Suppose that the government of Zanzi decides that there is a need to reduce cigarette smoking in
their country. The cigarette market in Zanzi can currently be described by the following demand and
supply equations:
Demand for cigarettes: Q = 1125 – 12.5P
Supply of cigarettes: Q = 1100P - 1100
The government proposes implementing a quantity control of 500 units: this quantity control would
limit the number of cigarettes that could be sold in Zanzi to exactly 500 units. The government has
asked you to evaluate this program by answering the following series of questions.
Answers
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A) Use the supply and demand curves to find the equilibrium price and quantity:
1125 – 12.5P = 1100P – 1100
2225 = 1112.5P or P = $2
Q = 1125 – 12.5(2) = 1100 cigarettes
B) To calculate the consumer surplus we first need to determine the y-intercept for the demand curve: so, use the demand curve and set Q = 0 to find this y-intercept. Thus, 0 = 1125 – 12.5P or P = 90. Consumer surplus is thus equal to (1/2)($90/cigarette - $2/cigarette)(1100 cigarettes) = $48,400.
C) To calculate the producer surplus we first need to determine the y-intercept of the supply curve: so, use the supply curve and set Q = 0 to find this y-intercept. Thus, 0 = 1100P – 1100 or P = 1. Producer surplus is thus equal to (1/2)(($2 /cigarette - $1/cigarette)(1100 cigarettes) = $550.
D) To find the price consumers must pay in order to demand only 500 cigarettes use the demand equation and substitute Q = 500 into that equation. Thus, 500 = 1125 – 12.5P or P = $50.
E) To find the price producers must receive in order to supply only 500 cigarettes use the supply equation and substitute Q = 500 into that equation. Thus, 500 = 1100P – 1100 or P = approximately $1.45.
F) If producers must receive a price of $1.45 per cigarette and demanders must pay a price of $50 per cigarette in order for only 500 cigarettes to be consumed, this implies that the price for the right to sell a unit of cigarettes in Zanzi must be equal to $50 - $1.45 or $48.55.
G) Consumer surplus with this quantity control is equal to (1/2)($90/cigarette - $50/cigarette)(500 cigarettes)
= $10,000.
Producer surplus with this quantity control is equal to (1/2)($1.45/cigarette - $1/cigarette)(500 cigarettes)
= $112.50.
Government revenue from this quantity control program = ($50/cigarette - $1.45/cigarette)(500 cigarettes)
= $24,275.
H) Deadweight loss from this quantity control program
= (1/2)($50/cigarette - $1.45/cigarette)(1100 cigarettes – 500 cigarettes)
= $14,565.