As in the lemons model, suppose that there is one seller and one buyer who may exchange a good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it is uniformly distributed on [0,1]). There is a fixed price of p = 1/2 at which trade may occur, which happens if and only if both the buyer and the seller agree to trade. Before deciding whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of u. The seller's payoff is p if trade occurs and vif trade does not occur. The buyer's payoff is 3v/2-p-c if trade occurs and he first learned the value of v; 3v/2-p if trade occurs and he did not learn. the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade does not occur and he did not learn the value of v. Find the probability that trade occurs for each c € (0, 1). Solution: If the buyer chooses not to learn the value, we know from the lemons model that trade will not occur for any v> 0 (since 3/2 < 2). If the buyer pays the cost to learn the value, he is willing to buy if and only if 3v/2≥ 1/2, that is, if and only if v≥ 1/3. The seller is willing to sell if and only if n ≤ 1/2 The buyer's ernected novaff is
As in the lemons model, suppose that there is one seller and one buyer who may exchange a good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it is uniformly distributed on [0,1]). There is a fixed price of p = 1/2 at which trade may occur, which happens if and only if both the buyer and the seller agree to trade. Before deciding whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of u. The seller's payoff is p if trade occurs and vif trade does not occur. The buyer's payoff is 3v/2-p-c if trade occurs and he first learned the value of v; 3v/2-p if trade occurs and he did not learn. the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade does not occur and he did not learn the value of v. Find the probability that trade occurs for each c € (0, 1). Solution: If the buyer chooses not to learn the value, we know from the lemons model that trade will not occur for any v> 0 (since 3/2 < 2). If the buyer pays the cost to learn the value, he is willing to buy if and only if 3v/2≥ 1/2, that is, if and only if v≥ 1/3. The seller is willing to sell if and only if n ≤ 1/2 The buyer's ernected novaff is
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
how to construct: can you explain all parts
max┬(v^'∈[0,1]) Pr(b_2<b(v^' ))(v_1-1/2 (b(v^' )+E[b(v_2 )∣v_2<v^' ]))". "
![As in the lemons model, suppose that there is one seller and one buyer who may exchange a
good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of
v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it
is uniformly distributed on [0,1]). There is a fixed price of p = 1/2 at which trade may occur,
which happens if and only if both the buyer and the seller agree to trade. Before deciding
whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of u. The seller's
payoff is p if trade occurs and vif trade does not occur. The buyer's payoff is 3v/2-p-c if
trade occurs and he first learned the value of v; 3v/2-p if trade occurs and he did not learn
the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade
does not occur and he did not learn the value of u. Find the probability that trade occurs for
each c € (0, 1).
Solution: If the buyer chooses not to learn the value, we know from the lemons model that
trade will not occur for any v> 0 (since 3/2 < 2). If the buyer pays the cost to learn the
value, he is willing to buy if and only if 3v/2≥ 1/2, that is, if and only if v≥ 1/3. The seller
is willing to sell if and only if v ≤ 1/2. The buyer's expected payoff is
3v
1
Pr
P² ( 1 ≤ 0 ≤ 12 ) ² [2/07 - 12/1
E
<<
SUS-C²
-c=
11
68
==C.
If e≤ 1/48, the buyer will learn and trade will occur with probability 1/6. Otherwise, trade
occurs with probability 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F609dbd69-2d00-4841-aec2-a392b4858745%2F71a1e1fe-0441-4f99-bfc5-4a1ca0edba12%2Fuiph83c_processed.png&w=3840&q=75)
Transcribed Image Text:As in the lemons model, suppose that there is one seller and one buyer who may exchange a
good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of
v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it
is uniformly distributed on [0,1]). There is a fixed price of p = 1/2 at which trade may occur,
which happens if and only if both the buyer and the seller agree to trade. Before deciding
whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of u. The seller's
payoff is p if trade occurs and vif trade does not occur. The buyer's payoff is 3v/2-p-c if
trade occurs and he first learned the value of v; 3v/2-p if trade occurs and he did not learn
the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade
does not occur and he did not learn the value of u. Find the probability that trade occurs for
each c € (0, 1).
Solution: If the buyer chooses not to learn the value, we know from the lemons model that
trade will not occur for any v> 0 (since 3/2 < 2). If the buyer pays the cost to learn the
value, he is willing to buy if and only if 3v/2≥ 1/2, that is, if and only if v≥ 1/3. The seller
is willing to sell if and only if v ≤ 1/2. The buyer's expected payoff is
3v
1
Pr
P² ( 1 ≤ 0 ≤ 12 ) ² [2/07 - 12/1
E
<<
SUS-C²
-c=
11
68
==C.
If e≤ 1/48, the buyer will learn and trade will occur with probability 1/6. Otherwise, trade
occurs with probability 0.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education