Suppose that there are two types of people in the economy, honest types (HTs) an

Question

Suppose that there are two types of people in the economy, honest types (HTs) and less-than honest types (LTHTs). For simplicity, assume that the marginal tax rate on income is constant at 50%. Assume also that only one type of cheating is possible and that it lowers taxable income by $5,000. Cheating can be caught only by doing audits, which are random and occur 10% of the time. The dollar penalty for cheating is Z. For the LTHTs, the marginal benefit of the cheating is measured in dollars saved. For the HTs, however, the marginal benefit of cheating is the dollars saved minus $1,500, since these people have to compromise their integrity to cheat. Find Z such that the HTs are indifferent between cheating and not cheating. [1 mark] Find Z such that the LTHTs are indifferent between cheating and not cheating. [1 mark] Find the range of Z (for example, Z > $3,000) such that the HTs will not cheat and the LTHTs will cheat. [1 mark]

Explanation / Answer

A) For HTs:

Reduction in taxable income by cheating = 5000

Therefore net dollar saving = 5000 * (1 - 50%) = 2500

Marginal benefit = 2500 - 1500 = 1000

In order to be indifferent between cheating and not cheating, if penalty in audit (Z) equate to the net savings of 1000 (As calculated above) then it will be indifferent point for HTs. However audit % is 10% therefore:

Z*10% + 0*90% = 1000

Z = 10000

B) For LTHTs:

Reduction in taxable income by cheating = 5000

Therefore net dollar saving = 5000 * (1 - 50%) = 2500

Marginal benefit = 2500

In order to be indifferent between cheating and not cheating, if penalty in audit (Z) equate to the net savings of 1000 (As calculated above) then it will be indifferent point for HTs. However audit % is 10% therefore:

Z*10% + 0*90% = 2500

Z = 25000

C) Range such that the HTs will not cheat and the LTHTs will cheat:

Z range = 10000 to 25000

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