Question

The demand for sugar is given by: QD= 420 -0.25P. The supply of sugar is given by: QS= 4P -1110. The equilibrium quantity without a tax is 330 units. The government levies a $85 per unit tax on the suppliers of sugar. Calculate deadweight loss from this tax.

Answer 1

the equilibrium before tax is at Qd=Qs
equating it
420-0.25P=4P-1110
4.25P=1530
P=1530/4.25
P=$360
Q=330 as given
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after tax the supply shifts to left
converting the supply function to inverse supply function
Q=4P-1110
4P=Q+1110
P=0.25Q+277.5
adding tax to the price
P=0.25Q+277.5+85
P=0.25Q+362.5
converting to a normal form
Q=4P-1450
equating to the demand curve
420-0.25P=4P-1450
4.25P=1870
P=440=the price buyer pa after tax
Q=420-0.25*440
Q=310
Price producer receives =price buyer pay - tax
=440-85
=355
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deadweight loss =0.5*( change in quantity)* tax
=0.5*(330-310)*85
=$850
the deadweight loss is $850