Question

Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y) Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y respectively. Assuming utility functions of individuals A and B to be UA=XA YA 2 and UB=XB 2 YB where Xi and Yi for i= {A, B} represent individual i’s consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy?

30 Aug 2022
Answer :
Word Count : 544

A Pareto-optimal allocation is a situation where no individual can be made better off without making at least one individual worse off. In other words, it is an allocation where no further exchange is possible without reducing the utility of at least one individual.

Let's start by finding the initial endowments of each individual:

Individual A: 5 units of good X and 3 units of good Y
Individual B: 3 units of good X and 4 units of good Y
Now, we need to find the utility level of each individual at this initial endowment. For individual A, the utility is given by UA = XA + YA^2, and for individual B, the utility is given by UB = XB^2 YB. Plugging in the initial endowment values, we get:

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