values, 1/2 and 1: Pr(0-1)= a and Pr(0= qual to s. Suppose that the search engine induces expected relevance 0. Show th is v² = 1- 28 8€ What is the price charged by a firm of quality and its profit? Express search engine's fee and profit in terms of 0*, 0 and s. Suppose that a = 1/8. What is search engine's profit if it induces high if its profit when it induces distorts search, i.e. 0 = 1/2? Which fee sh

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Consider a version of Eliaz and Spiegler model. Suppose that v is distributed uniformly on (0, 1], and
relevance parameter takes two values, 1/2 and 1: Pr(0-1)= a and Pr(0=1/2) = 1-a. Let search cost
be equal to s.
1. Suppose that the search engine induces expected relevance 0. Show that consumer reservation values
is
v² = 1-
28
0e
2. What is the price charged by a firm of quality and its profit?
3. Express search engine's fee and profit in terms of 0, 0 and s.
4. Suppose that a = 1/8. What is search engine's profit if it induces high relevance, i.e. * = 1? What
if its profit when it induces distorts search, i.e. 0 = 1/2? Which fee should search engine choose?
Transcribed Image Text:Consider a version of Eliaz and Spiegler model. Suppose that v is distributed uniformly on (0, 1], and relevance parameter takes two values, 1/2 and 1: Pr(0-1)= a and Pr(0=1/2) = 1-a. Let search cost be equal to s. 1. Suppose that the search engine induces expected relevance 0. Show that consumer reservation values is v² = 1- 28 0e 2. What is the price charged by a firm of quality and its profit? 3. Express search engine's fee and profit in terms of 0, 0 and s. 4. Suppose that a = 1/8. What is search engine's profit if it induces high relevance, i.e. * = 1? What if its profit when it induces distorts search, i.e. 0 = 1/2? Which fee should search engine choose?
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