(Tax evasion) A household with income Y decides how much income to un- derreport (R). The household is taxed at rate t. The available income after reporting Y - R is Y - (Y – R) The government monitors households and can detect tax evasion with probability p. If the govern- ment finds the household misreported income, the available household income becomes Y(1- t) – P(R) Henceforth, the expected after-tax income of misreporting R is: (1- p) Y - t(Y – R)]+p[Y(1-t) – P(R)] i) What is the optimal amount of income misreported when Y 100, the tax rate t = 0.25, the probability that the government detects tax evasion is p 0.2, and the penalty if found evading is P(R) = ? ii) How would tax evasion change if the household is taxed at t = 0.4. Interpret the difference with your answer in i).
(Tax evasion) A household with income Y decides how much income to un- derreport (R). The household is taxed at rate t. The available income after reporting Y - R is Y - (Y – R) The government monitors households and can detect tax evasion with probability p. If the govern- ment finds the household misreported income, the available household income becomes Y(1- t) – P(R) Henceforth, the expected after-tax income of misreporting R is: (1- p) Y - t(Y – R)]+p[Y(1-t) – P(R)] i) What is the optimal amount of income misreported when Y 100, the tax rate t = 0.25, the probability that the government detects tax evasion is p 0.2, and the penalty if found evading is P(R) = ? ii) How would tax evasion change if the household is taxed at t = 0.4. Interpret the difference with your answer in i).
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
Related questions
Question
![(Tax evasion) A household with income Y decides how much income to un-
derreport (R). The household is taxed at rate t. The available income after reporting Y - R
is
Y - t(Y – R)
The government monitors households and can detect tax evasion with probability p. If the govern-
ment finds the household misreported income, the available household income becomes
Y(1 – t) – P(R)
Henceforth, the expected after-tax income of misreporting R is:
(1- p) Y – t(Y – R)] + p[Y(1 – t) – P(R)]
i) What is the optimal amount of income misreported when Y = 100, the tax rate t = 0.25, the
probability that the government detects tax evasion is p = 0.2, and the penalty if found evading is
P(R) = ?
ii) How would tax evasion change if the household is taxed at t = 0.4. Interpret the difference
with your answer in i).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e8aa205-32aa-4f07-9b5c-13bb56a777db%2Fdcbe7a7d-f992-442f-b422-af608cf19192%2F8j8fgsb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(Tax evasion) A household with income Y decides how much income to un-
derreport (R). The household is taxed at rate t. The available income after reporting Y - R
is
Y - t(Y – R)
The government monitors households and can detect tax evasion with probability p. If the govern-
ment finds the household misreported income, the available household income becomes
Y(1 – t) – P(R)
Henceforth, the expected after-tax income of misreporting R is:
(1- p) Y – t(Y – R)] + p[Y(1 – t) – P(R)]
i) What is the optimal amount of income misreported when Y = 100, the tax rate t = 0.25, the
probability that the government detects tax evasion is p = 0.2, and the penalty if found evading is
P(R) = ?
ii) How would tax evasion change if the household is taxed at t = 0.4. Interpret the difference
with your answer in i).
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