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?

A) 3.53 dollars
B) 3.11 dollars
C) 0.42 dollars
D) 96.12 dollars
E) 34.59 dollars

Question

Anthony Shepard · Accepted Answer

Final Answer : A, Explanation :  The deadweight loss is the loss of consumer and producer surplus that results from a tax. In this case, the tax is 20 cents per gallon, so the deadweight loss is:```DWL = (1/2) * (20 cents/gallon) * (Q1 - Q2)```where Q1 is the quantity of gasoline sold before the tax and Q2 is the quantity of gasoline sold after the tax.To find Q1 and Q2, we need to solve the demand and supply equations for p:```Demand: Q = 776 - 200pSupply: Q = 2890 + 1,500p```Solving for p in the demand equation, we get:```p = (776 - Q)/200```Substituting this into the supply equation, we get:```Q = 2890 + 1,500((776 - Q)/200)```Solving for Q, we get:```Q = 3,459 gallons```So, Q1 = 3,459 gallons.To find Q2, we need to substitute the tax into the demand equation:```Q = 776 - 200(p + 0.20)```Solving for p, we get:```p = (776 - Q)/200 - 0.20```Substituting this into the supply equation, we get:```Q = 2890 + 1,500((776 - Q)/200 - 0.20)```Solving for Q, we get:```Q = 3,111 gallons```So, Q2 = 3,111 gallons.Substituting these values into the deadweight loss equation, we get:```DWL = (1/2) * (20 cents/gallon) * (3,459 gallons - 3,111 gallons)``````DWL = 3.48 dollars```Therefore, the deadweight loss resulting from this tax is 3.48 dollars.

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