# Problem set 3 of Welfare economics

Universitat Pompeu Fabra, 1996/1997

Due May 7, 1997.

Consider an economy with two individuals and two commodities. The preference relation of one individual is represented by the utility function U1(x,y)=x+y, and of the second individual by the utility function U2(x,y)=a(x+2y), where a>0.

1. Draw the Edgeworth box when the total resources are (2,2).
2. Draw the set of possible utility pairs for a=1.
3. What is (or are) the "social optimum" (or optima) recommended by the Social Welfare Function W=u1+u2. What allocations (in the Edgeworth box) correspond to this optimum (or optima)?
4. Repeat exercises 2 and 3 above for a=4.
5. Find in the Edgeworth box a Pareto efficient allocation that corresponds to a price equilibrium in which the incomes of both individuals are equal. (Hint: if the endowments of both individuals are equal, so their incomes are). Find the corresponding utility pair in the drawing of possible utility pairs when a=4.
6. What would you consider as a social optimum for this economy? Why? (Here you are asked for your personal opinion; you have to reason it, but not necessarily on the material discussed in class or in this problem set). Do not write more than 10 lines.