You are the benevolent ruler of a very small kingdom consisting of two subjects (indexed by i 1 , 2) The subjects in your kingdom consume two different goods, x 1 and x 2, which can be purchased at prices of p 1 and p 2, respectively Suppose the two subjects have identical cardinal utility functions, Ui ( x 1 , x 2) log( x 1) (1 )log( x 2) with 0 for i 1 , 2 also subject 1 has income y 1, while subject 2 has income y 2 a You wonder whether you can improve matters in your kingdom through an optimal distribution of income, i e , you would like to maximize the sum of your subjects utility, V 1( y 1 t, p 1 , p 2) V 2( y 2 t , p 1 , p 2), where t is a transfer from subject 2 to subject 1 (which could be negative) Given this criterion, what is the optimal value of t b) How do your results depend on assuming that utility is cardinal rather than ordinal You are the benevolent ruler of a very small kingdom consisting of two subjects (indexed by i 1,2) The subjects in your kingdom consume two different goods, X1 and X2, which can be purchased at prices of p and p2, respectively Suppose the two subjects have identical cardinal utility functions, U (21,22) a log(21) (1 a) log(x2) with a 0 for i 1, 2 also subject 1 has income yi, while subject 2 has income y2 (a) You wonder whether you can improve matters in your kingdom through an optimal distribution of income, i e , you would like to maximize the sum of your subjects' utility, Vi(y1 1, P1, P2) V2(Y2 T, P1, P2), where t is a transfer from subject 2 to subject 1 (which could be negative) Given this criterion, what is the optimal value of T (b) How do your results depend on assuming that utility is cardinal rather than ordinal T

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You are the benevolent ruler of a very small kingdom consisting of two subjects (indexed by i = 1 , 2). The subjects in your

You are the benevolent ruler of a very small kingdom consisting of two subjects (indexed by i = 1, 2). The subjects in your kingdom consume two different goods, x1 and x2, which can be purchased at prices of p1 and p2, respectively. Suppose the two subjects have identical cardinal utility functions,

Ui(x1, x2) = log(x1) + (1 - )log(x2)

with > 0 for i = 1, 2; also subject 1 has income y1, while subject 2 has income y2.

a You wonder whether you can improve matters in your kingdom through an optimal distribution of income, i.e., you would like to maximize the sum of your subjects utility, V1(y1 + t, p1, p2) + V2(y2 - t, p1, p2), where t is a transfer from subject 2 to subject 1 (which could be negative). Given this criterion, what is the optimal value of t?

b) How do your results depend on assuming that utility is cardinal rather than ordinal? image text in transcribed

= You are the benevolent ruler of a very small kingdom consisting of two subjects (indexed by i = 1,2). The subjects in your kingdom consume two different goods, X1 and X2, which can be purchased at prices of p and p2, respectively. Suppose the two subjects have identical cardinal utility functions, U (21,22) = a log(21) + (1 - a) log(x2) with a > 0 for i = 1, 2; also subject 1 has income yi, while subject 2 has income y2. = (a) You wonder whether you can improve matters in your kingdom through an optimal distribution of income, i.e., you would like to maximize the sum of your subjects' utility, Vi(y1 + 1, P1, P2) + V2(Y2 T, P1, P2), where t is a transfer from subject 2 to subject 1 (which could be negative). Given this criterion, what is the optimal value of T? (b) How do your results depend on assuming that utility is cardinal rather than ordinal? T