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 ≤ 7, 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 < ƒ <1-t. Thus if the firm is audited, it pays tr+(t+ƒ)(π-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.
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 ≤ 7, 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 < ƒ <1-t. Thus if the firm is audited, it pays tr+(t+ƒ)(π-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.
Chapter1: Making Economics Decisions
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Transcribed Image Text: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 ≤ π, and thus pay tr in tax. However, if the firm is audited, it must pay additional tax
on unreported profit 7-r at a rate of t+f, where 0 < ƒ < 1–t. Thus if the firm is audited,
it pays tr+(t+f)(π-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 ?
(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?
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