ECONOMICS TUTOR HELP PLEASE! (Answer A and B only) There is one good, available

Question

ECONOMICS TUTOR HELP PLEASE! (Answer A and B only)

There is one good, available in unit quantity to be distributed between 2 agents,Andrea and Bob, with utility functions u(x) and v(x) respectively. Let u(x)=x1/3and v(x)=3x. Assume that u and v measure ‘utils,’ a meaningful unit ofinterpersonally comparable utility.

(A) Calculate the equation of the utility possibility frontier.

(B) Using a computer or a scientific calculator, calculate approximately what point on the utility possibility frontier equalizes the utilities of the agents.

Explanation / Answer

1) When there are two consumers consuming a good, the utility possibility frontier is constructed by adding the two utility functions:

u(x) + v(x)

= x1/3 + 3x

2) If the utilities are to be equal, then it implies:

u(x) = v(x)

x1/3 = 3x

x = 27x3

(x - 27x3) = 0

1 - 27x2 = 0

x = 0.192

Use this to find the two utilities:

u(x) = 0.57

v(x) = 0.57

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