F(D1)=( One way to think about this is that demand curves slope down for at least two reasons 1)diminishing returns at the individual level (for continuous goods)and (2) heterogeneity of demand across people (for discrete goods) In many cases the latter is easier to work with and closer to reality
F p1 1 1 p1 . One way to think about this is that demand curves slope down for at least two reasons: (1) diminishing returns at the individual level (for continuous goods) and (2) heterogeneity of demand across people (for discrete goods). In many cases, the latter is easier to work with and closer to reality
Back to MWG: The Properties of Aggregate Demand Let x,(p1, p2, ...,PL, w1,w2,., wy) denote the demand for the jth consumer, out of a total of j consumers Aggregate demand x(P1,P2,pL,W1,w22,) ∑ x,(p1, p2, ...,pL, wi) We are interested in two specific issues (1) to what extent does aggregate demand display similar properties(e.g. law of demand)to individual demand, and (2) to what extent can we use a representative consumer framework to
Back to MWG: The Properties of Aggregate Demand Let xjp1, p2,...,pL,w1,w2,...,wJ denote the demand for the jth consumer, out of a total of J consumers. Aggregate demand xp1, p2,..., pL,w1,w2,...,wJ j1 J xjp1, p2,..., pL,wj We are interested in two specific issues: (1) to what extent does aggregate demand display similar properties (e.g. law of demand) to individual demand, and (2) to what extent can we use a representative consumer framework to
capture aggregate outcomes
capture aggregate outcomes
Definition 4.C1: The aggregate demand function x(p, w) satisfies the weak axiom if p·x(p,)≤ w and x(p,)≠x(P,) implies p·x(p,)>w This may not hold-Individual demand functions may satisfy the weak axiom, but the aggregate may not Note to Students, etc. the next examples may be helpful, and I included them because mwg does little on this but i will go over them quickly and I dont see this material as crucial
Definition 4.C.1: The aggregate demand function xp,w satisfies the weak axiom if p xp ,w w and xp ,w xp,w implies p xp,w w . This may not hold– Individual demand functions may satisfy the weak axiom, but the aggregate may not. Note to Students, etc., the next examples may be helpful, and I included them because MWG does little on this, but I will go over them quickly and I don’t see this material as crucial
An example of the weak axiom failing Assume that there are two consumers each of which has wealth w=1 and each of which faces the same prices for two goods(1 and 2) a little example Initially the price for both goods is one We consider the change so that the price for good one is 1 +0 and the price for good two is 1-0, 0>0 First agent has a utility function x1-maxxl, a]+Ex2, where e is quite small
An example of the weak axiom failing: Assume that there are two consumers each of which has wealth w 1 and each of which faces the same prices for two goods (1 and 2). A little example: Initially the price for both goods is one. We consider the change so that the price for good one is 1 and the price for good two is 1 , 0. First agent has a utility function x1 maxx1, x2, where is quite small