Daily demand for gasoline at Billy-Bob's Mobile Station is described by Q = 980 - 300p, where Q are gallons of gasoline sold and p is the price in dollars.Billy-Bob's supply is Q = 22,980 + 3,000p.Suppose the state government places a tax of 18 cents on every gallon of gasoline sold.What is the deadweight loss resulting from this tax?
A)4.02 dollars
B)0.40 dollars
C)4.42 dollars
D)93.42 dollars
E)58.91 dollars

Question

Quizplus · Accepted Answer

To find the deadweight loss, we need to first find the new equilibrium quantity and price after the tax is imposed.

The new demand equation with the tax is:

Qd = 980 - 300(p+0.18) 
Qd = 980 - 300p - 54

And the new supply equation is:

Qs = 22,980 + 3,000p - 540

At the new equilibrium, Qd = Qs:

980 - 300p - 54 = 22,980 + 3,000p - 540

Solving for p, we get:

p = $2.00

And plugging that back into either the demand or supply equation, we get:

Q = 6,476

To find the deadweight loss, we need to compare the consumer surplus and producer surplus before and after the tax.

Before the tax:

Consumer Surplus = ($2.80 - $1.00) * 9,800 / 2 = $14,020

Producer Surplus = ($2.80 - $2.20) * 9,800 / 2 = $2,940

Total Surplus = $16,960

After the tax:

Consumer Surplus = ($2.80 - $2.18) * 6,476 / 2 = $1,624.48

Producer Surplus = ($2.18 - $2.00) * 6,476 / 2 = $577.68

Total Surplus = $2,202.16

Deadweight Loss = $16,960 - $2,202.16 - $9,800 * 0.18 = $4.42

Therefore, the answer is C.

Daily Demand for Gasoline at Billy-Bob's Mobile Station Is Described