Question

Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same preferences as Jim? b. Who has the same indifference curves as Jim? c. Explain why the answers to (a) and (b) differ.

Answer 1

Answer: 1

(a) MRS is the rate at which a consumer is ready to give up some units of good 1 to get an additional unit of good 2 while maintaining same level of satisfaction. Jim's preferences for x and y is MRS = y/x

Jim's W (ny) = ny MUX MUY Jemy's u(,y)= 10002y + 2000 Mい。 Mux - 10001 - MUу 1000x Tammy's ulay = xylion) 29 - 1y? MUx MUY y-2a9², 4(1-2xy 1-2x²y n(1-2xy) = y) Dave's U (N,y) = -b - (10+244) (lotaxy MU, y - (-1)( lo+2 x4) X 2 , (9) MUY

Marjoe's ulny) = (y +1000) = xy + 10000 MU 1000 MUу Pat's ( Up, y)) = o.sxy - 10,000 Billy's (u(ny) - 14y. I Musly MUY fran est un, y) = -xy Mex MUn ho. so, Jerry Tammy Daves & Pat have same preferences as Tim

b) Jerry, pat, Dave and Bill have the same in difference Curves as a Jim, but Tammy and Francis have different preferences francis' untitty functions is a decreasing transformanation OF Jims. So he ordes his in difference curves in ene Oppo Site way Tammy's untiy functim is a transformanatin Of Jim's but is sometimes increasing Sometimes decreasing o answer a and b are different because of the tun. cauation of contity function, if the eauation is a ou adyatic equations, les difference Cuove has a con of the two utilty Chape iyre spective of the MRS value of the tovo u amctims. While if it is a finear equation than the cuves is a straight downwayd tine respective of me O