Suppose you are hired by the Martin Guitar Company as an economic consultant. Yo
ID: 1197202 • Letter: S
Question
Suppose you are hired by the Martin Guitar Company as an economic consultant. You estimate the demand to be Q=8000-2P. Suppose the supply of Martin Guitars is given by Q= -2000+3P. Suppose a per-unit excise tax of $40 per guitar is levied on the consumers.
What price will sellers receive after the tax is levied?
What price will consumers pay after the tax is levied?
What percent of the tax will be paid by the consumers of Martin guitars?
What percent of the tax will be paid by the suppliers of Martin guitars?
How many guitars will be sold after the tax is imposed?
How much consumer surplus do consumers get after the tax?
What is the deadweight loss created by this tax?
Explanation / Answer
The demand function is
Q = 8000 - 2P ......(1)
Write it in inverse form as:
P = 4000 - Q/2 ......(2)
The supply function is
Q = -2000 + 3P ......(3)
Write in inverse form as
P = (Q+2000)/3 ......(4)
At equilibrium, demand equals supply. That is,
-2000 + 3P = 8000 - 2P
5P = 10,000
P = 2000
at this price, Q = 4000 [=8000 - 2(2000)].
Therefore, original quantity demanded and supplied in 4000 units and the original orice is $2000.
After tax is levied, the demand curve shifts downwards by $40.
Therefore new demand curve is
P = (4000 - Q/2) - 40
P = 3960 - Q/2 ......(5)
or equivalently,
Q = 7920 - 2P
Equate new supply and demand.
7920 - 2P = -2000 + 3P
5P = 9920
P = $1984
which is the market price after tax. The quantity after tax is 3952 [=7920 - 2(1984)] units.
Price sellers receive = $1984
Price buyer pay = $1984 + $40 = $2024
% of tax borne by buyers = [(2024 - 2000)/40] 100 = 60%
% of tax borne by sellers = [(2000 - 1984)/40] 100 = 40%
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