Question

Suppose the market supply and demand for guitars in San Francisco are given by Demand: P=1000-0.25Q, Supply: P=200+Q.

What is the equilibrium price and quantity of the product? What is the price elasticity of demand at equilibrium price?

Now assume there is a $10 per unit excise tax. What price will buyers pay after tax is imposed? What is the quantity of theh good that will be sold? What is the deadweight loss?

Answer 1

At the point of equilibrium, the demand = supply.
Equating the two equations we get:
1000 - 0.25Q = 200 + Q
800 = 1.25Q
Q = 800/1.25
Q = 640 units

P = 200 + Q = 200 + 640 = $840

Price Elasticity of demand = % change in quantity demanded / % change in price
The following table shows changes increase and decrease in equilibrium price and effects of demand.

Price	% change in Price	Demand	% change in Demand	Price Elasticity of Demand
$ 840.00		640
$ 756.00	-10%	976	0.525	-5.25
$ 924.00	10%	304	-0.525	-5.25

With the impostion of tax, the new supply curve will be:
P = 210 + Q
(Use the same supply curve but increase the price by the tax amount)
Equating the demand and supply equations:
1000 - 0.25Q = 210 + Q
790 = 1.25Q
Q = 790/1.25
Q = 632 units

P = 210 + 632 = $842

Deadweight loss = 1/2 * Drop in demand * Tax revenue = 1/2 * 8 * 10 = $40