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The government is going to impose a policy in the market for cigarettes and ask you for advice
The government is going to impose a policy in the market for cigarettes and ask you for advice. We have few observations for a typical day of this market as follow: P A 10 B 20 C 30 D 40 90 60 30 0 QS 0 10 20 30 a. Model the demand side assuming the quantity demand is a linear function of price. (explain you model in plain English, using graph, and math) b. Model the supply side assuming the quantity supplied is a linear function of price. (explain you model in plain English, using graph, and math) c. Find the free market equilibrium. (Do not forget to check your answer) d. What are the consumer surplus and producer surplus in the free market? Government consider four policies: 1. A minimum legal price at $35. 2- A maximum quantity sold at 25 cigarettes per day. 3. A $4 tax on selling 4. A $2 tax on consumption e. Which policy causes the smallest quantity sold? f. Which policy causes the smallest deadweight loss? 8. Which policy is better for consumers in term of consumer surplus? h. Which policy is better for producers in term of producer surplus? i. Which policy causes the highest revenue for the government? 1. Which policy do you suggest?
Expert Solution
Linear Demand function: P = a - bQD
10 = a - 90b...........(1)
40 = a - 0...............(2)
From (2), a = 40
Plugging in (1),
10 = 40 - 90b
90b = 30
b = 1/3 = 0.33
Demand function: P = 40 - (Q / 3)
(b)
Linear supply function: P = c + dQS
10 = c + 0.............(1)
40 = c + 30d.........(2)
(2) - (1) yields:
30d = 30
d = 1
c = 10
Supply function: P = 10 + Q
(c)
In equilibrium, demand = supply.
40 - (Q/3) = 10 + Q
120 - Q = 30 + 3Q
4Q = 90
Q = 22.5
P = 10 + 22.5 = 32.5
(d)
From demand function, when Q = 0, P = 40 (vertical intercept)
Consumer surplus = (1/2) x (40 - 32.5) x 22.5 = (1/2) x 7.5 x 22.5 = 84.375
From supply function, when Q = 0, P = 10 (vertical intercept)
Producer surplus = (1/2) x (32.5 - 10) x 22.5 = (1/2) x 22.5 x 22.5 = 506.25
please see the attached file for the complet solution.
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