In Surburbia the demand and supply curves for gasoline are given by the following equations where P...

Question

In Surburbia the demand and supply curves for gasoline are given by the following equations where P is the price per gallon and Q is the quantity of gasoline in gallons:
Market Demand: Q = 10,000 – 1000P
Market Supply: Q = 2000P + 4000
a. What is the slope of the demand curve? What is the slope of the supply curve?
b. What is the equilibrium price and equilibrium quantity of gasoline in Surburbia? Show your work in finding these answers.
c. What is the value of consumer surplus (CS) in this market? What is the value of producer surplus (PS) in this market? Show your work in finding these answers. In your answer be sure to include the units of measurement throughout your work.
d. Suppose that the government of Surburbia decides that less gasoline should be consumed in Surburbia due to concerns about climate change. The government decides to enact an excise tax so that the total consumption of gasoline falls by 3000 gallons from its equilibrium quantity. The government has asked you to advise them as to the size of the excise tax that will be necessary in order to achieve this goal. Assume that the only thing that changes in this market is the excise tax and also assume that this excise tax is levied on producers of gasoline.
e. Given the excise tax you calculated in (d): [Hint: you may find it helpful to do step (vii) before you tackle the rest of the steps!]
i. What is the total tax revenue that will be collected from this excise tax?
ii. What is the consumer tax incidence (CTI) equal to given this excise tax?
iii. What is the producer tax incidence (PTI) equal to given this excise tax?
iv. What is the deadweight loss (DWL) from this excise tax?
v. What is the change in consumer surplus due to this excise tax?
vi. What is the change in producer surplus due to this excise tax?
vii. Draw a diagram of the market for gasoline illustrating this excise tax. Make sure your graph is completely and carefully labelled!
f. Instead of the excise tax described in (d), suppose the government of Surburbia decides to approach the problem of too much gasoline being produced and consumed in Surburbia by targeting a particular price for gasoline. Suppose the government mandates that the price per gallon of gasoline must be $8 per gallon. How big must the excise tax be in order for the government of Surburbia to achieve their goal of the price of gasoline being $8 per gallon?
g. Given the excise tax you calculated in (f): [Hint: you may find it helpful to do step (vii) before you tackle the rest of the steps!]
i. What is the total tax revenue that will be collected from this excise tax?
ii. What is the consumer tax incidence (CTI) equal to given this excise tax?
iii. What is the producer tax incidence (PTI) equal to given this excise tax?
iv. What is the deadweight loss (DWL) from this excise tax?
v. What is the new consumer surplus given this excise tax?
vi. What is the new producer surplus given this excise tax?
vii. Draw a diagram of the market for gasoline illustrating this excise tax. Make sure your graph is completely and carefully labelled!

David · Accepted Answer

a. Be careful on this question: this is not a hard question, but it does require that you recognize that both 
the demand and the supply equations are written in x-intercept form and not y-intercept form. That 
means that the coefficient for P represents the reciprocal of the slope, or 1/m. So, for the demand 
equation we see that the coefficient for P is -1000 and we plug this value into the equation: 1/m = -
1000. Solving for m, the slope of the line, we get m = -1/1000 for the slope of the demand curve. We 
will follow a similar procedure for the slope of the supply curve: 1/m = 2000 or m = 1/2000: the slope 
of the supply curve is 1/2000.
b.  To find the equilibrium we need to set the demand equation equal to the supply equation: 10,000 – 
1000P = 2000P + 4000 or 3000P = 6,000 or P = 2. That is, the equilibrium price of gasoline is $2 per 
gallon. To find the equilibrium quantity you can substitute P = 2 into either the demand or the supply 
equation: Q = 10,000 – 1000(2) – 8,000 gallons of gasoline is demanded when the price of gasoline is 
$2 per gallon; or, Q = 2000(2) + 4000 = 8,000 gallons of gasoline is supplied when the price of 
gasoline is $2 per gallon.
c. CS = (1/2)($10 per gallon - $2 per gallon)(8,000 gallons) = $32,000 
               PS = the sum of the area of a triangle and the area of a rectangle = (1/2)($2 per gallon - $0 per 
gallon)(8000 gallons – 4000 gallons) + ($2 per gallon - $0 per gallon)(4000 gallons) = $12,000 
The diagram below illustrates these areas: 
 
Note: that producer surplus is only the area above the supply curve and beneath the equilibrium price that is also 
in the first quadrant: the triangle that “sits” below the horizontal axis is not included in this calculation since it 
does not represent anything meaningful from an economic point of view.
d. The government wants to implement an excise tax that will result in total gasoline consumption falling 
by 3000 gallons. That means that the government wants Surburbia to end up consuming 5,000 gallons 
of gasoline instead of their current consumption level of 8,000 gallons of gasoline. If we set Q = 5000, 
then we find that demanders will demand this level of gasoline if the price per gallon is $5. (Q = 10,000 
– 1000P and 5000 = 10,000 – 1000P and therefore P = $5 per gallon of gasoline.) If we set Q = 5000,

In Surburbia the demand and supply curves for gasoline are given by the following equations where P is the price per gallon and Q is the quantity of gasoline in gallons: Market Demand: Q = 10,000 –...

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