Economics 450 - Assignment 6
Q1. A worker is searching for a job that will last a month (no matter how long it takes to find it). Each week, the worker receives exactly one job offer, and the cost of job search for a week is $360. The best possible job pays $4,000, the worst pays $2,000, and any wage between these extremes is equally likely (e.g. there is a 60% chance that any given job pays at least $2,800). What search strategy would maximize the expected wage, net of search costs?
Q2. A profit-maximizing firm uses two inputs, energy and labor, to make a single product. The firm faces perfectly elastic supply curves for labor and energy, and a perfectly elastic demand curve for its product--it takes all prices as given.
a. Suppose that all prices rise by 20% (including the wage rate, the price of energy, and the price of the firm's product). How will the firm's demand for labor be affected?
b. If the wage rate did not change, while both the price of energy and the product price increased by 20%, how would the firm's demand for labor be affected?
Q3. Suppose a country has 100 million inhabitants. The population can be divided into the employed, the unemployed, and the persons who are out of the labor force (OLF). In any given year, the transition probabilities among the various categories are given by
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Moving into:
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Employed
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Unemployed
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OLF
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Moving From
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Employed
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0.94
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0.02
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0.04
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Unemployed
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0.20
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0.65
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0.15
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OLF
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0.05
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0.03
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0.92
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These transition probabilitites are interpreted as follows. In any given year, 2 percent of the workers who are employed become unemployed; 20 percent of the workers who are unemployed find jobs, and so on. What will be the steady-state unemployment rate?
Q4. Consider an economy with three types of jobs. The table below shows the jobs, the frequency with which vacancies open up on a yearly basis, and the income associated with each job. Searching for a job costs $C per year and generates at most one job offer. There is a 20 percent chance of not receiving an offer in a year. (Note: The expected search duration for a job with probability p of appearing is 1/p years.)
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Job Type
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Frequency
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Income
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A
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30 percent
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$60,000
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B
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20 percent
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$100,000
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C
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30 percent
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$80,000
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As a function of C, specify the optimal job search strategy if the worker maximizes her expected income net of search costs.