The economic staff of the U.S. Department of the Treasury has been asked to reco

Question

The economic staff of the U.S. Department of the Treasury has been asked to recommend a new tax policy concerning the treatment of the foreign earnings of U.S. firms. Currently the foreign earnings of U.S. multinational companies are taxed only when the income is returned to the United States. Taxes are deferred if the income is reinvested abroad. The department seeks a tax rate that will maximize total tax revenue from foreign earnings. Find the optimal tax rate if:
a. B(t) = 80

The economic staff of the U.S. Department of the Treasury has been asked to recommend a new tax policy concerning the treatment of the foreign earnings of U.S. firms. Currently the foreign earnings of U.S. multinational companies are taxed only when the income is returned to the United States. Taxes are deferred if the income is reinvested abroad. The department seeks a tax rate that will maximize total tax revenue from foreign earnings. Find the optimal tax rate if: B(t) = 80 - 100t B(t) = 80 - 240t² B(t) = 80 - 80?t where B(t) is the foreign earnings of U.S. multinational companies returned to the United States and t is the tax rate.

Explanation / Answer

Tax revenue R(t) = tax rate * foreign earnings. = t * B(t)

To maximize tax revenue, dR(t)/dt = 0.

a) R(t) = 80t - 100t^2

dR(t)/dt = 80-200t

80 - 200t = 0, so, t = 80/200 = 0.4

Thus optimal tax rate = 0.4 = 40%

b) R(t) = 80t - 240t^3

dR(t)/dt = 80-720t^2

80 - 720t^2 =0 . so t^2 = 80/720 = 1/9. so t = 1/3

Thus optimal tax rate = 1/3 = 0.333 = 33.33%

c) R(t) = 80t - 80*t^1.5

dR(t)/dt = 80-120t^0.5

80 - 120t^0.5 = 0. so, t^0.5 = 80/120 = 2/3. so t = (2/3)^2 = 4/9

Thus optimal tax rate = 4/9 = 0.4444 = 44.44%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.