Question

Suppose that in the market for widgets, the supply curve is the typical upward-sloping line, and the demand curve is the typical downward-sloping line. A tax of $4.80 per unit is imposed on widgets and the price rises by $3.25. The equilibrium quantity before the tax imposition was 400,000 widgets and the equilibrium quantity after the tax is 364,000 widgets. The deadweight loss from the tax is

Select one:

A. more than $74,150 but less than $76,600      

B. more than $76,600 but less than $79,050

C. more than $79,050 but less than $81,500

D. more than $81,500 but less than $83,950      

E. more than $83,950 but less than $86,500

Suppose that the equilibrium quantity in the market for gadgets has been 85,000 per month. Then a tax of $6 per gadget is imposed on gadgets. As a result, the price paid by buyers increases by $4 and the after-tax price received (and kept) by sellers falls by $2. Given this tax imposition, the government is able to raise $481,740 per month in tax revenue. We can conclude that the imposition of the tax

(x)   has reduced the equilibrium quantity of gadgets by more than 4,450 but less than 4,675 gadgets per month.

(y) has caused a deadweight loss by an amount more than $13,750 but less than $14,500 per month.

(z)   has reduced consumer surplus by more than $328,750 per month and has reduced producer surplus by more than $164,775 per month.

Select one:

A. (x), (y) and (z)

B. (x) and (y), only

C. (x) and (z), only

D. (y) and (z), only

E. (y) only

Answer 1

Solution:

1. Dead weight loss is the area of small triangle lost out of total surplus.

Dead weight loss = (1/2)*change in equilibrium quantity*tax rate

DWL = (1/2)*(400000 - 364000)*4.8 = $86,400

So, DWL lies between 83950 and 86500. Thus, correct option is (E).

2. With tax revenue of $481,740, and tax rate of $6, we can find new equilibrium quantity using formula:

Tax revenue = tax rate*quantity

481740 = 6*new Q

Q' = 481740/6 = 80,290 units

So, reduction in equilibrium quantity = 85000 - 80290 = 4710 units

Dead weight loss (just like in above question) = (1/2)*change in quantity*tax rate

DWL = (1/2)*4710*6 = $14,130

Change in consumer surplus = tax burden born by buyers*new quantity (so, this is the amount they pay as taxes) + (1/2)*tax burden on buyers*chabge in quantity (and this is the amount of DWL share they own)

Change in consumer surplus = 4*80290 + (1/2)*4*4710 = $330,580

Similarly, change in producer surplus = 2*80290 + (1/2)*2*4710 = $165,290

So, only statements Y and Z are correct.

Thus, correct option is (D).