1. Suppose the de cigarettes is Q = P-3, where P is the price per pack of cigare
ID: 1118082 • Letter: 1
Question
1. Suppose the de cigarettes is Q = P-3, where P is the price per pack of cigarettes and M is average weekly income. a. What is the equilibrium price and quantity if M 500? b. What is the elasticity of demand and elasticity of supply at this price and quantity? Suppose the government imposes a cigarette tax of $3 per pack. C. What is the new equilibrium quantity? d. What is the price paid by producers? e. What is the price faced by consumers? f. What is the government revenue from the tax? g. What is the change in producer surplus and in consumer surplus? h. How much is the tax revenue? How much is the deadweight loss?Explanation / Answer
Demand: Q = 5 - 0.5P + 0.02M = 5 - 0.5P + (0.02 x 500) = 5 - 0.5P + 10 = 15 - 0.5P
Supply: Q = P - 3
(a) In equilibrium, Quantity demanded = Quantity supplied
15 - 0.5P = P - 3
1.5P = 18
P = $12
Q = 12 - 3 = 9
(b)
Elasticity of demand (Ed) = (dQS / dP) x (P / QD)
From demand function, Ed = - 0.5 x (12 / 9) = - 0.67
Elasticity of supply (Es) = (dQS / dP) x (P / QS)
From supply function, Es = 1 x (12 / 9) = 1.33
(c) The $3 tax will shift suply curve left by $3 at every level of output and new supply function will be
Q = P - 3 - 3 = P - 6
Equating with demand function,
15 - 0.5P = P - 6
1.5P = 21
P = $14 (Price paid by buyers)
Q = 15 - (0.5 x 14) = 15 - 7 = 8
(d)
Price received by sellers = Price paid by buyers - Unit tax = $14 - $3= $11
(e)
Price paid by buyers = $14
(f)
Government revenue = Unit tax x After-tax equilibrium quantity = $3 x 8 = $24
NOTE: As per Chegg answering guidelines, first 6 parts are answered.
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