the ecomonics of information.docx

1、the ecomonics of informationThe Economics of Information 11Stigler G J. The economics of informationJ. The journal of political economy, 1961: 213-225.In economics, the information known by actors is generally taken to be given and is often assumed to be perfect. This paper adds a dimension to infor

2、mation-related problems by considering the search for information. The paper attempts to analyze systematically one important problem of information-the ascertainment of market price. The nature of search:Even for homogenous goods, the asking prices of sellers are not equal. The existence of these p

3、rice differences is termed price dispersion.The paper emphasizes the fact that dispersion of asking prices always exists in the market. Price dispersion derives from two sources: Consumers being unaware of all of the prices at which a good is available (market ignorance) Additional services provided

4、 by seller (customer service, variety of stock) In a market, each seller has its own price for a good. Each buyer, unless a market is completely centralized, will not know all of the asking prices which various sellers quote at any given time because prices change frequently. Therefore, each buyer d

5、oes not know the minimum price for which he can purchase a good. As a result, a buyer engages in search. For buyers, search is defined as a process of surveying a number of sellers to determine the lowest price.*In the market, both sellers and buyers will search the prices. But in this presentation,

6、 most of time I only illustrated the search behavior of buyers, since the condition of sellers is parallel to the analysis for buyers. The benefits of searchBecause of the price dispersion, the buyers can find lower price and save money through searching. Then, at any time, there will be a frequency

7、 distribution of the asking prices. Asking prices P1,P2,Pn are i.i.d F(p): the cdf of asking prices; f(p) the pdf of asking prices. The cdf of minimum prices with n searches is The pdf of minimum prices with n searches is The expected minimum prices with n searches is E(n) is a decreasing function o

8、f n, and Therefore, as n increases, the minimum price decreases at a decreasing rate.NOW, taking two specific examples to illustrate:(1) If the distribution of asking prices is a uniform distribution between 0 to 1 (because of its algebraic simplicity)The cdf of minimum prices with n searches is The

9、 pdf of minimum prices with n searches is The expected minimum prices with n searches The variance of the minimum price is Note that as the number of searches (n) increases, the average minimum price and its variance both decrease at a decreasing rate.Furthermore, The paper introduces a concept-expe

10、cted savings from an additional unit of search, which are given by the product of the quantity purchased (q) and the absolute value of the expected reduction of minimum prices with each additional search: When search amount n is fixed, the more price dispersion in the market, the expected saving fro

11、m will be larger. The savings will also obviously be greater, the greater the expenditure on the commodity.(2) If the distribution of asking prices is a normal distribution. Note that as the number of searches (n) increases, the average minimum price and its variance both decrease.The cost of search

12、Indeed, search will help buyers increase expected savings. However, there is a search behaviour, there is a search cost.a) The cost of search is proportional to the number of sellers from which the buyer inquires about the goods price.b) The main cost is time, so high income buyers face higher searc

13、h costsc) At the optimum level of search: (expected marginal return) = (cost of search)d) For unique goods (there are few buyers or sellers in the market), the cost of search is much higher since the cost of search must be devided by the fraction of potential buyers in the population which is being

14、searched. (If there is only one potential seller in 100 sellers, the cost of search is increased by 100 times. )There two methods to decrease search costs by identifying potential buyers and sellers(1) “Specialized traders” centralize trading. They provide a meeting place for potential buyers and se

15、llers. (2)Advertising (classifieds)a obvious modern method to identifying buyers and sellers. Buyers and sellers are listed, reducing search, but the cost of placing the advertisement must also be considered.Dealer marketFor dealer: how the demand curve facing a dealer is determinedOnce a seller cho

16、oses a price p, all buyers for whom this p is the minimum price will buy from this seller. If there are r sellers quote the same price p , the number of possible buyers is Nb, and the distribution of asking prices is uniform, then the expected number of buyers for the seller is given by: where (1) F

17、or and if n2As the price falls, the number of buyers increases at an increasing rate.(2) LetThen, if ,the number of buyers increases with increased search. For buyer: how to deciede search(amount and time)(1) For a unique purchase(like house selling), its transaction only has one period. The equatio

18、n defining optimim search isthe cost of search = the expected marginal return(?)(2) If purchases are repetitive, the transaction will continue several periods. There is an effect of search on the volume of goods purchased. Now, we consider a two periods phurchase. Let the expected minimum price be p

19、1=E(n1) in period 1 and let the expected minimum price in period 2, with r a measure of the correlation between sellers successive asking prices, beIf the cost of search is per unit, total expenditures for a fixed quantity of purchases(Q) per unit of period are, neglecting interest,TE is at minimun,

20、 when(1) If r = 1, which means the correaltion of asking prices of dealers in successive time periods is perfect, then p2 = p1 , n2=0, n2 is determined by. The initial search is the only one that need be undertaken. The expected savings of the search will be the present value of the discounted futur

21、e savings on futures purchases over the planning horizon of the buyer.(2) If r = 0, which means that prices are uncorrelated across time periods, then the search done in each period will be independent of previous experiences and n1 = n2. (3) If 0r1, take E(n)=e-n for example, we can know TE is mini

22、mum whenIf the correlation of successive price is positive, customer search will be larger in the initial period than in subsquent periods.The authors finds that the correlation of successive asking prices of sellers usually positive. And a positive correlation justifies the widely held view that in

23、experienced buyers pay higher prices in a market than do experienced buyers. The inexperienced buyers have no accumulated knowledge of asking prices, and even with pay with an optimum amount of search they will pay higher prices on average. AdvertiseingFor buyers, advertisng can help them to reduce

24、search cost by identifying sellers.Model: Suppose a given advertisement of size a will inform c per cent of the pontential buyers in a given period, so c=g(a). A certain fraction b, of potential customer will be born and die(departure or forgetting the seller) in a stable population.In the first per

25、iod Total number of potential customers: N The probability of being informed: cThe number of potential customers being informed should be: cNIn the second period The number of these potential customers who have be informed in first period: cN(1-b) The number of new potential customers who are be inf

26、ormed in this period: cbN The number of potential customers who were not informed in the first period but are informed in the second period: c(1-b)N-cN(1-b)The total number of customers who have informed by this period:cN1+(1-b)(1-c)In the kth period Total number of potential customers being informe

27、d: As k goes large, this approaches Let, is the probability that any one seller will inform any buyer(any one buyer will identify any seller)If there are r sellers, the probability that a customer will identify m sellers isHence, if r sellers advertise, the average number of sellers a customer will

28、identify is r with variance r(1-).And the value of the information to buyers is approximately:, where is the expected savings because of searching m times.For sellers, whats their decision for advertising?MonopolyFirst we consider a monopolistic situation. In this case, the value of search in the fa

29、ce of price dispersion is absent. A monopolist will advertise (and price the product) so as to maximize his profitsProfit Function: p=f(q) is the demand curve of the individual buyer, pa is advertising expenditure, is production costs other than advertising. The conditions for maximize profit:From e

30、quation (1), we obtain(1) The marginal cost = marginal revenue (2) , is the elasticity of a buyers demand curveIn addition, combining equation (1) and (2) we obtainthe marginal revenue from advertising expenditure=the absolute value of the elasticity of demandCompetitive MarketAssumptions:There are

31、r firms and all firms are identical. All buyers have identicall demand curves and engage in a equal amount s of search.Under competition, the amount of advertising by any one firm(seller) can be determined as follow:1. Finding the fraction of potential buyers who will canvass the seller iFor one tim

32、e search(s=1): The amount of sellers that each buyer on average will know sellers For buyers who know seller i: The percent of buyers who will canvass seller i: The percent of buyers who will not canvass seller i: For s searches (s=s): The amount of sellers that each buyer in average will know: For buyers who know seller i: The percent of buyers who will canvass sell