Daily demand for gasoline at Billy-Bob's Mobile Station is described by Q = 776 - 200p, where Q are gallons of gasoline sold and p is the price in dollars. Billy-Bob's supply is Q = 2890 + 1,500p. Suppose the state government places a tax of 20 cents on every gallon of gasoline sold. What is the deadweight loss resulting from this tax?

Question

Quizplus · Accepted Answer

To find the deadweight loss, we need to first find the quantity of gasoline sold before and after the tax is implemented.

Before the tax: 
Q = 776 - 200p (equation for demand) 
Q = 2890 + 1500p (equation for supply)

Setting these two equations equal, we get: 
776 - 200p = 2890 + 1500p 
Solving for p, we get: 
p = $1.54 per gallon

We can then substitute this price back into either the supply or demand equation to find the quantity sold: 
Q = 776 - 200(1.54) = 442 gallons

After the tax: 
With a 20 cent tax, the price per gallon increases to $1.74. So, the quantity sold is: 
Q = 776 - 200(1.74) = 366 gallons

Deadweight loss is calculated as the triangle formed by the initial equilibrium quantity, the quantity after the tax, and the points where the demand and supply curves intersect the vertical line representing the tax.

Therefore, the deadweight loss is: 
(442-366) * (1.74-1.54) / 2 = $3.53

So, the answer is A) 3.53 dollars.

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