Suppose there are 2 individuals in a simple exchange economy with utilities- U(1)= ax1 + x2, U(2)= y1y2. Endowments are (x1,x2)=(4,0) and (y1,y2)=(1,5).

We are asked the values of 'a' such that the above allocation is pareto optimal.

The answer as given (and explained) is MRS of A >= MRS of B implies pareto optimality. How did we arrive here?

URL for reference: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

URL for actual problem: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

Suppose there are 2 individuals in a simple exchange economy with utilities $U_{1}= ax_{1} + x_{2}$ and $U_{2}= y_{1}y_{2}$. 

Endowments are $(x_{1},x_{2})=(4,0)$ and $(y_{1},y_{2})=(1,5)$.

We are asked the values of $a$ such that the above allocation is pareto optimal.

The answer as given is $MRS_{A} \ge MRS_{B}$ implies pareto optimal. 

How did we arrive here?

URL for reference: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

URL for actual problem: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

Suppose there are 2 individuals in a simple exchange economy with utilities- U(1)= ax1 + x2, U(2)= y1y2. Endowments are (x1,x2)=(4,0) and (y1,y2)=(1,5).

We are asked the values of 'a' such that the above allocation is pareto optimal.

The answer as given (and explained) is MRS of A >= MRS of B implies pareto optimality. How did we arrive here?

URL for reference: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

Suppose there are 2 individuals in a simple exchange economy with utilities- U(1)= ax1 + x2, U(2)= y1y2. Endowments are (x1,x2)=(4,0) and (y1,y2)=(1,5).

We are asked the values of 'a' such that the above allocation is pareto optimal.

The answer as given (and explained) is MRS of A >= MRS of B implies pareto optimality. How did we arrive here?

URL for reference: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34

URL for actual problem: http://www.econschool.in/stuff-of-interest/anotherpost/dse-2013-q34