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 Name _________________________________________________________ 11

BONUS Using your answers in Question 4 CALCULATE the (2.5) consumer burden and the (2.5) producer burden of the tax

Answer 1

A. 1. Pre-tax equilibrium:

10 - 0.5P = -5 + 2P; So, P = 6; Q = 7000;

Graph:

2. Under $1 tax, buyers pay $6.8; sellers receive $5.8; quantity = 6600.
Government revenue = 6600 (1*6.6 = 6600)
The graph has been enlarged to a different scale to clearly see the prices and quantity aftet tax:

B. Labelled graph:

C. The slope of the demand and supply curves indicate the burden of tax borne by consumers and producers. The demand curve has a slope of 0.5 (as per demand function); and supply curve has a slope of 2 (as per supply function). It means that when there is $1 change in price, demand changes by 0.5 units of quantity, and supply changes by 2 units of quantity.
This makes demand inelastic (demand changes by less than proportionate) and supply elastic (supply changes more than proportionate).
It also means that consumers bear more burden than producers as demand ccurve is inelastic and supply curve is elastic.

Bonus: Consumer buden = $0.80; Producer burden = $0.20
Consumers and producers share the $1 tax in the ratio of their elasticities or slope of the respective curves as 4:1 (2:0.5 = 4:1). So Consumers pay 1*(4/5) = $0.80 and producers pay 1*(1/5) = $0.20.