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EC207_mt1

# EC207_mt1 - The Colorado College Department of Economics...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 Midterm 1 Do all 4 questions. Time: 2 hours and 15 minutes. Please abide by and sign the Honor Pledge. Turn in question paper along with answer booklet. Be neat and clear with graphs. Good luck. 1. (a) Suppose a consumer gets utility from 2 goods X and Y. The consumer’s utility function is given by U = x 0.5 y 0.5 The consumer’s budget constraint is given by 80 = 2x+4y (i) Set-up the consumer’s Lagrangian function. Use it to derive the optimal purchase of the two goods. Show calculations (8 points) (ii) What is the consumer’s maximum utility? (2 points) (b) Amit gets utility from two goods x and y with the following utility function U = x +2y Both goods x and y are priced at \$1 each and his income is \$10. (i) Derive the marginal utility that Amit gets from good x and y, respectively. Next obtain Amit’s MRS along the indifference curve. (ii) Using equi-marginal principle show Amit’s optimum purchase of the two goods.

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