University of the Witwatersrand School of Economic and Finance Advanced Microeconomic Theory (ECON 4036); Test 2 Date: 16September 2021 Duration: 3 Hours Instructions 1.Attempt all the questions. 2.Make sure that your student number is clearly written on every page ofyour script
1.Define the following concepts (5 points each) i.Consumption set Memo Definition1:Letx=(x1,x2x3......... xn ) be a consumption vector containing different quantity ofeach ofncommodities. Then the set ofxdenoted as Xis referred toconsumption setwherex∈X is represented by a point R +¿ n x=¿ . ii.Budget set Memo Definition2:Letpx≤ ya budget line whereyis fixed money income of the consumer andpx=∑ i n pixi is total expenditure onngoods. 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.Axiomof completeness Memo For consumptionvectorsxandyinXwhereXconsumption set, eitherx≽yor 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 Continuityaxiom: For allR +¿ n x∈¿ , the 'at least as good as' set≽(x¿ andthe 'no better than' set≼(x¿ are closed v.Axiom of monotonicity Memo Strict Monotonicity; For allx1andx0inR +¿ n ¿ , ifx0≥ x1, thenx0≽x 1 whilex0>x1thenx0≻x1 . This axiomsays 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 allx,yand z inX ,ifx≽yandy≽z ,thenx≽zThis 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).