Suppose that a market has the following supply and demand equations:
Demand: QD = 380 - 10p
Supply: QS = 80 + 5p
If the government imposes a specific tax of ? on suppliers, what will be the price buyers pay and sellers receive, quantity, and government revenue from the tax (as functions of ?). What tax level maximizes the revenue the government collects from the tax?
First, compute the after-tax equilibrium price by equating the demand to the supply with tax:
400 - 10p = 80 + 5(p - ?)
p = 20 + ?/3
Therefore the buyers pay a price = 20 + ?/3 and sellers receive a price = 20 - 2?/3. The equilibrium quantity is found by plugging the buyers' price into the demand equation:
Q = 180 - 3.33?.
The government revenue from the tax is:
GR = (180 - 3.33?) × ?
To maximize the revenue generated, we take the derivative of the GR function with respect to the tax and set equal to zero:
dGR/d? = 180 - 6.67? = 0
Thus the revenue-maximizing tax rate is ? = $27
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