# Question

Suppose a firm is equally likely to earn $2 million this year or lose $3 million. The firm faces a tax rate of 40% on each dollar of taxable income, and the firm pays no taxes on losses. In this simple one-period scenario, ignore the carry back and carry forward rules. The firm’s expected taxable income is thus a loss of $500,000 calculated as .50(−$3) + .50($2). What is the firm’s expected marginal tax rate? Suppose a second firm is equally likely to earn $3 million this year or lose $2 million. This firm also faces a tax rate of 40% on each dollar of taxable income (and the firm pays no taxes on losses). Again in this simple one-period scenario, ignore the carry back and carry forward rules. The firm’s expected tax- able income is thus a profit of $500,000 calculated as .50($3) + .50(−$2). What is the firm’s expected marginal tax rate? Explain and discuss your results. Why is the first firm’s marginal tax rate not 0%? Why is the second firm’s marginal tax rate not 40%?

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