(x1,x2)P1x1+p2x2≤p11+P2O2, X1≥0,x≥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=p1o1+p202
Budget Constraints Revisited x2 1 x1 2 p1 x1 + p2 x2 = p11 + p22
Budget Constraints revisited x2 p1X1+p2X2=p1o1+p202 Budget set {(x1,x2)P1x1+P2X2sP11+p202, x1≥0,X2≥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 + +