Econ2101 practice exam detailed solutions

# Econ2101 practice exam detailed solutions - ECON2101...

This preview shows pages 1–7. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECON2101 - Practice Exam Solutions Jonathan Lim April 19, 2010 Practice Midterm-Exam 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 have-2¢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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 25

Econ2101 practice exam detailed solutions - ECON2101...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online