Suppose the demand for a product is given by P = 30 – 3Q. Also, the supply is gi

Question

Suppose the demand for a product is given by P = 30 – 3Q. Also, the supply is given by P = 10 + Q.

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

For the next 3 questions, assume that there is a $4 per unit excise tax levied on the consumers of the product.

C) What price will buyers pay after the tax is imposed?
D) What is the deadweight loss created by the tax?
E) What is the quantity of the good that will be sold after the tax is imposed?

Explanation / Answer

Suppose the demand for a product is given by P = 30 – 3Q. Also, the supply is given by P = 10 + Q.

A) What is the equilibrium price and quantity of the product?

P = 30 - 3Q = 10 + Q solve for Q and then for P

20 = 4Q

5 = Q

P = 30 - 3(5) = 30 - 15 = $15

B) What is the price elasticity of demand at the equilibrium price? 1 (equilibrium is always unit elastic)

For the next 3 questions, assume that there is a $4 per unit excise tax levied on the consumers of the product.

C) What price will buyers pay after the tax is imposed? $15 + 4 = $19
D) What is the deadweight loss created by the tax?

Q bought: 19 = 30 - 3Q; Q = 11/3 = 3.66 which is 1.33 less than previous

The change in price is $4

So the deadweight loss is $4 x 1.33 = about $5.33

E) What is the quantity of the good that will be sold after the tax is imposed?

The new quantity is 11/3 = 3.66

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