PS1+exc+5.8+Solutions - Different Types of Tastes 124 5.8...

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Unformatted text preview: Different Types of Tastes 124 5.8 Everyday Application: Inferring Tastes for “Mozartkugeln”: I love the Austrian candy “Mozartkugeln”. Thelepartofmy budget, and the only factor determining my willingness to pay for additional Mozartkugeln is how many I already have. A: Suppose you know thatI am willingto give up $1 of “other consumption” to getone moreMozartkugel when I consume bundle A — 100 Mozartkugeln and $500 in other goods per month (a) What is my MRS when my Mozartkugeln consumption remains unchanged from bundle A butI only consume $200 per month in other goods? Answer: Since the only factor determining mywillingness to pay for additional Momtkugeln is how manyI already have, the MRS is unchanged when other consumption goes to $200. I would therefore still be willing to trade $1 in other consumption for 1 more Mozartkugel. (b) Are my tastes quasilinear? Could they be homothetic? Answer: My tastes as defined are quasilinear in Mozartkugeln. They could be homothetic if my MRS is also independent of Mourtkugel consumption — in which case Mourtkugeln and other consumption would be perfect substitutes. (c) You notice that this month I am consuming bundle B — $600 in other goods and only 25 Mozartkugeln. When questioning me about my change in behavior (from bundle A), I tell you that I am just as happy as I was before. The following month you observe thatI consume bundle C — 400 Mozartkugeln and $300 in other goods, and I once gain tell you my happiness remains unchanged. Does the new information aboutB and C change your answer in (b)? Answer: Graph 5.7 illustrates bundles A, B and C and an indifference curve running through all three bundles (since I am equally happy at each bundle). Knowing about these three bundles lying on the same indifference curve tells me that Momtkugeln and other goods could not be perfect substitutes. Thus, my tastes cannot be homothetic (since we know they are quasilinear). 25 loo 209 300 qoo Noamfkuge‘n Graph 5.7: Mozartkugeln and other goods (d) Is consumption (other than of Mozartkugeln) essential fi2r me? Answer: Since we know my tastes are quasilinear in Mourtkugeln, the MRS is the same along any vertical line in our graph. Thus, I know that there is some indifference curve like the second one drawn in the graph that intersects the horizontal axis at a point like D. In fact, all indifference curves must intersect the horizontal axis at some point. Thus, it is possible for me to have utility greater than at the origin without consuming any other goods. Other goods are therefore not essential for me. 125 Different Types of Tastes B: Suppose my tastes could be modeled with the utility function u(x1,x2) = 2016(1):5 + x2, where x1 refers to Mozartkugeln and x2 refers to other consumption. (a) Calculate the MRS for these tastes and use your answer to prove that my tastes are quasilinear in x1 . Answer: The MRS is 0u/0x1 _ _ 0.5(20)x;°-5 10 MRS = — — __. 6u/0x2 1 xii-5 (5.17) Since the MRS is independent of the level of x2, we know that tastes are quasilinear in x1. (b) Consider the bundles A, B and C as defined in partA. Verify that they lie on one indifference curve when tastes are described by the utility function defined above. Answer: Plugging in the values for the three bundles, we get u(100, 500) = 20000005) + 500 = 20000) + 500 = 700 u(25, 600) = 200(250-5) + 600 = 200(5) + 600 = 700 (5.18) u(400, 300) = 200(4000-5) + 300 = 200(20) + 300 = 700. (c) Verifli that the MRS at bundle A is as described in partA and derive the MRS at bundles B and C. Answer: Equation (5.17) gives us that MRS = —10/(x(1"5). Thus, at bundle A where x1 = 100, MRS— 10/(1000-5) = —1 as described in part A. At B and C, the MRS is —2 and —1/2 respectively. ((1) Verifli that the MRS at the bundle (100,200) corresponds to your answer to A(a). Answer: Using equation (5.17), we again get MRS = 10/ (10005) = —1. (e) How much “other goods” consumption occurs on the indifference curve that contains (100,200) when my Mozartkugeln consumption falls to 25 per month? What about when it rises to 400 per month? Answer: My utility at (100,200) is u(100, 200) = 2000005) + 200 = 20(10) + 200 = 400. When Momtkugel consumption falls to 25, the utilityI get from the first term in the utility func- tion falls to 20(250'5) = 100. Thus, in order to get the same utility as I do at (100,200), I must have 300 in other consumption. When Momtkugel consumption is 400, on the other hand, my utility from the first portion of the utility function is 20(4000'5) = 20(20) = 400. Thus, to stay on the same indifference curve, I must have zero in other consumption. (f) Are Mozartkugeln essential for me? Answer: No. Suppose I have $700 in other good consumption. Then my utility is 700 — just as it is at A, B and C. So I can get more utility than I would at the origin without consuming Momtkugeln. ...
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This note was uploaded on 02/13/2011 for the course ECON 100A taught by Professor Woroch during the Fall '08 term at University of California, Berkeley.

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