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 U_{1}(x,y)=x+y, and of the second individual by the
utility function U_{2}(x,y)=a(x+2y), where a>0.

- Draw the Edgeworth box when the total resources are (2,2).
- Draw the set of possible utility pairs for a=1.
- What is (or are) the "social optimum" (or optima) recommended by the
Social Welfare Function W=u
_{1}+u_{2}. What allocations (in the Edgeworth box) correspond to this optimum (or optima)? - Repeat exercises 2 and 3 above for a=4.
- 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.
- 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.

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Nir Dagan / Contact information / Last modified: January 4, 1999.