Q1 Signaling when education is productive III Now suppose that there are two groups of workers: H types (higher productivity) and L types (lower productivity). Let CH (e) denote a Type H worker's cost function for obtaining education and let CL(e) denote the cost function for a Type L worker. mH(e) is the marginal product of labor for a Type H worker and mL(e) is the marginal product for a Type L worker.
Q1 Signaling when education is productive III Now suppose that there are two groups of workers: H types (higher productivity) and L types (lower productivity). Let CH (e) denote a Type H worker's cost function for obtaining education and let CL(e) denote the cost function for a Type L worker. mH(e) is the marginal product of labor for a Type H worker and mL(e) is the marginal product for a Type L worker.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Q1 Signaling when education is productive I
Now suppose that there are two groups of workers: H types (higher productivity) and L types
(lower productivity). Let CH (e) denote a Type H worker's cost function for obtaining education
and let cL(e) denote the cost function for a Type L worker. mH(e) is the marginal product of
labor for a Type H worker and mL(e) is the marginal product for a Type L worker.
A fraction p are Type H and the other 1 –p workers are Type L. As usual, the utility that a
worker receives from working is the wage minus cost:
u(e) = w(e) – c(e)
In the following two parts of this problem, you will be given different sets of cost functions,
marginal product values, and a value for p.
Transcribed Image Text:Q1.3
Cost functions:
CL(e) = 0.75 - e?
сн (е) — 0.25 - е?.
%3D
Marginal products:
mı(e) = 2.e
тн(е) — 4- е
Share of workers that are Type H:
p= 0.25
What is the minimum value of ē that could be consistent with a separating equilibrium? Round
your answer to at least three decimal places.
Q1.4
Using the same numbers and cost functions from the previous question, what is the maximum
value of ē that could be consistent with a separating equilibrium? Round your answer to at least
three decimal places.
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