which of the following functions represents the same preferences as above Due: J

Question

which of the following functions represents the same preferences as above Due: July 13, 2016 Problem #1 Consider the set, X, of pairs of (a, b), where a and b are integers not smaller than 0 and not bigger than 9. Define the preferences over elements of X (a, b)(c,d)"(a=c a>c a=c (a, b)(c, d) b-d. b24 Can you think of a utility function that represents preferences Problem #2 Consider the following utility function U(21, 72) 144. Which of the following functions represents the same preferences as the abov utility function? Justify your answer. a) V( 1,22) = + 7, 1,22) =1 +2. Cit2 Problem #3 Imagine that preferences of a given individual are represented with Assume that the prices of the two goods consumed by this individual ar given by pi and p2. Furthermore, assume that the individual earns income I. i) Derive the demands of the individual for the two goods. ii) Verify that the demands happen to be homogenous of degree 0. iii) Plot the two demands as a function of income.

Explanation / Answer

a) If we transforn V(x1,x2) = ex1x2 - 2 in form of U then it will be eU/2/e72 - 2 so it can be tranformed into monotonic transformation hence have the same preference while V(x1,x2) = e(x1+x2)+2 cannot be transformed in terms of U so it do not have same preference

V(x1,x2) = -1/x1x2 + 7 in form of U will be -1/sqrt(U-144) + 7 so it can be tranformed into monotonic transformation hence have the same preference while V(x1,x2) = x1 + x2 cannot be transformed in terms of U so it do not have same preference

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