Tax Evasion

Question 1

What do Y and X denote?

Answer 1

Y= Actual income X= Declared income

Question 2

What is the value of income if not caught evading?

Answer 2

Yn = Y - tX - tax paid on declared income

Question 3

What is the value of income if caught evading?

Answer 3

Yc = Y(1-t) -Ft(Y-X) - pay full tax - fine levied on tax that has been evaded

Question 4

What is the standard Expected utility for tax evasion?

Answer 4

E(U(X)) = p U(Yc) + (1-p) U(Yn) -p = probability caught

Question 5

What is the after tax income for X=0 and X=Y?

Answer 5

• X=0 after tax: 1) Yn = Y 2) Yc = Y(1-t) -Ft(Y) = Y(1 - t(1+F)) - X=Y after tax: Yn = Yc = Y (1-t)

Question 6

What can be determined if the IDC is steeper than the opportunity line at X=Y?

Answer 6

The rational consumer will evade at least some income.

Question 7

What is the slope of the opportunity line?

Answer 7

-F

Question 8

What is the slope of the utility function?

Answer 8

^{-[(1-p) U’(Yn)]} / _{[p U’(Yc)]}

Question 9

combining the two slopes, when should people evade taxes?

Answer 9

• when p(1+F) < 1 - This is true almost all the time

Question 10

How does an increase in the probability of being caught affect the diagram?

Answer 10

• Decreases the slope of the Indifference Curve - Evasion becomes less likely

Question 11

how does an increase in the fine rate affect the diagram?

Answer 11

• It increases the slope of the opportunity line - increase in F = increased X ( reduced evasion)

Question 12

How does an increase in the tax rate affect the diagram?

Answer 12

Shifts the opportunity line towards the origin

Question 13

What is the levels puzzle?

Answer 13

• for observed values, p(1+F) is smaller than 1, suggesting everyone should avoid - in reality a very small proportion of people evade

Question 14

What is Yitzhaki’s puzzle?

Answer 14

-Change in tax rate has a pure income effect on decisions - Increase in the tax rate = poorer consumer = increased risk aversion = less evasion -This is not the case in reality

Question 15

What is the objective function for tax evasion in prospect theory?

Answer 15

V = w(p) v(Yc - r) + (1-w(p)) v(Yn - r) - function has been amended so weightings add to one

Question 16

What are some of the suggested reference levels for the objective function in prospect theory?

Answer 16

1) Income if declared honestly (r = (1-t)Y 2) Expected value of gamble: r= w(p)Yc + (1-w(p))Yn 3) Rablen 2017, weighted average: r = @(.)Yc + (1 - @(.))Yn

Question 17

How can prospect theory solve the levels puzzle?

Answer 17

• In the editing phase we can set caught as a loss and not caught as a gain - Adds more loss aversion, steeper loss of utility if caught evading taxes. -reduces level of evasion as people fear being caught more -overweighting of p means people think they’re more likely to be caught

Question 18

how does prospect theory solve Yitzhaki puzzle?

Answer 18

• not solved, increase in t still gives increased in X - can be somewhat explained by reversing the puzzle, assume tax payers feel richer after rise, therefore increase evasion

Question 19

draw the diagram for the optimal tax evasion decision

Answer 19