# 4 - MS&amp;E 241: ECONOMIC ANALYSIS Thomas A. Weber 4....

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MS&E 241: ECONOMIC ANALYSIS Thomas A. Weber 4. Demand Theory II Winter 2009 Stanford University Copyright © 2009 T.A. Weber All Rights Reserved -2- MS&E-241-Winter-2009-TAW AGENDA Demand Aggregation Standard Welfare Measures Welfare Changes Key Concepts to Remember

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-3- MS&E-241-Winter-2009-TAW Demand Aggregated Over Many Individuals: Market Demand Function If following properties hold for each individual demand function: Continuity Homogeneity of Degree Zero Walras’ Law Then they hold for the market demand function MARKET DEMAND FUNCTIONS -4- MS&E-241-Winter-2009-TAW Is it possible to find aggregate demand function D(p,w) (for n individuals), such that In general, if everyone faces the same price vector p, then aggregate demand can be written as a function of p, but NOT necessarily also as a function of aggregate income w, unless 1 (, ) n kk k Dpw x pw = = ? / x w ∂∂ MARKET DEMAND FUNCTIONS (Cont’d) 1 0 k n k k k x dw w = = 1 0 n k k dw = = for any small wealth change dw that leaves aggregate wealth the same, i.e., for which 1 ( ,..., ) n dw dw dw = In other words, all the have to be the same across all consumers. 1 n k k ww = = for Wealth effects must compensate each other in the aggregate no matter how the wealth is re-distributed among the individuals!
-5- MS&E-241-Winter-2009-TAW MARKET DEMAND FUNCTIONS (Cont’d) Proposition . A (necessary and) sufficient condition for demand aggregation to be possible is when preferences are such that each consumer k’s indirect utility v k is quasilinear (“of the Gorman form”), i.e., (, ) () kkk k vpw ap bpw =+ Proof: (sufficiency only) By the definition of indirect utility it is Thus, (, (,) ) kk vp ep u u = (, ) (, ( (, ) ) ) ) ) (, ) (, ) k k k k k k pp p ww k k p w v pw v pw e pu x pw v pwh pu x pw vpw v pwxpw += + ' k x pw b p wb p =− And therefore is the same for any consumer k, no matter what his or her wealth level w k . QED -6- MS&E-241-Winter-2009-TAW MARKET DEMAND FUNCTIONS (Cont’d) A market demand functions is useful for making statements about the consumer responses to changes in price and/or aggregate income. Example. Sometimes the market demand function is also useful to explain other aggregate effects, such as the “bandwaggon effect,” under which the demand for a good depends on the expectation about how many consumers will adopt the product.

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-7- MS&E-241-Winter-2009-TAW NETWORK EXTERNALITIES Externalities exist when the action of one agent directly affects the environment of another agent; network externalities are externalities between participants of a common network “How much would you pay for the first fax machine?” Complementarity Direct (e.g., in 2-way networks, “exchange transactions”) Indirect (e.g., Microsoft Word) Necessary Conditions: - Compatibility - Interoperability Aggregate Demand depends on the Expected Demand -8- MS&E-241-Winter-2009-TAW GENERATING FULFILLED EXPECTATIONS DEMAND CURVE Demand in the Presence of Network Externalities P ( Q , S ) Q S 1 > 0 S 2 >S 1 Q 1 = S 1 Q 2 = S 2 P ( Q , Q ) S 0 = 0 Bandwaggon Effect
-9- MS&E-241-Winter-2009-TAW P(Q,S) = P(Q,0) + f (S) P Willingness to pay f(S) Externality function, f(0) = 0, f ’’ < 0 Q Output

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## 4 - MS&amp;E 241: ECONOMIC ANALYSIS Thomas A. Weber 4....

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