There are two types of (college graduate) workers in financial industry: A (able) type and C (challenged) type. Potential employers in finance will pay $160,000 a year to a type A and $60,000 to a type C. Unfortunately, employers cannot observe the worker's type while each worker knows his or her own type. However, a market research informs all employers and workers that 60% of the population is type A and 40% is type C. Additionally, it is known to everyone that the worker types differ in their tolerance for taking an analytical course rather than easy ones in college. The A types regard the cost of each analytical course as equivalent to $3,000 a year of salary, while the C types regard it as $15,000 a year of salary. Alternative employment opportunities outside of the financial industry yield the A types a salary of $125,000 and the C types a salary of $30,000. Suppose an employer in this industry use this differential to screen his applicants and tell the A types from the C types. The employer's hiring policy states the following: "Anyone who has taken a certain number, n, or more of the analytical courses will be regarded as an A and paid $160,000, and anyone who has taken fewer than n will be regarded as a C and paid $60,000." The minimal number of analytical courses to achieve separation of types is The maximal number of analytical courses to achieve separation of types is Type integers in the blanks.
There are two types of (college graduate) workers in financial industry: A (able) type and C (challenged) type. Potential employers in finance will pay $160,000 a year to a type A and $60,000 to a type C. Unfortunately, employers cannot observe the worker's type while each worker knows his or her own type. However, a market research informs all employers and workers that 60% of the population is type A and 40% is type C. Additionally, it is known to everyone that the worker types differ in their tolerance for taking an analytical course rather than easy ones in college. The A types regard the cost of each analytical course as equivalent to $3,000 a year of salary, while the C types regard it as $15,000 a year of salary. Alternative employment opportunities outside of the financial industry yield the A types a salary of $125,000 and the C types a salary of $30,000. Suppose an employer in this industry use this differential to screen his applicants and tell the A types from the C types. The employer's hiring policy states the following: "Anyone who has taken a certain number, n, or more of the analytical courses will be regarded as an A and paid $160,000, and anyone who has taken fewer than n will be regarded as a C and paid $60,000." The minimal number of analytical courses to achieve separation of types is The maximal number of analytical courses to achieve separation of types is Type integers in the blanks.
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
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Transcribed Image Text:There are two types of (college graduate) workers in financial industry: A (able) type and C
(challenged) type. Potential employers in finance will pay $160,000 a year to a type A and $60,000
to a type C. Unfortunately, employers cannot observe the worker's type while each worker knows
his or her own type. However, a market research informs all employers and workers that 60% of
the population is type A and 40% is type C. Additionally, it is known to everyone that the worker
types differ in their tolerance for taking an analytical course rather than easy ones in college. The A
types regard the cost of each analytical course as equivalent to $3,000 a year of salary, while the C
types regard it as $15,000 a year of salary. Alternative employment opportunities outside of the
financial industry yield the A types a salary of $125,000 and the C types a salary of $30,000.
Suppose an employer in this industry use this differential to screen his applicants and tell the A
types from the C types. The employer's hiring policy states the following:
"Anyone who has taken a certain number, n, or more of the analytical courses will be regarded as
an A and paid $160,000, and anyone who has taken fewer than n will be regarded as a C and paid
$60,000."
The minimal number of analytical courses to achieve separation of types is
The maximal number of analytical courses to achieve separation of types is
Type integers in the blanks.
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