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Unformatted text preview: ECON2101  Practice Exam Solutions Jonathan Lim April 19, 2010 Practice MidtermExam ECON2101: Solutions 1 Question 2.3 (A) All you need to do is mark 2 points and join them. The graph is given below: 1 (B) For simplicity I will denote the price of good x as P x and the price of good y as P y . We know that the feasible bundles which exhaust your income is 4 of good x and 6 of good y and 12 of good x and 2 of y . This implies we has the following budget equations: P x & 4 + P y & 6 = M; P x & 12 + P y & 2 = M: From the above equation we can solve them simultaneously and we obtain the following equation: 4 P y = 8 P x This implies the price ratio to be: P x P y = 1 2 : This implies that the price of good x is only half of that of good y . (C) Given the price ratio of 1 = 2 this implies that we can swap 1 unit of good x for 2 units of good y . Thus this implies from our budget line P x & 4 + P y & 6 = M , that to exhaust income, we can consume 16 units of good x . (D) Given the price ratio of 1 = 2 this implies that we can swap 1 unit of good x for 2 units of good y . Thus this implies from our budget line P x & 4 + P y & 6 = M , that to exhaust income, we can consume 8 units of good y . (E) Remember that the budget equation is of the following form: P x x + P y y = M; since P x = 1 , P ( x ) P y = 1 2 and M = 16 this implies: x + 2 y = 16 : (F) Following for the above argument this implies the following: since P x = 3 , this implies: 2 3 x + 6 y = 48 : 2 Question 3.2 (A) We are given the following information, the bundle (1,16) is given by the indi/erence curve x 2 = 20 & 4 p x 1 . For the bundle (36,0) this is given by the indi/erence curve x 2 = 24 & 4 p x 1 . This implies the following indi/erence curves: (B) Remembering that more is always better this implies the following diagram: 3 Thus implying a convex set. (C) From basic calculus, this implies that the &rst order condition are given by: @x 2 @x 1 = & 2 x 1 = 2 1 Note that the two indi/erence curve yields identical &rst order conditions. If one want to be thorough or if the &rst order conditions we would need to identify which indi/erence curve it belongs to then we can ascertain which &rst order condition to use. Since we have identical &rst order condition it doesn¡t matter for this question. Thus given this we have2¢3. (D) Following the same formula we have, 1. (E) Incidentally this is the same as in D and E 2¢3 and 1. (F) Yes it does exhibit diminishing rates of substitution for the previous reasons are previously. (G) Yes, they do exhibit convex preferences. 4 3 Question 4.1 (A) We are told that his utility function is given by U ( x A ;x B ) = x A x B . This implies 200 for the bundle (40,5). Implying that the indi/erence curve through (40,5) includes all commodity bundles ( x A ;x B ) such that x A x B = 200 . Thus the equation with x B as the dependent variable is x B = 200 x A Diagrammatically we have: (B) Now we have the bundle (15 ; 20) which implies a utility level of 300 > 200 . Thus he will prefer this bundle.See diagram below: 5 We know that to remain indi/erent he has to have a utility level of 200 which implies 200 = 20 x A , which implies x A = 10 thus he is will to trade 30 Apples....
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 Fall '10
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 Utility, St. Petersburg paradox

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