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

30-3Q= 10+Q 4Q=20 Q=5 P= 10+5= 15 Ed= dq/dp *P/Q Since Q= 10- P/3 (solve P=30-3Q for Q) dQ/dp= -1/3 So we have -1/3*15/5= -1 New supply curve is P= 14+Q 14+Q=30-3Q 4Q=16 Q=4 P= 18 Deadweight loss is (18-14)(1)*1/2= 2

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