A society consists of two people with utilities U1 and U2, and the social welfare function is W = α1U1 + α2U2. Draw a utility possibilities frontier similar to the ones in Figure 10.8. Use calculus to show that where social welfare is maximized, as α1/α2 increases, Person 1 benefits, and Person 2 is harmed?
Figure 10.8 Welfare Maximization

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(a) (b) UPF UPF -w3 w w2 w2 W3 Jane's utility Jane's utility Denise's utility Denise's utility 6