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In: Economics

There are two types of works: some have a high productivity, aH, and some have low productivity, aL.

There are two types of works: some have a high productivity, aH, and some have low productivity, aL. Workers can get a job after leaving high school or they can 2 go to college at a cost of cH for high productivity workers and cL for low productivity workers. Assume that aH > aL > 0 and cL > cH > 0. Education has no impact on productivity. Describe a separating equilibrium in which employers pay workers a wage equal to the expected productivity conditional on the level of education. What conditions must be satisfied by the parameters aH, aL, cH and cL in order for such as separating equilibrium to exist?

Solutions

Expert Solution

1.Productivity of high types= aH, Productivity of low types= aL, aH>aL>0

2.Cost of education for high type= cH, Cost of education for low type= cL, cL>cH>0

3. employers pay workers a wage equal to the expected productivity conditional on the level of education

A worker of type ai produces (i could be L or H) output which is worth ai to the employer.

Let us assume that there is p fraction (p lies between 0 and 1) of low type workers in the market.

The education level e is perfectly observable by the employers.

Getting more education is more costly for low ability workers than for high ability workers since cL>cH>0

Objective: Is it possible for high type to credibly signal to employers their quality by getting more education than low types

If a type ai worker gets a wage w and education c, her utility is w - ci

- firms can observe the education level and not ai (type of worker)

Let u(e)= Pr(a=aH|c), that is, the belief of firm when it observes a worker with education c

Let w(e) be the wage that firm gives when it sees a worker with education e.

- Zero profit condition implies that w(c) = u(c) aH + [1-u(c)] aL.

- Wages depend solely on beliefs.

- If u(c) is not constant in c, then workers with different education level will get different wages

Let ci be the education level chosen by a worker with type i.

- Separating equilibria: c(aH) not equal to c(aL).

- In a separating equilibrium, µ (c (H)) = 1 and µ (c(L)) = 0.

This means, w (c (aH)) = aH and w (c (aL)) = aL.

- Also, in separating equilibriium, c(aL) = 0

Lets suppose that c(aL) > 0.

- If a type aL worker chooses c = 0, he gets wage w (0) = u (0) aH + [1 -u(e)]aL

-The utility that he will get from doing so is w (0) -c (0) > aL- c (0) > aL -c (aL), hence this worker will choose e = 0 than to choose e = e (aL) > 0.

Rahul Sunny answered 2 years ago
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