Consider the following competitive labour market. There are many identical firms that can hire workers. Each firm produces the same output using a constant returns to scale technology and the price of output is set to one. The market determines a wage level w for labour. Let 0 denote the number of units of output that a worker can produce. There is asymmetric information. Worker productivity levels are privately known and are uniformly distributed on the interval [50, 000, 100, 000]. Let r(0) denote the reservation wage of an employee with productivity 0. (a) Explain fully what is meant by a competitive equilibrium in this market. (b) Suppose that r(0) = 0.80. Derive and graphically illustrate the firm's expected revenue conditional on workers choosing to accept employment. (c) Find the competitive equilibrium and calculate the percentage of the population that will be unemployed. (d) What would happen if, instead of types 0 being uniform on the interval [50, 000, 100, 000], we had just two equally-likely types, 0 = 50,000 and 0 = 100,000? %3D %3D

Consider the following competitive labour market. There are many identical firms that can hire workers. Each firm produces the same output using a constant returns to scale technology and the price of output is set to one. The market determines a wage level w for labour. Let 0 denote the number of units of output that a worker can produce. There is asymmetric information. Worker productivity levels are privately known and are uniformly distributed on the interval [50, 000, 100, 000]. Let r(0) denote the reservation wage of an employee with productivity 0. (a) Explain fully what is meant by a competitive equilibrium in this market. (b) Suppose that r(0) = 0.80. Derive and graphically illustrate the firm's expected revenue conditional on workers choosing to accept employment. (c) Find the competitive equilibrium and calculate the percentage of the population that will be unemployed. (d) What would happen if, instead of types 0 being uniform on the interval [50, 000, 100, 000], we had just two equally-likely types, 0 = 50,000 and 0 = 100,000? %3D %3D

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

Consider the following competitive labour market. There are many identical firms that
can hire workers. Each firm produces the same output using a constant returns to scale
technology and the price of output is set to one. The market determines a wage level w for
labour.
Let 0 denote the number of units of output that a worker can produce. There is asymmetric
information. Worker productivity levels are privately known and are uniformly distributed
on the interval [50, 000, 100, 000]. Let r(0) denote the reservation wage of an employee
with productivity 0.
(a) Explain fully what is meant by a competitive equilibrium in this market.
(b) Suppose that r(0) = 0.80. Derive and graphically illustrate the firm's expected revenue
conditional on workers choosing to accept employment.
(c) Find the competitive equilibrium and calculate the percentage of the population that
will be unemployed.
(d) What would happen if, instead of types 0 being uniform on the interval [50, 000, 100, 000],
we had just two equally-likely types, 0 = 50,000 and 0 = 100, 000?
%3D

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