1) Suppose supply is given by: P = 10 + 2Q, and demand is given by: P = 120 - 3Q
ID: 1125271 • Letter: 1
Question
1) Suppose supply is given by: P = 10 + 2Q, and demand is given by: P = 120 - 3Qd. A) Find equilibrium price and quantity. B) What are the demand and supply elasticities at equilibrium? C) Next, suppose the government imposes an excise tax of $10 per unit. What is the price that consumers pay, the price that sellers receive after paying the tax, and the tax revenue? D) Show the portion of the tax that is borne by consumers and what portion is borne by producers using the elasticity method. (Consumers share is: ettea E) What is the deadweight loss due to taxation?Explanation / Answer
(A) In equilibrium, demand price equals supply price.
10 + 2Q = 120 - 3Q
5Q = 110
Q = 22
P = 10 + (2 x 22) = 10 + 44 = $54
(B)
Demand function: P = 120 - 3Qd
3Qd = 120 - P
Qd = 40 - (P / 3)
Supply function: P = 10 + 2Qs
2Qs = P - 10
Qs = 0.5P - 5
Elasticity of demand = (dQd/dP) x (P/Qd) = - (1/3) x (54/22) = - 0.82
Elasticity of supply = (dQs/dP) x (P/Qs) = 0.5 x (54/22) = 1.23
(C)
After tax, supply curve shifts left by $10 at every output level and new supply function is
Qs = 0.5(P - 10) - 5 = 0.5P - 5 - 5 = 0.5P - 10
Equating with Qd,
40 - (P / 3) = 0.5P - 10
120 - P = 1.5P - 30
2.5P = 150
P = $60 (Price paid by buyers)
Price received by sellers = $60 - $10 = $50
Q = 40 - (60/3) = 40 - 20 = 20
Tax revenue = Q x Unit tax = 20 x $10 = $200
(D)
Tax burden of consumers = 1.23 / (1.23 + 0.82) = 1.23 / 2.05 = 0.60 (60%)
Tax burden of producers = 1 - 0.6 = 0.4 (40%)
(E)
Deadweight loss = (1/2) x Unit tax x Difference in quantity
= (1/2) x $10 x (22 - 20) = $5 x 2 = $10
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