Jim\'s utility function is u(ri, z2) zur2- Jerry\'s utility function is u zi,z2)

Question

Jim's utility function is u(ri, z2) zur2- Jerry's utility function is u zi,z2)-1000rir2 2000. Tammy's utility function is u(r1,z2) 2). Oral's utility function is u(zi, r2) 1/(10+2r122 Marjoe's utility function is u(z1,z2) z1(z2+1000). Pat's utility function is u(zi, r2) 0.5riz2 10000. Billy's utility function is u(zi,r2) z1/z2. Francis's utility function is u(zi, zr) -rizz. (1) Who has the same preferences as Jim? (2) Who has indifference curves whose general shape is similar to Jim's indifference curves (3) Explain why the above answers differ.

Explanation / Answer

Answer)

1)      Jerry, Pat and Oral have same preferences as Jim as their utility functions are monotonic transformations of Jim’s utility function.

2)      Jerry, Tammy, Pat, Oral and Francis have the indifference curves similar in shape as Jim’s indifference curve.

3)      Tammy’s utility function is a transformation of Jim’s utility function but it is sometimes increasing and sometimes decreasing, thus even with similar IC’s the preferences are not the same. Also, Francis’s utility function is a decreasing transformation of Jim’s utility function, so his utility from his indifference curves increases in the opposite way as in the case of Jim’s.

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