PS5_S - METU Department of Economics Econ 101 Introduction...

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1/8 METU Department of Economics Econ 101: Introduction to Economics I Sections 01-02-03 Fall 2011 PROBLEM SET 5 (With Answers) PART A- PROBLEMS 1. A consumer has an income of I = 300 TL per month and he wishes to spend all of it on two goods X and Y, whose prices are 15 TL and 20 TL, respectively. a) Express the budget line algebraically and draw the diagram. b) How will (i) and (ii) be affected by following situations (assume each time you start from initial budget constraint). i. Doubling of money income and doubling of all absolute prices. Nothing changes. Budget Line: 15X + 20Y = 300 ii. Doubling of money income and doubling of price of X. iii. Doubling of price of Y, assuming all other things constant. Y X 15 20 15X + 20Y = 300 𝑰 = ??? , 𝑷 ? = ?? 30X + 20Y = 600 Y X 7,5 20 15 𝑷 ? = ?? 15X + 40Y = 300 Y X 30 20 15
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2/8 iv. An increase in money income by 60 TL. 2. The following two tables illustrate Mehmet’s total utilities from watching movies in a theater (T) and renting movies on DVD (V). Suppose that Mehmet has a monthly entertainment budget of 48 TL, each movie in a theater costs 12 TL, and each DVD rental is 6 TL. 0 0 0 12 0.00 0 0 0 6 0.00 1 90 90 12 7.50 1 110 110 6 18.33 2 170 80 12 6.67 2 195 85 6 14.17 3 245 75 12 6.25 3 265 70 6 11.67 4 305 60 12 5.00 4 330 65 6 10.83 5 355 50 12 4.17 5 385 55 6 9.17 6 400 45 12 3.75 6 430 45 6 7.50 7 435 35 12 2.92 7 460 30 6 5.00 a) Complete the tables. b) Does Mehmet’s response to both goods obey the law of diminishing marginal utility? Explain your answer. As Mehmet watches more of movies in theaters (or rent DVDs), the utility derived from each additional movie in theater (or DVD) is less than the utility derived from the movie (or DVD) watched before. As the number of both movies in theaters and DVDs watched increase, the marginal utility derived from additional unit decreases. Therefore the utility that Mehmet derived from successive units of both goods diminishes as total consumption of the goods increases, so that Mehmet’s response to both goods obey the law of diminishing marginal utility. c) Given his budget of 48 TL, what combination of theater movies and rental DVDs will maximize Mehmet’s level of satisfaction (i.e. at consumer equilibrium, how much of each good will be consumed)? = = = Y X 18 24 20 15 15X + 20Y = 360
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3/8 To maximize the level of satisfaction; = must hold. This holds for folowing pairs of movies in theater and DVD; (1, 6) and (4, 7). But also the budget constraint must hold. This holds for the first bundle; if Mehmet watches 1 unit of movie in theater and rents 6 DVDs, his utility will be maximized. 3. Suppose that there exist a branch of Çatı Restaurant in Kızılay. Assume that, in the METU campus, there is no substitute of it, i.e. there is no Arkabahçe Restaurant, but there are much more substitutes in Kızılay.
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