Witwatersrand **We aren't endorsed by this school
ECON 4036A
Feb 27, 2023
Uploaded by DeanStrawWren113 on coursehero.com
University of the Witwatersrand School of Economic and Finance Advanced Microeconomic Theory (ECON 4036); Test 2 Date: 16 September 2021 Duration: 3 Hours Instructions 1. Attempt all the questions. 2. Make sure that your student number is clearly written on every page of your script
1. Define the following concepts ( 5 points each ) i. Consumption set Memo Definition1: Let x =( x 1 ,x 2 x 3 ......... x n ) be a consumption vector containing different quantity of each of n commodities. Then the set of x denoted as X is referred to consumption set where x X is represented by a point R + ¿ n x = ¿ . ii. Budget set Memo Definition2: Let px≤ y a budget line where y is fixed money income of the consumer and px = i n p i x i is total expenditure on n goods. Then the subset; R + ¿ n , px≤ y x x = ¿ Β = ¿ is referred to as a budget set. Alternatively if you draw a graph and shade the area under budget line with inclusion of the budget line, you will get the full score. iii. Axiom of completeness Memo For consumption vectors x and y in X where X consumption set , either x y or y x . This axiom formalize the notion that the consumer can make
comparison i.e. he has the ability to discriminate and necessary knowledge to evaluate the alternatives . iv. Axiom of continuity Memo Continuity axiom: For all R + ¿ n x ¿ , the 'at least as good as' set ( x ¿ and the 'no better than' set ( x ¿ are closed v. Axiom of monotonicity Memo Strict Monotonicity; For all x 1 and x 0 in R + ¿ n ¿ , if x 0 ≥ x 1 , then x 0 x 1 while x 0 > x 1 then x 0 x 1 . This axiom says that if one bundle contains at least as much of every commodity as another bundle, then the one is at least as good as the other. vi. Axiom of transitivity Memo For all x , y and z in X , if x y and y z ,then x z This axiom requires that the consumer pair wise ranking of alternative is consistent. However, recent experimental results invalidate this assumption (behavioral economics has much to offer here).
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