Deep Thought To recommend a lazy job candidate: In my opinion, you will be very fortunate to get this person to work for you. To recommend a person who is totally inept: I most enthusiastically recommend this candidate with no qualifications whatsoever. To describe an ex-employee who had problems getting along with fellow workers: I am pleased to say that this candidate is a former colleague of mine. To describe a candidate who is so unproductive that the job would be better left unfilled: I can assure you that no person would be better for the job. (Translation: Today’s lesson teaches how to access a job applicant when cheap talk is worthless. ) BA 210 Lesson III. 6 Market Failure and Signaling 1
Overview BA 210 Lesson III. 6 Market Failure and Signaling 2
Overview This lesson considers games where players want to reveal information about themselves (not just about their actions, as in Lesson 5) but they find it hard because their interests conflict. In particular, just talking is not believable. For example, consider King Solomon’s Dilemma: Two women came before King Solomon, disputing who was the true mother of a child. The Bible takes up the story in 1 Kings 3: 24 -28 … BA 210 Lesson III. 6 Market Failure and Signaling 3
Overview Then the king said, “Bring me a sword. ” So they brought a sword for the king. He then gave an order: “Cut the living child in two and give half to one and half to the other. ” The woman whose son was alive was filled with compassion for her son and said to the king, “Please, my lord, give her the living baby! Don’t kill him!” But the other said, “Neither I nor you shall have him. Cut him in two!” Then the king gave his ruling: “Give the living baby to the first woman. Do not kill him; she is the mother. ” When all Israel heard the verdict the king had given, they held the king in awe, because they saw that he had wisdom from God to administer justice. King Solomon was indeed wise. But he was also lucky. How would the story have been different if the second woman had studied game theory? BA 210 Lesson III. 6 Market Failure and Signaling 4
Lesson Overview Lesson III. 6 Market Failure and Signaling Example 1: Adverse Selection and Market Failure Example 2: Signaling and Screening Example 3: The Dilemma of Pooling Summary Review Questions BA 210 Lesson III. 6 Market Failure and Signaling 5
Example 1: Adverse Selection and Market Failure BA 210 Lesson III. 6 Market Failure and Signaling 6
Example 1: Adverse Selection and Market Failure Comment: Employers know less about the skills of potential employees than does the employee, with other important matters like work attitude and collegiality even harder to observe. Buyers of used cars know less about a car than do the sellers. And insurance companies know less about the heath and driving skills of insurance applicants than do the applicants. In those examples, cheap talk cannot be screened for information by the less informed player. Unskilled, lazy, and obnoxious potential employees will claim to have skills and will act hard working and collegial during interviews to get higher pay. Sellers of used cars will withhold any problems about their cars. And insurance applicants who are bad risks will claim good health and driving habits to get lower rates. For those same reasons, cheap talk cannot signal information by the more informed player since the other player knows there are incentives to lie. BA 210 Lesson III. 6 Market Failure and Signaling 7
Example 1: Adverse Selection and Market Failure If there are no other ways to screen or signal information, then insurance companies would have to offer the same rates to all applicants, say 5 cents per dollar of coverage. That rate would be especially attractive to applicants who know there own risk (of illness or car crash) exceeds 5%. Hence, the pool of applicants for that insurance policy will have a larger proportion of poorer risks than the proportion of those risks in the population as a whole. The insurance company thus selectively attracts an unfavorable, or adverse, group of customers. That phenomenon is common in transactions involving asymmetric information (one player knows more than the other) and is known as adverse selection. Adverse selection can exclude some mutually-beneficial agreements. BA 210 Lesson III. 6 Market Failure and Signaling 8
Example 1: Adverse Selection and Market Failure Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A (impatient, timeconscious, status-conscious, ambitious) employees contribute $160, 000 per year to profits. And Type B (patient, easy-going, apathetic) employees contribute $60, 000 per year to profits. Suppose Type A workers have existing jobs paying $125, 000 per year, and Type B have existing jobs paying $30, 000 per year. Suppose there is no way for the employer to tell Type A workers from Type B workers and, so, must offer each the same wage. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Determine the wage demand, and which types work for Employer Earl. BA 210 Lesson III. 6 Market Failure and Signaling 9
Example 1: Adverse Selection and Market Failure Answer: The wage demand depends on the positive fraction f of Type A workers and the remaining positive fraction (1 -f ) of Type B workers in the general population. A random worker in the general population is thus Type A with probability f and Type B with probability (1 -f ). The expected value of a random worker is $160, 000 x f + $60, 000 x (1 -f ) = $60, 000 + $100, 000 x f. In particular, $60, 000 + $100, 000 x f is the best acceptable wage demand from a random worker in the general population. But is that wage enough for both types to gain from employment? BA 210 Lesson III. 6 Market Failure and Signaling 10
Example 1: Adverse Selection and Market Failure On the one hand, if $60, 000 + $100, 000 x f > $125, 000, or f > 0. 65, then both types of workers gain from Employment with Earl. So $60, 000 + $100, 000 x f is, indeed, the wage demand, and both types work for Employer Earl. On the other hand, if $60, 000 + $100, 000 x f < $125, 000, or f < 0. 65, then Type A workers would loose from Employment with Earl. So only Type B workers make wage demands. Anticipating that, the expected value of a random job applicant falls to $60, 000, which is now is the best acceptable wage demand. So $60, 000 is the wage demand, and only Type B works for Employer Earl. BA 210 Lesson III. 6 Market Failure and Signaling 11
Example 1: Adverse Selection and Market Failure Comment: When $60, 000 + $100, 000 x f < $125, 000, or f < 0. 65, Type B works for Employer Earl. So, markets fail to bring about an agreement between Employer Earl and Type A workers. That is unlike the bargaining problems in Part II where every possible mutually-beneficial gain from an agreement was realized. The only issue for our analysis was how to divide that gain. BA 210 Lesson III. 6 Market Failure and Signaling 12
Example 2: Signaling and Screening BA 210 Lesson III. 6 Market Failure and Signaling 13
Example 2: Signaling and Screening In games where cheap talk (costless communication) cannot be screened for information by the less informed player and cheap talk cannot signal information by the more informed player, costly communication can be used for screening and signaling. What about costly communication? Can an employer screen for information by investigating a potential employee’s college record? Or can a potential employee signal for information by taking college courses that he would not take otherwise? BA 210 Lesson III. 6 Market Failure and Signaling 14
Example 2: Signaling and Screening Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $160, 000 per year to profits. And Type B employees contribute $60, 000 per year to profits. Suppose Type A workers have existing jobs paying $125, 000 per year, and Type B have existing jobs paying $30, 000 per year. Suppose Type A workers regard the cost of completing a hard college course as $3, 000 a year of salary, and Type B workers as $15, 000. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed hard courses. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). For each type of worker, determine wage demands and the number of completed classes. BA 210 Lesson III. 6 Market Failure and Signaling 15
Example 2: Signaling and Screening Answer: Consider finding an appropriate integer number N so the Employer knows that anyone who has completed at least N courses must be a Type A worker (and so should be granted a wage demand of $160, 000), and anyone who has not must be Type B (and so should be granted a wage demand of $60, 000). There are two types of constraints on N: incentive compatibility and participation. BA 210 Lesson III. 6 Market Failure and Signaling 16
Example 2: Signaling and Screening Incentive compatibility constrains the number N of courses to be high enough so Type B workers (to be paid $60, 000) do not bother to meet it, and low enough so Type A workers (to be paid $160, 000) will meet it. Incentive compatibility for Type B requires $60, 000 > $160, 000 - $15, 000 x N, or N > 6. 67, meaning N > 7. Incentive compatibility for Type A requires $160, 000 - $3, 000 x N > $60, 000, or N < 33. 33, meaning N < 33. BA 210 Lesson III. 6 Market Failure and Signaling 17
Example 2: Signaling and Screening Participation constrains the number N of courses so Type B and Type A workers each benefit from job agreements of $60, 000 to Type B workers and $160, 000 to Type A workers. Participation for Type B requires $60, 000 > $30, 000, which is true regardless of N. Participation for Type A requires $160, 000 - $3, 000 x N > $125, 000, or N < 11. 67, meaning N < 11. BA 210 Lesson III. 6 Market Failure and Signaling 18
Example 2: Signaling and Screening Putting it all together, the Employer should pick any number N between 7 and 11 and accept a wage demand of $160 K per year for workers that have completed at least N courses, and accept a wage demand of $60 K per year for the other workers, who would complete 0 courses. Comment: Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $3, 000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 7), the cost of the information asymmetry is $3, 000 x 7 = $21, 000 per year. BA 210 Lesson III. 6 Market Failure and Signaling 19
Example 3: The Dilemma of Pooling BA 210 Lesson III. 6 Market Failure and Signaling 20
Example 3: The Dilemma of Pooling Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $160, 000 per year to profits. And Type B employees contribute $60, 000 per year to profits. Suppose Type A workers have existing jobs paying $125, 000 per year, and Type B have existing jobs paying $30, 000 per year. Suppose Type A workers regard the cost of completing a hard college course as $3, 000 a year of salary, and Type B workers as $15, 000. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed hard courses. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Would all workers be better off if Employer Earl did not use the number of completed courses to screen job candidates? BA 210 Lesson III. 6 Market Failure and Signaling 21
Example 3: The Dilemma of Pooling Answer: From previous calculations, if Employer Earl does use the number of completed courses to screen job candidates, then Employer Earl should pick any number of courses between 7 and 11 and accept a wage demand of $160 K per year for workers that have completed at least N courses, and accept a wage demand of $60 K per year for the other workers. BA 210 Lesson III. 6 Market Failure and Signaling 22
Example 3: The Dilemma of Pooling Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $3, 000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 7), the cost of the information asymmetry is $3, 000 x 7 = $21, 000 per year, leaving Type A workers with $160, 000$21, 000 = $139, 000 net wages. BA 210 Lesson III. 6 Market Failure and Signaling 23
Example 3: The Dilemma of Pooling Dropping the screening by course selection avoids the $21, 000 per year cost of the information asymmetry but means pooling all workers together, paying them the same. From previous calculations, $60, 000 + $100, 000 x f is the best acceptable wage demand from a random worker in the general population, which depends on the positive fraction f of Type A workers in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $60, 000 + $100, 000 x f > $139, 000, or f > 0. 79. BA 210 Lesson III. 6 Market Failure and Signaling 24
Example 3: The Dilemma of Pooling For example, if 80% of the population were Type A, and 20% Type B. Then the common salary is. 8 x $160, 000 +. 2 x $60, 000 = $140, 000. Type B workers prefer the pooling equilibrium (salary $140, 000) to the screening equilibrium (salary $60, 000). And Type A workers also prefer the pooling equilibrium (salary $140, 000) to the screening equilibrium (net salary $139, 000). BA 210 Lesson III. 6 Market Failure and Signaling 25
Example 3: The Dilemma of Pooling Comment: That pooling equilibrium creates a Prisoner’s dilemma for Type A workers. Working with the 80%-20% of types, all Type A workers are best off by accepting the pooling equilibrium, but individually each worker could signal by offering to complete 1 course and work for $140, 000 + $10, 000 per year. BA 210 Lesson III. 6 Market Failure and Signaling 26
Example 3: The Dilemma of Pooling Employers would agree to pay $140, 000 + $10, 000 per year for a worker that completes 1 course because only Type A workers would be willing to take 1 course for an extra $10, 000 per year. As more Type A workers take 1 course to signal their type, the average value of the pooled workers decreases, which increases the salary gap between Type A workers and pooled workers, which requires more courses to signal. This process continues until all Type A workers signal by taking 7 courses, and we are back at the equilibrium with separation of types based on screening (or signaling). BA 210 Lesson III. 6 Market Failure and Signaling 27
Summary BA 210 Lesson III. 6 Market Failure and Signaling 28
Summary In any screening or signaling problem we consider, there is a good (labor, cars, wrenches, …) that is either High Quality or Low Quality, where the High Quality good has higher value to the Buyer ($160 > $60), and higher opportunity or production cost to the seller ($125 > $30). The seller of either quality makes a take-it-or-leave-it offer to the buyer. Quality is known to the seller, but not to the buyer. The only way for the Seller of the high quality good to credibly communicate to the buyer is for the Seller to pay for units of a signal (education, a service warranty, a replacement warranty, …). BA 210 Lesson III. 6 Market Failure and Signaling 29
Summary For that signal to communication credibly, the signal quantity N must satisfy incentive compatibility constraints that Sellers with Low Quality (to be paid $60 if his good is known to be Low Quality) do not bother to signal (60 > 160 -15 N), and low enough so Sellers with High Quality (to be paid $160 if his good is known to be High Quality) will signal. In particular, it must be true that the signal is cheaper for the Seller of the High Quality good than for the Seller of the Low Quality good ($3 < $15). BA 210 Lesson III. 6 Market Failure and Signaling 30
Summary The signal must also satisfy the participation constraint that the transaction benefits the Seller of the High Quality good after paying for the signal (160 - 3 N > 125). The Seller of the Low Quality good always benefits from a transaction since he does not pay for the signal ($60 > $30). Finally, we only consider the cases where the potential gain from transacting the High Quality good ($160 -$125) is higher than the potential gain from the Low Quality good ($60 -$30). BA 210 Lesson III. 6 Market Failure and Signaling 31
Review Questions § You should try to answer some of the following questions before the next class. § You will not turn in your answers, but students may request to discuss their answers to begin the next class. § Your upcoming cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams. BA 210 Lesson III. 6 Market Failure and Signaling 32
Review Questions Review Question 1 BA 210 Lesson III. 6 Market Failure and Signaling 33
Review Questions Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A (impatient, timeconscious, status-conscious, ambitious) employees contribute $130, 000 per year to profits. And Type B (patient, easy-going, apathetic) employees contribute $80, 000 per year to profits. Suppose Type A workers have existing jobs paying $70, 000 per year, and Type B have existing jobs paying $40, 000 per year. Suppose there is no way for the employer to tell Type A workers from Type B workers and, so, must offer each the same wage. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Determine the wage demand, and which types work for Employer Earl. BA 210 Lesson III. 6 Market Failure and Signaling 34
Review Questions Answer: The wage demand may depend on the positive fraction f of Type A workers and the remaining positive fraction (1 -f ) of Type B workers in the general population. A random worker in the general population is thus Type A with probability f and Type B with probability (1 -f ). The expected value of a random worker is $130, 000 x f + $80, 000 x (1 -f ) = $80, 000 + $50, 000 x f. In particular, $80, 000 + $50, 000 x f is the best acceptable wage demand from a random worker in the general population. But is that wage enough for both types to gain from employment? BA 210 Lesson III. 6 Market Failure and Signaling 35
Review Questions If $80, 000 + $50, 000 x f > $70, 000, which is true for every f > 0, then both types of workers gain from Employment with Earl. So $80, 000 + $50, 000 x f is, indeed, the wage demand, and both types work for Employer Earl, regardless of the value of f > 0. BA 210 Lesson III. 6 Market Failure and Signaling 36
Review Questions Review Question 2 BA 210 Lesson III. 6 Market Failure and Signaling 37
Review Questions Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $160, 000 per year to profits. And Type B employees contribute $60, 000 per year to profits. Suppose Type A workers have existing jobs paying $125, 000 per year, and Type B have existing jobs paying $30, 000 per year. Suppose Type A workers regard the cost of completing a hard college class as $3, 000 a year of salary, and Type B workers as $15, 000 a year of salary. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed classes. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Would all workers be better off if Employer Earl did not use the number of completed classes to screen job candidates? BA 210 Lesson III. 6 Market Failure and Signaling 38
Review Questions Answer: First, suppose Employer Earl does use the number of completed classes to screen job candidates. Consider finding an appropriate integer number N so the Employer should accept a wage demand of $120 K per year for workers that have completed at least N courses, and a wage demand of $70 K per year to the other workers. There are two constraints on N, incentive compatibility and participation. BA 210 Lesson III. 6 Market Failure and Signaling 39
Review Questions Incentive compatibility constrains the number N of courses to be high enough so Type B workers do not bother to meet it, and low enough so Type A workers will meet it. Incentive compatibility for Type B requires $70, 000 > $120, 000 - $12, 000 x N, or N > 4. 16, meaning N > 5. Incentive compatibility for Type A requires $120, 000 - $4, 000 x N > $70, 000, or N < 12. 5, meaning N < 12. BA 210 Lesson III. 6 Market Failure and Signaling 40
Review Questions Participation constrains the number N of courses so Type B and Type A workers both accept the job offers of $70, 000 to Type B workers and $120, 000 to Type A workers. Participation for Type B requires $70, 000 > $30, 000, which is true regardless of N. Participation for Type A requires $120, 000 - $4, 000 x N > $40, 000, or N < 20. BA 210 Lesson III. 6 Market Failure and Signaling 41
Review Questions Putting it all together, the Employer should pick any number between 5 and 12 and accept a wage demand of $120 K per year for workers that have completed at least N courses, and accept a wage demand of $70 K per year for the other workers. Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $4, 000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 5), the cost of the information asymmetry is $4, 000 x 5 = $20, 000 per year, leaving Type A workers with $120, 000$20, 000 = $100, 000 net wages. BA 210 Lesson III. 6 Market Failure and Signaling 42
Review Questions Dropping the screening by course selection avoids the $20, 000 per year cost of the information asymmetry but means pooling all workers together, paying them the same. The expected value of a random worker is $120, 000 x f + $70, 000 x (1 -f ) = $70, 000 + $50, 000 x f , so $70, 000 + $50, 000 x f is the best acceptable wage demand from a random worker in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $70, 000 + $50, 000 x f > $100, 000, or f > 0. 6. BA 210 Lesson III. 6 Market Failure and Signaling 43
Review Questions Review Question 3 BA 210 Lesson III. 6 Market Failure and Signaling 44
Review Questions Question: Suppose Employer Earl has use for two kinds of employees. Skilled and hard working Type A employees contribute $160, 000 per year to profits. And Type B employees contribute $60, 000 per year to profits. Suppose Type A workers have existing jobs paying $125, 000 per year, and Type B have existing jobs paying $30, 000 per year. Suppose Type A workers regard the cost of completing a hard college class as $3, 000 a year of salary, and Type B workers as $15, 000 a year of salary. Suppose there is no way for the employer to directly tell Type A workers from Type B workers, but the employer can confirm the number of completed classes. Finally, suppose potential employees can make a wage demand that the employer must either accept or reject (but not counter). Would all workers be better off if Employer Earl did not use the number of completed classes to screen job candidates? BA 210 Lesson III. 6 Market Failure and Signaling 45
Review Questions Answer: First, suppose Employer Earl does use the number of completed classes to screen job candidates. Consider finding an appropriate integer number N so the Employer should accept a wage demand of $140 K per year for workers that have completed at least N courses, and a wage demand of $80 K per year to the other workers. There are two constraints on N, incentive compatibility and participation. BA 210 Lesson III. 6 Market Failure and Signaling 46
Review Questions Incentive compatibility constrains the number N of courses to be high enough so Type B workers do not bother to meet it, and low enough so Type A workers will meet it. Incentive compatibility for Type B requires $80, 000 > $140, 000 - $20, 000 x N, or N > 3. Incentive compatibility for Type A requires $140, 000 - $2, 000 x N > $80, 000, or N < 30. BA 210 Lesson III. 6 Market Failure and Signaling 47
Review Questions Participation constrains the number N of courses so Type B and Type A workers both accept the job offers of $80, 000 to Type B workers and $140, 000 to Type A workers. Participation for Type B requires $80, 000 > $40, 000, which is true regardless of N. Participation for Type A requires $140, 000 - $2, 000 x N > $100, 000, or N < 20. BA 210 Lesson III. 6 Market Failure and Signaling 48
Review Questions Putting it all together, the Employer should pick any number between 3 and 20 and accept a wage demand of $140 K per year for workers that have completed at least N courses, and accept a wage demand of $80 K per year for the other workers. Those acceptances separate Type A from Type B workers, but it comes at the communication cost of $2, 000 x N per year paid by the Type A workers. Even if the smallest number of courses were picked (N = 3), the cost of the information asymmetry is $2, 000 x 3 = $6, 000 per year, leaving Type A workers with $140, 000$6, 000 = $134, 000 net wages. BA 210 Lesson III. 6 Market Failure and Signaling 49
Review Questions Dropping the screening by course selection avoids the $6, 000 per year cost of the information asymmetry but means pooling all workers together, paying them the same. The expected value of a random worker is $140, 000 x f + $80, 000 x (1 -f ) = $80, 000 + $60, 000 x f , so $80, 000 + $60, 000 x f is the best acceptable wage demand from a random worker in the general population. In particular, all workers would be better off if Employer Earl dropped screening job candidates if $80, 000 + $60, 000 x f > $134, 000, or f > 0. 9. BA 210 Lesson III. 6 Market Failure and Signaling 50
BA 210 Introduction to Microeconomics End of Lesson III. 6 BA 210 Lesson III. 6 Market Failure and Signaling 51
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