Question

Suppose that the demand for curve is QD = 1000-40P, (where QD is the number of gallons of liquor demanded and P is the price per gallon), and the supply curve for liquor is QS =60P (where QS is the number of gallons supplied). For all the questions below, graph and calculate (and label) all intercept, slopes and equilibrium points. a. Compute equilibrium prices and quantities in the absence of the tax. b. In an effort to reduce alcohol consumption, SMU is considering a 40% tax on liquor sold on campus (the tax is levied on consumers). Compute how the tax would affect the price paid by consumers and the price received by producers. c. Calculate the consumer and producer burdens of this tax. d. How much revenue does the tax on consumers (part b) raise for SMU? How much of the revenue comes from consumers, and how much from producers? e. What is the deadweight loss? f. What if SMU instead levies a 40% tax on producers? Redo parts b) and c) for this new tax. g. What happens to consumer and producer burdens if SMU decides to put a price floor of $10.50? Does it matter if the tax is imposed on consumers or producers? Explain.

Answer 1

a. Q_D = 1000 - 40P is the equation of demand curve and Q_S = 60P is the equation of the supply curve.

For demand curve, if P=0, Q_D = 1000 and if Q_D = 0, P=1000/40 =25 . Hence, demand curve has vertical intercept of 25 and horizontal intercept of 1000.

For supply curve, Q_S = 60P is a linear curve passing through origin and when P=1 , Q_S = 60 , When P=25, Q_S = 60*25 = 1500. Plotting price on vertical axis and quantity on horizontal axis, Q_D and Q_S curves are shown below:

Now, in absence of tax, for equilibrium, demand = supply

or, Q_D = Q_S

or, 1000 - 40P = 60P

or, 1000 = 100P

or, P = $ 10 per gallon

and equilibrium quantity Q = 60*10 = 600 gallons

b. When tax of 40% is levied , supply curve shifts to the left .

Q_S^* = 60P - 40/100*60P = 60*60P/100 = 36P (The new supply curve is also shown in the diagram above as Q_S*)

For equilibrium after tax, 1000 - 40P = 36P

or, 76P = 1000

or, P = 1000/76 = $13.15

and equilibrium Q^* = 36P = 36*13.15 = 474 approx

c. In the given figure aea a and b is the tax burden for consumers while area c and d is the tax burden for producers.

d. Revenue from consumers = area a+area b

= length * breadth

= 474 * (13.15-10)

= 474 * 3.15

=$1493 approx