Times are tough in the labor market for new lawyers. In this market there are two types of lawyer, the high-skill kind, and the low-skill kind. The fraction of low-skill lawyers is X, where as usual, X is between O and 1. The high-skill kind will bring in business to a law firm worth 86,760, while the low-skill kind only brings in 55,557 dollars worth of business to a law firm. Unfortunately, it's impossible to tell whether a potential hire is a high-skill or a low-skill worker until it's too late and they have already been hired. Legal firms are, for various arcane reasons, all risk-neutral. Fortunately, the legal association has introduced a new certification exam, and they will let potential lawyers take this exam for the low, low price of 7,879. How tremendously generous of them. High-skill workers can easily pass this exam without too much effort, but low-skill workers will have to take an additional preparation course, which will cost them 43,221. What is the highest X can be before we have only the separating equilibrium for these lawyers?

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Times are tough in the labor market for new lawyers. In this market there are two types of lawyer,
the high-skill kind, and the low-skill kind. The fraction of low-skill lawyers is X, where as usual, X is
between O and 1. The high-skill kind will bring in business to a law firm worth 86,760, while the
low-skill kind only brings in 55,557 dollars worth of business to a law firm. Unfortunately, it's
impossible to tell whether a potential hire is a high-skill or a low-skill worker until it's too late and
they have already been hired. Legal firms are, for various arcane reasons, all risk-neutral.
Fortunately, the legal association has introduced a new certification exam, and they will let
potential lawyers take this exam for the low, low price of 7,879. How tremendously generous of
them. High-skill workers can easily pass this exam without too much effort, but low-skill workers
will have to take an additional preparation course, which will cost them 43,221.
What is the highest X can be before we have only the separating equilibrium for these lawyers?
Transcribed Image Text:Times are tough in the labor market for new lawyers. In this market there are two types of lawyer, the high-skill kind, and the low-skill kind. The fraction of low-skill lawyers is X, where as usual, X is between O and 1. The high-skill kind will bring in business to a law firm worth 86,760, while the low-skill kind only brings in 55,557 dollars worth of business to a law firm. Unfortunately, it's impossible to tell whether a potential hire is a high-skill or a low-skill worker until it's too late and they have already been hired. Legal firms are, for various arcane reasons, all risk-neutral. Fortunately, the legal association has introduced a new certification exam, and they will let potential lawyers take this exam for the low, low price of 7,879. How tremendously generous of them. High-skill workers can easily pass this exam without too much effort, but low-skill workers will have to take an additional preparation course, which will cost them 43,221. What is the highest X can be before we have only the separating equilibrium for these lawyers?
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