a)
To calculate: The amount of wage rate and associated risk to get the job.
a)
Explanation of Solution
Given
(a).
Let u1 denote the utility of the first job. Since the first job gives a constant work hour of 8 hours at an hourly wage of $50, the utility would be:
Let u2 denote the utility of the risky job. Sometimes the salesman gets 4 hours of work with probability 0.5 and sometimes he gets 12 hours of work with probability 0.5, then the expected utility from the risky job is:
The risky job will be chosen ifu1 > u2
Hence, for an hourly wage rate higher than 53.6, the risky job will be taken.
b)
To show: Whether the imposition of proportional tax on income will impacts decisions regarding choice of job.
b)
Explanation of Solution
If the proportional tax is imposed on both the risky job and a certain job, then results do not change as the expected utility difference remains the same. Let us check:
Let the proportional tax rate be, t. Utility in case of a certain job will be:
Utility in case of the risky job will be:
The risky job will be chosen if u1 > u2
The wage rate for both jobs remains the same so, the person’s choice will not be impacted.
c)
To calculate: Let us calculate the utility to decide whether the decision will be impacted or not:
c)
Explanation of Solution
Utility in case of constant working hours:
In this case, 300 will not be taxed and 100 (400-300) will be taxed at the rate of 50%
Utility in case of random working hours:
In this case, also 300 will not be taxed and wages above 300 will be taxed at the rate of 50%
Since, in this case, the equation of wages has changed the decision will also change.
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Chapter 13 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
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