Question

Consider the market for pumpkin spice latte (PSL), Q is in thousand cups. Due to its “addictive” nature, local government is considering imposing a $1.00 tax on each cup. The demand and supply are: QD = 10 - 0.5P QS = -5 + 2P

A. (8) SOLVE for the pre-tax and tax prices and quantities: [HINT: It may help to draw the graph before calculating (b)] 1. (1) pre-tax equilibrium price and quantity in the pumpkin spice latte market 2. (6) price paid by buyers and price received by sellers under a $1.00 tax after paying the tax and the new equilibrium quantity under a $1.00 tax 3. (1) Government revenue from the tax Name _________________________________________________________ 10

B. (3) DRAW the PSL market and LABEL the following clearly 1. (1) pre-tax equilibrium P and Q 2. (1) Pb and Ps and Government revenue under a tax 3. (1) CS and PS and DWL under a tax

C. (4) EXPLAIN how demand and supply elasticity relates to consumer and producer burden of the tax

Answer 1

a) At equilibrium, demand = supply

10 - 0.5P = -5 + 2P

P = 6

At this P, Q = 7

Price paid by buyer = Price received by seller = 6

After tax, price paid by buyer rises to 6.8 while price received by seller falls to 5.8 (detailed explanation about burden of tax in part c). Tax revenue is area of portion B + D in diagram below $1 * 6.4 = $6.4

b)

	Before Tax	After tax
	Value	Area of portion	Value	Area of portion
Price paid by buyer	$6	-	$6.8	-
Price received by seller	$6	-	$5.8	-
Consumer Surplus	49	A + B + C	43.56	A
Producer surplus	12.25	D + E + F	10.89	F
Government Revenue	-	-	6.6	B + D
Deadweight Loss	-	-	0.2	C + E

c) At a tax of $1, tax will be shared among both buyers as well as sellers which will fall in the ratio of (demand curve touching price axis - equilibrium price) to (equilibrium price - supply curve touching price axis) which is (20 - 6) / (6 - 2.5) = 14 / 2.5

· Burden on consumers would be [14 / (14 + 2.5)] of total tax which is 80% of $1 which is $0.8 while burden on producer is [2.5 / (14 + 2.5)] of total tax which is 20% of $1 which is $0.2