Question

a) Suppose that a provincial government collects income tax revenues using a linear income tax schedule. A taxpayer who has a zero income in a given year receives a $500 as a living allowance from the government. If a taxpayer who has an annual income of $30,000 pays $4000 in taxes, what is the marginal tax rate? Draw the linear income tax schedule on a diagram. Is the tax schedule regressive? Justify your answer. (2.5 marks)

b) Using a simple economic model, explain the factors that will reduce the level of tax evasion. Use a suitable diagram(s) to illustrate. Briefly discuss the strengths and shortcomings of the model. (2.5 marks)

Answer 1

A.

Marginal tax rate = Tax/Income = 4000/30000 = 13.3%

or

Linear tax equation, Tax = (0.133) * Income - 500

Let Income be 5000, Tax = 165. Let income be 5001, Tax = 165.133

This as per marginal tax rate formula, Tax rate = (165.133-165)/(5001-5000) = .133 = 13.3%

Using Excel, we compute the schedule and draw the graph, which can be seen as a straight upward sloping line.

As seen its a progressive income tax schedule. the tax rate increases with the taxable income.

B.

Expected Utility Maximization Approach

The taxpayer has a choice between two main strategies: (1) to declare his actual income, or (2) to declare less than his actual income. If he chooses the first option, he will have to pay the full amount of the tax. However, if he chooses the second option, he can pay less than the full amount, but he will have to face the probability of being detected and penalized. His problem is to maximize the expected utility derived from his income after tax and penalty.The taxpayer’s objective function is

where,

W is the taxpayer’s actual income which is exogenously given and is known to the taxpayer but not to the tax authority;

θ is a constant tax rate, θ > 0;

X, the income reported to the tax authorities, is the taxpayer’s decision variable, X > 0;

p is the probability that the evasion will be detected;

n is the penalty rate on unreported income, Π > 0;

U is the utility from disposable income; and

E(U) is the expected utility.

The taxpayer chooses his declared income (X) so as to maximize his expected utility [E(U)].