Suppose the market supply and demand for guitars is given by: Demand: P = 300 -
ID: 1198752 • Letter: S
Question
Suppose the market supply and demand for guitars is given by:
Demand: P = 300 - (1/2)Q
Supply: P = 100 + (1/3)Q
What is the equilibrium price and quantity of the product?
What is the price elasticity of demand at the equilibrium price?
For the next three questions, assume there is a $20 per unit tax levied on the consumers of guitars. What price will buyers pay after the tax is imposed?
What is the quantity of the good that will be sold after the tax is imposed?
What is the deadweight loss created by the tax?
Explanation / Answer
-- Equilibrium Price = 180.
-- Equilibrium quantity = 240.
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Price elasticity of demand at equilibrium price:
Price elasticity of demand at equilibrium price:
Change in quantity demanded / Change in price
P = 300 – (1/2)Q; change in price = 600 – 480 = 120.
180 = 300 – (1/2)Q
(1/2)Q = 300 – 180; change in Q = 120 x 2 = 240.
Price elasticity of demand at equilibrium price = 240 / 120 = 2.
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Change in quantity demanded / Change in price
600 / 240 = 2.5%
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Price the consumers will pay after 20% tax is imposed:
P = 180 + 20% on 180
P = 180 + 36 = 216.
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Quantity sold after the tax is imposed:
P = 300 – (1/2)Q; 1/2Q = 300 – P
Q = 600 – 2P; Quantity sold after the tax = 600 – (2x210)
Quantity sold after the tax = 600 – 410 = 190.
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Dead weight loss:
Deadweight Loss = .5 * (P2 - P1) * (Q1 - Q2)
0.5 (216 – 180) * (240-190)
0.5 x 36 x 50 = 900.
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