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Answer Key 3 Utility Functions, the Consumer's Problem, Demand Curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Econ |
| Abstract | (1) Perfect Substitutes. Suppose that Jack's utility is entirely based on number of hours spent camping (c) and skiing (s). Sketch Jack's indifference curves. u(c, s) = 3c + 2s (1) (a) What is Jack's MRS of hours spent camping for hours spent skiing? ANSWER. To get the number of camping hours Jack is willing to forego in order to spend another hour skiing take the ratio of the partial derivatives of the utility function as follows. ∂u/∂s ∂u/∂c = 2 3 (2) Since Jack only get 2 3 as much happiness per hour skiing as he does per camping hour, he is only will to give up 2 3 hours of camping to get an additional hour of skiing. (b) Let p c = 1 be the price to Jack of spending an hour camping and p s the price per hour of skiing. Solve for p * s , the price at which a utility-maximizing Jack might mix his time between the two activities. If p s > p * s what will Jack do? ANSWER. To find p * s just set MRS equal to the price ration as follows. ∂u/∂s ∂u/∂c = p * s p c (3) ⇒ 2 3 = p * s Since Jack only gets 2 3 as much happiness per hour skiing as he does camping, the price of skiing cannot be any higher than 2 3 the price of camping in order to lure Jack away from his tent under the stars to the those crowded ski slopes. Once the price of skiing gets any higher than that, he is back to the woods full-time. (c) Write down Jack's demand functions for both activities. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://home.wlu.edu/~gusej/econ210/hw/ak3.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
