In Italy, firms pay tax on reported profits at a constant proportionate rate t € (0,1). If the firm's profit is, the owner of the firm can choose to report any amount of profit r where 0 ≤r ≤, and thus pay tr in tax. However, if the firm is audited, it must pay additional tax on unreported profit -r at a rate of t+f, where 0

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
icon
Related questions
Question

please  only do: if you can teach explain steps of how to solve each part: 

what is the optimization to use for foc? 

please solve p

 

21. In Italy, firms pay tax on reported profits at a constant proportionate rate t€ (0, 1). If the
firm's profit is, the owner of the firm can choose to report any amount of profit r where
0 ≤r ≤, and thus pay tr in tax. However, if the firm is audited, it must pay additional tax
on unreported profit -r at a rate of t+f, where 0<f<1-t. Thus if the firm is audited,
it pays tr+(t+f)(n-r) in tax. The probability of being audited is p. Assume that the owner
of each firm maximizes expected utility with a strictly increasing von Neumann-Morgenstern
utility function that depends only on after-tax profit.
(a) What is the smallest auditing probability p* for which a risk neutral owner is willing to
report the firm's full profit ?
Solution: A risk neutral owner maximizes the expected after-tax profit, which is given
by
p(n-tn-f(nr)) + (1 − p)(x − tr) = π- tpx − ƒp + (fp-(1-p)t)r.
Given that r ≤, this is maximized when r = if and only if fp-(1-p)t≥ 0, that is,
if and only if p≥t=P².
(b) If the auditing probability is equal to p* from part (a), will a risk averse owner report
the full profit, less than the full profit, or is it impossible to determine?
Solution: When p = p, the expected value of after-tax profit does not depend on the
reported profit r. Since r = involves no uncertainty and r < involves uncertainty, a
risk averse owner prefers the certain lottery giving the same expected value. Therefore,
she will report the full profit.
Transcribed Image Text:21. In Italy, firms pay tax on reported profits at a constant proportionate rate t€ (0, 1). If the firm's profit is, the owner of the firm can choose to report any amount of profit r where 0 ≤r ≤, and thus pay tr in tax. However, if the firm is audited, it must pay additional tax on unreported profit -r at a rate of t+f, where 0<f<1-t. Thus if the firm is audited, it pays tr+(t+f)(n-r) in tax. The probability of being audited is p. Assume that the owner of each firm maximizes expected utility with a strictly increasing von Neumann-Morgenstern utility function that depends only on after-tax profit. (a) What is the smallest auditing probability p* for which a risk neutral owner is willing to report the firm's full profit ? Solution: A risk neutral owner maximizes the expected after-tax profit, which is given by p(n-tn-f(nr)) + (1 − p)(x − tr) = π- tpx − ƒp + (fp-(1-p)t)r. Given that r ≤, this is maximized when r = if and only if fp-(1-p)t≥ 0, that is, if and only if p≥t=P². (b) If the auditing probability is equal to p* from part (a), will a risk averse owner report the full profit, less than the full profit, or is it impossible to determine? Solution: When p = p, the expected value of after-tax profit does not depend on the reported profit r. Since r = involves no uncertainty and r < involves uncertainty, a risk averse owner prefers the certain lottery giving the same expected value. Therefore, she will report the full profit.
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Limited Willpower
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
Economics
ISBN:
9780190931919
Author:
NEWNAN
Publisher:
Oxford University Press
Principles of Economics (12th Edition)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education