Government Intervention 7 - FRQ, per-unit tax
Conversations welcome -
2014 AP Microeconomics Exam - FRQ, question 3
(a) Draw a CLG (correctly labelled graph) of the gasoline market in which demand is relatively inelastic and the supply is relatively elastic.
You must know that inelastic demand is drawn more vertical (inelastic = I) and elastic is more like the the lines of the E, horizontal... So elastic (supply) is more horizontal and inelastic (demand) is drawn steeper.
(b) Suppose the Gov't imposes a $2 per unit tax on the producers of gasoline. On your graph from part (a), show each of the following after the tax imposed.
- The price paid by buyers, labeled Pb
- The after tax price received by sellers, labelled Ps
- The quantity, labeled Q
- So the price paid by buyers is simply the equilibrium price of the demand and new (s+tax) supply curve. Draw a dotted line over to the price axis and mark it Pb
- The after tax (net) price received by sellers is the amount of the tax. In essence the horizontal distance between the two parallel supply curves. But, to get the after tax price start at the new equilibrium (s+tax) and follow the dotted line down to the original supply curve, look left,, make a dotted line across to the price axis and mark it Ps.
- The quantity demanded at the new higher (higher prices mean less Qd) is less than at the original lower price. Draw a straight line down from the new (s+tax) equilibrium and label the new quantity as Qt.
(C) Using the labeling on your graph, explain how to calculate the total tax revenue collected by the government.
Since Pb is the market price paid by the consumer and the net amount kept by the seller we could write this as
- Pb-Ps times the quantity sold, which is Qt, so (Pb-Ps*Qt)
or
- since we know the tax $2 and we know the quantity sold, then ($2 * Qt)
or
- (Pb * Qt) - (Ps * Qt) I'm not writing that out:)
(d) Will the tax burden fall entirely on the buyer, entirely on the seller, more on the buyer and less on the seller, more on the seller and less on the buyer, or equally on the buyer and seller. Explain.
Look at the graph,, its easy to see that the consumer (buyer) will pay more of the tax. When the demand curve is inelastic the buyers bear most of the tax incidence.
Hope this helps.
2. The graph above shows the market for a good that is subject to a per-unit tax. (a) Using the labeling on the graph, identify the following:
- equilibrium price and quantity before the tax.
easy, Yes? The equilibrium before the tax is where the supply curve crosses the demand curve. (NOT the supply curve that says, Supply + Tax)
The equilibrium price before the tax is (follow the dashed line across to the price axis) $12
The equilibrium quantity before the tax is (follow the dashed line down to the quantity axis) 100
The equilibrium quantity before the tax is (follow the dashed line down to the quantity axis) 100
- The area representing the Consumer surplus before the tax.
The consumer surplus before the tax is the areas, A,B,C and F.
- The area representing the Producer surplus before the tax.
The producer surplus before the tax is the areas, D,G,and E. or 100. Why 100 you ask?
Area of a triangle is 1/2 B*H or (one-half, base times height.) So the base is 100, the height of the producers surplus (up the price axis) is 2 (12-10=2) so, 2 X 100 = 200 *1/2 = 100.
(b) Assume the tax is now imposed. Does the price paid by the buyers rise by the full amount of the tax? Explain!
Remember that the two supply curves are parallel so the tax is the vertical distance between them. In essence the tax shifted the supply curve leftward. Tax is a determinate of supply so a shift occurs.
Where the supply+tax curve crosses the demand curve is the new equilibrium, at that point follow the dotted line down until it touches the original supply curve ,, then look left. (follow the dotted line to the price axis) and you will see a price of $11.
Go back to the supply+tax curve where it crosses the demand curve, and look left. (follow the dotted line to the price axis) and you will see a price of $13.
- $13 minus $11 = $2 , two dollars is the tax.
Consider that the former supply/demand equilibrium was at $12 and now the supply+tax/demand equilibrium is at $13. The equilibrium price has only moved from $12 to $13 so the price paid by the buyers has risen by $1. ($12 to $13 is 1 dollar) So the buyers have not paid the full amount of the tax.
Elasticity explanation - Supply is not perfectly elastic,, or demand is not perfectly inelastic or demand/supply have the same elasticities.
(C) Using the labeling on the graph, identify each of the following (after the imposition of the tax).
- The net price paid to the sellers.
Remember that net means (tax taken out) so the amount the seller receives minus the tax.
If the equilibrium price is $13 and the tax is (we now know) $2 then 13-2 is $11. So the seller receives $11 per unit.
- The amount of tax revenue.
Dollar amount of tax ($2) times, multiplied by, the quantity sold or (go to supply+tax equilibrium and follow the dotted line straight down to the quantity axis) 80. $2 X 80 = $160
In essence the government tax is two dollars and the sellers sells 80 units,, the government gets $160 dollars in tax revenue.
- The area representing the consumer surplus (after the imposition of the tax).
The area representing the consumer surplus is the area A.
- The area representing the producer surplus (after the imposition of the tax).
The area representing the the producer surplus is the area B.
Now, On the graph above what if the questions had been worded differently,, such as
- The area representing the change in consumer surplus.
Discussions welcome -
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