A Model of search price Dispersion The discount store We denote by Eb, the expected number of customers shopping at the discount store. To calculate Ebp, observe that p pNp implies that all a- L consumers who search buy at the discount store, simply because their search provides them with the knowledge of which store is discounting. In addition, on average, 1/3 of the H-3 consumers who buy at random will randomly arrive at the discount store( the lucky ones). Hence, since there are only two stores the expected number of consumers who shop at the discount store is given by 助=-L+2 3=3-L+-P) ga (16.5) The discount store takes pND as given and chooses pd that maximizes expected profit given by E丌D≡ PpEbD=pD L LPND-PD The first-order condition is given by 0= H/3-L+4pND/(9a)-8pD/(9a). Hence, the best- response function of the discount store is given by PD≡Rp(pND) a(H-3L 8 (166)
A Model of Search & Price Dispersion
A Model of search price Dispersion The expensive store We denote by eby the expected total number of customers shopping at the two expensive stores. To calculate EbND. observe that H-3 consumers do not search and therefore buy at random hence. since there are only two stores the expected number of consumers who shop at the expensive stores is given by EAND=<As 3—=x2+4=PND) -8) (167) 9 The owner of the expensive stores takes PD as given and chooses pND that maximizes expected profit given by ErND≡ PNDEbND=PND (pD-pnd) 9 The first-order condition is given by 0=2H/3+4pD/(9a)-8pND/(9a). Hence, the best-response function of the owner of the expensive stores is given by PND≡RNDD) 3aH +2 (168)
A Model of Search & Price Dispersion
A Model of search price Dispersion Price dispersion equilibrium The best-response functions of the discount store(16.6) and the expensive stores(16.)are drawn in Figure 16.2. The unique equilibrium PD BRND BR -3L1 3a(H-3L 6H-3) PND Figure 16.2 The determination of the discount and expensive prices prices are found by solving(16.6)and(16.8). The consumer who is indifferent to the choice between searching and buying at random is then found by substituting the equilibrium prices into (16.4).Hence, PD 2, Pin- a(5H-3L a(2H -3L ,and geH+3L (169)
A Model of Search & Price Dispersion
A Model of search price Dispersion Note that L<< H and that pD< pND Since we assumed that h> The following proposition is straightforwardly from(16.9) Proposition 16.7 An increase in the cost of search parameter, a, will increase the prices charged by all stores. Also, the difference in prices between an expensive store and the discount store, PND-PD, increases with an increase in the search cost, and declines to zero as the search cost becomes negligible (a++0) The interesting conclusion that we can draw from Proposition 16.1 is that an increase search cost increases the monopoly power of both types of stores. In contrast, when search cost is negligible( a-0), competition between the two stores intensifies and all prices drop to the competitive level (zero in our case). Thus, search cost explains why different stores charge different prices b enabling the stores to differentiate themselves from rival stores by labeling themselves as"discount' or"nondiscount, "thereby reducing competition According to(16.5)and(16.7), the expected number of buyers at each store is given by Eb 2(2H-3D)、5H-3L_BbND 9 18 (1610) Thus, the expected number of shoppers in the discount store is greater than the expected number of shoppers at an expensive store since the discount store attracts both informed and uninformed consumers whereas the nondiscount store attracts uninformed consumers onl
A Model of Search & Price Dispersion
Search Theory Now we assume that stores charge different prices and analyze how consumers behave in the presence of price dispersion more precisely, we analyze how consumers with search costs conduct their shopping and how they determine how many stores to visit when searching for the lowest price
Search Theory • Now we assume that stores charge different prices and analyze how consumers behave in the presence of price dispersion. More precisely, we analyze how consumers with search costs conduct their shopping and how they determine how many stores to visit when searching for the lowest price