QUANTITATIVE ECONOMICS

Substitute $4 as P in either equation to get the equilibrium quantity, which is 1,200
units.
Step 2
Rearrange the supply function to take account of the specific tax that is set and then find the
new equilibrium.
E.g.
If the government imposes a specific tax of $0.75, then the supply function is
changed, because the producers will have to pay the tax and so the price they
receive falls by $0.75. Thus, the price in the equation is (P - 0.75) at each level.
If we put this in the equation, we get Q S = - 400 + 400(P - 0.75).
Then, we can simplify the supply function.
Q S = - 400 + 400(P - 0.75)
Q S = - 400 + (400xP) – (400 x 0.75)
Q S = - 400 + 400P – 300
Q S = -700 + 400P
Now, equilibrium is where the old demand equation meets the new supply equation:
2000 – 200P = -700 + 400P
2700 = 600P
P = $4.50
Substitute $4.50 as P in either equation to get the new equilibrium quantity, which is
1,100 units.
Step 3
Calculate the further effects that are requested by the question in terms of consumer
expenditure, producer revenue, government revenue, consumer surplus or producer surplus.
E.g. Consumer expenditure goes from 1200 units at $4 = $4,800, to 1100 units at $4.50 =
$4,950 – an increase of $150.
Producer revenue, after paying the tax of $0.75 per unit, goes from 1200 units at $4
= $4,800 to 1100 units at $3.75 1 = $4,125 – a fall of $675.
Government revenue is 1100 units at a tax per unit of $0.75 = $825.
Now you have a go!
1 This is because the producers get $4.50 per unit, but have to pay $0.75 in tax.
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