2x1x2 412 0 Joe Bob has a utility function given by ux1P2 a

+2x1x2+ 4.12 (0) Joe Bob has a utility function given by u(x1,P2) = a. (a) Compute Joe Bob\'s marginal rate of substitution: MRS(x1,x2) = (b) Joe Bob\'s straight cousin, Al, has a utility function v(xi, r2) Compute Al\'s marginal rate of substitution. MRS(zi,x2) = c) Do u(,2) and v(r1, x2) represent the same preferences? transformation of Al\'s? (Hint: Some have said that Joe Bob is square.) Can you show that Joe Bob\'s utility function is a monotonic

Solution

1- marginal rate of substitution is the rate at which we are able to substitute one good for other such that the level of satisfaction remains the same.

it is given by MUX/MUY

HERE IT IS =

2- HERE THE MRS OF JOE = MUX/MUY = 1

C- YES BOTH OF THEM REPRESENTS THE SAME PREFERENCES AS REPRESENTED BY THE SAME MRS,

SO HERE WE CAN SEE THAT BOB\'S FUNCTION I A MONOTONE TRANSFORMATION

AS IT IS THE SQUARE OF JOE UTILITU FUNCTION

I.E

(X1+X2)^2