These next five problems consider tax incidence. Suppose the market supply and d

Question

These next five problems consider tax incidence. Suppose the market supply and demand for guitars in Happy Valley are given by: Demand: P = 1500 - 0.5Q Supply: P = 150 + 0.25Q 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 $30 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

Demand : P = 1500 - 0.5Q

Supply: P = 150 + 0.25Q

At equlibrium, Supply = Demand

P = 1500 - 0.5Q =  P = 150 + 0.25Q

1500 - 0.5Q = 150 + 0.25Q

1350 = 0.75Q

Q = 1800

P= 1500 - 0.5Q

P = 1500 -0.5(1800)

P = $600

1) OptionD, P= $600 and Q =1800

2) Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

Price Elasticity of Demand = -1800 /6 = -3 (potion C)

3) After taxof $30 is leived on consumers ,

consumers will pay $630 (option B)

4) Quantity of goods that are sold after tax is leived is,

Demand, P = 1500 - 0.5 Q

630 = 1500 -0.5Q

870 = 0.5Q

Q = 1740 (option E , none of the above)

5) Deadweight loss = $ 180 (option E , NONE OF THE ABOVE)

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