please only do: if you can teach explain steps of how to solve each part how was formula retrieve? why? Utility from reporting full tax = (1-t)π why this U(w) = w Expected utility (from reporting less profit) what is this? = Auditable profit*(after-tax income with audit) + Auditable profit*(after-tax income without audit) Expected utility from reporting less profit = (π - tr - (t+f)(π-r)+(1-p)(π-tr) Utility from reporting full tax = (1-t)π p(π - tr - (t+f)(π-r)+(1-p)(π-tr) < (1-t)π pπ - ptr - p(t+f)(π-r)+(π-tr)-p(t+f)(π-r)+(π-tr)< π-p(t+f)(π-r)-tr < -tπ p*>t(π-r)/(t+f)(π-r) As a result, the value of p* should be at least equal to t/(t+f)
please only do: if you can teach explain steps of how to solve each part how was formula retrieve? why? Utility from reporting full tax = (1-t)π why this U(w) = w Expected utility (from reporting less profit) what is this? = Auditable profit*(after-tax income with audit) + Auditable profit*(after-tax income without audit) Expected utility from reporting less profit = (π - tr - (t+f)(π-r)+(1-p)(π-tr) Utility from reporting full tax = (1-t)π p(π - tr - (t+f)(π-r)+(1-p)(π-tr) < (1-t)π pπ - ptr - p(t+f)(π-r)+(π-tr)-p(t+f)(π-r)+(π-tr)< π-p(t+f)(π-r)-tr < -tπ p*>t(π-r)/(t+f)(π-r) As a result, the value of p* should be at least equal to t/(t+f)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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please only do: if you can teach explain steps of how to solve each part how was formula retrieve?
why? Utility from reporting full tax = (1-t)π
why this
U(w) = w
Expected utility (from reporting less profit) what is this? = Auditable profit*(after-tax income with audit) + Auditable profit*(after-tax income without audit)
Expected utility from reporting less profit = (π - tr - (t+f)(π-r)+(1-p)(π-tr)
Utility from reporting full tax = (1-t)π
p(π - tr - (t+f)(π-r)+(1-p)(π-tr) < (1-t)π
pπ - ptr - p(t+f)(π-r)+(π-tr)-p(t+f)(π-r)+(π-tr)< π-p(t+f)(π-r)-tr < -tπ
p*>t(π-r)/(t+f)(π-r)
As a result, the value of p* should be at least equal to t/(t+f)
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.
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