Question

A risk neutral firm (seeking to maximize expected profits) can choose
between two mutually exclusive projects. One project yields a profit of
10 with certainty. The other project is risky, and yields a profit of 40
and a loss of 10, each with 50 percent chance. The government is
levying a tax on profits, denoted by 0<t<1. In case the firm suffers from
losses (negative profits), the (negative) tax is neither refundable nor can
the losses be carried forward and offset against future profits.
Characterize the excess burden as a function of t.

Answer 1

The total economic burden of a tax includes both payments that taxpayers make to the government and any lost economic value from inefficient activities undertaken in reaction to taxes.

Project 1: Payoff of 10 with certainity

Project 2:

Payoff of 40 or Payoff of -10, each with 50% chance

Expected payoff = 50%*40+50%*-10 = 15

Taxes to be paid = 15*t

Overall payoff after tax = 15*(1-t)

Firm will be indifferent between the 2 projects if payoffs becomes equal

i.e. 10 = 15*(1-t)

So, for t = 33.33% both projects seem equal

For t < 33.33%

Project 2 will be chosen

Excess burden will be taxes paid = 15*t

Payments that taxpayers make to the government.

For t > 33.33%

Project 1 will be chosen

Excess burden will be lost value due to taxes = 5

Any lost economic value from inefficient activities undertaken in reaction to taxes.

Total excess burden will be defined as follows

Max(15t, 5)

i.e. maximum of the two.

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