Suppose college students are of just two types: A (able) and C (challenged). Potential employers in a given job market are willing to pay $160,000 a year for type A and $60,000 to a type C. Other employment opportunities yield the A types a salary of $125,000 and C types a salary of $30,000. Suppose the types differ in their tolerance for taking a tough course rather than an easy one in college. Each type must make a sacrifice to take a tough course, but this sacrifice is smaller or easier to bear for the A types than it is for the C types. Specifically, the A types regard the cost of each tough course as equivalent to $3,000 a year of salary, while the C types regard it as $15,000 a year of salary. The potential employer wishes to use the above differential in costs to screen his applicants and tell the A types from the C types. Consider the following hiring policy: anyone who has taken a certain, n, or more of the tough courses will be regarded as an A type and paid $160,000, and anyone who has taken fewer than n tough courses will be regarded as a C type and paid $60,000. The aim of this policy is to create natural incentives whereby only the A types will take the tough courses, and the C types will not. Answer the following questions: a) List all possible values of n that satisfy both the incentive-compatibility condition and the participation condition. Suppose college students are of just two types: A (able) and C (challenged). Potential employers in a given job market are willing to pay $160,000 a year for type A and $60,000 to a type C. Other employment opportunities yield the A types a salary of $125,000 and C types a salary of $30,000. Suppose the types differ in their tolerance for taking a tough course rather than an easy one in college. Each type must make a sacrifice to take a tough course, but this sacrifice is smaller or easier to bear for the A types than it is for the C types. Specifically, the A types regard the cost of each tough course as equivalent to $3,000 a year of salary, while the C types regard it as $15,000 a year of salary. The potential employer wishes to use the above differential in costs to screen his applicants and tell the A types from the C types. Consider the following hiring policy: anyone who has taken a certain, n, or more of the tough courses will be regarded as an A type and paid $160,000, and anyone who has taken fewer than n tough courses will be regarded as a C type and paid $60,000. The aim of this policy is to create natural incentives whereby only the A types will take the tough courses, and the C types will not. Answer the following questions: a) List all possible values of n that satisfy both the incentive-compatibility condition and the participation condition
