Suppose that Bob's utility function is uB(qB,mB) = mB. (a) What is Bob's optimal consumption bundle...

 

Transcribed Image Text:

Suppose that Bob's utility function is uB(qB,mB) = mB. (a) What is Bob's optimal consumption bundle if his income is Y, the price of qB is pq and the price of mg is 1. Ann's utility function is the same as in Problem 1, except that we add a subscript to all her variables; e.g., uA(qA, MA)= A+MA. Suppose that Ann and Bob decided to pool their resources together. To determine their optimal consumption bundle, they decided to solve the problem maxqA mA.qBmB9A+MA+MB, subject to constraint pa(9A+9B)+(mA+MB) = 2Y (b) What is the solution to this maximisation problem? You do not have to use Lagrange (you can substitute the budget constraint); you can simplify the problem before solving it as you see fit. (c) There is some indeterminacy in the total consumption bundle (qA, 9B, MA, MB) that you have obtained in (b). Let us suppose that you want to make sure that neither Ann nor Bob is worse off than before they pooled their resources together. What consumption bundles would you give to each of them? (d) Suppose now that Ann's utility function is UA (9A, MA) =qAMA (as in lectures), while Bob's is still uB(qB, MB) = mg. As in (a), Ann and Bob decided to solve maxqA.ma.qB,mgqAMA+MB, You cannot ignore q0 because won't be defined, but you don't need to worry about this constraint either. subject to constraint pq (9A+qB)+(mA+MB) = 2Y What is the solution to this problem? As in the previous problem, you can use whatever method you like. Suppose that Bob's utility function is uB(qB,mB) = mB. (a) What is Bob's optimal consumption bundle if his income is Y, the price of qB is pq and the price of mg is 1. Ann's utility function is the same as in Problem 1, except that we add a subscript to all her variables; e.g., uA(qA, MA)= A+MA. Suppose that Ann and Bob decided to pool their resources together. To determine their optimal consumption bundle, they decided to solve the problem maxqA mA.qBmB9A+MA+MB, subject to constraint pa(9A+9B)+(mA+MB) = 2Y (b) What is the solution to this maximisation problem? You do not have to use Lagrange (you can substitute the budget constraint); you can simplify the problem before solving it as you see fit. (c) There is some indeterminacy in the total consumption bundle (qA, 9B, MA, MB) that you have obtained in (b). Let us suppose that you want to make sure that neither Ann nor Bob is worse off than before they pooled their resources together. What consumption bundles would you give to each of them? (d) Suppose now that Ann's utility function is UA (9A, MA) =qAMA (as in lectures), while Bob's is still uB(qB, MB) = mg. As in (a), Ann and Bob decided to solve maxqA.ma.qB,mgqAMA+MB, You cannot ignore q0 because won't be defined, but you don't need to worry about this constraint either. subject to constraint pq (9A+qB)+(mA+MB) = 2Y What is the solution to this problem? As in the previous problem, you can use whatever method you like.