Question

You have obtained information on the supply and demand for gasoline. The market supply function has been estimated to be Q_s= P and the market demand function has been estimated to be Q_d = 2.5 - 0.25P. The government has decided to implement a $2 per-unit tax on each unit (gallon) of gasoline sold. You have been hired to determine the likely impact of this tax.

a. What is the price of gasoline before the tax is implemented? What price do consumers pay after the $2 per-unit tax has been implemented?

b. Illustrate your answers for part (a) by drawing a graph that shows AND labels all relevant information.

c. Do consumers or producers/suppliers ultimately pay for more of the tax? Support your answer by calculating the tax burdens (or “tax incidence”) for each party.

Answer 1

a. The given equations are

Q_s = P ………………..demand equation

And

Q_d = 2.5 – 0.25P ………………… supply equation

Before tax is imposed to find the equilibrium price and quantity we equate demand and supply equations. So,

P = 2.5 -0.25 P

Solvingfor P we get

P = 2

And equivalent quantity is (putting value of P in demand or supply euation) we get

Q = 2

Now when $2 tax per unit is imposed then P_t = 2+2 = $4 ( where P_t = price after tax is imposed)

So, P_t = $4

And equivalent quantity demanded will fall due to rise in price. To get the quantity demanded here is put value of P_t in demand equation.

So, we get Q_dt = 2.5 – 0.25P_t = 1.5

And quantity supplied will be more due to rise in price. To get this we put the value of P_t in supply equation.

So, we get Q_st = 4

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b. the below graph is when no tax is imposed

Now when tax is imposed the grah would be like this. The tax incidences as asked in part c will also be clear from the below graph.

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c. in the graph of demand supply shown with tax we can see that area of triangle AEF is the deadweight loss.

Area of triangle = 1/2*base*height

so, deadweight loss = AEF area = 1/2 *AF *GE ( in the figure) = 1/2 * 2.5 * 0.5 = 0.625

tax incidence on consumers will be area of trapezium ABCE and on producer will be area of trapezium CDFE

area of trapezium is given by = height * ( sum of parallel sides) *1/2

so area of trapezium ABCE = 1/2* CB* ( AB+CE) = 1/2 * 2 * (1.5+2) = 1/2*2*3.5 =3.5

so tax incidence on cnsumers = $3.5

and

area of trapezium CDFE = 1/2 *CD * (CE+DF) = 1/2 * 0.5* (2+1.5) = 1/2 *0.5*3.5 = 0.875

so, tax incidence on producers = $ 0.875