Question

Suppose the coffee market in the US is given by the following equations for supply and demand: QS = 9 + 0.5p QD = 12 − p where Q is the quantity in millions of tons per year and p is the price per pound.

(a) Calculate the equilibrium price and quantity of coffee.

(b) At the equilibrium price, what is the price elasticity of demand?

(c) Suppose a tax of $0.75 is imposed on coffee producers. Calculate the new equilibrium price and quantity. What is the amount of the tax burden on consumers (hint: by how much has the price per pound consumers pay change?).

(d) Suppose the government wishes to help out consumers impacted by this tax by subsidizing coffee purchased by consumers at $0.75 per pound (i.e. a negative tax on consumers). To fund this, they raise the tax on sellers to $1.50 per pound sold. Discuss the impact of this policy on the price and quantity of coffee and the resulting net tax burdens.

Answer 1

a. Equilibrium occurs where Qd=Qs

9+0.5P=12-P

Equilibrium Price P*=3/1.5=$2

Equilibrium quantity Q*=12-2=10

b. Price elasticity of demand= (-1)(2/10)= -0.2

c. Tax=$0.75

Qs'=9+0.5(P-0.75)=9+0.5P-0.375= 8.625+0.5P

Qs'=Qd

8.625+0.5P=12-P

New Equilibrium Price P**=$2.25

New Equilibrium quantity Q**= 12-2.25=9.75

Tax burden on consumer=$2.25-$2=$0.25

d. Tax=$1.5

Subsidy= $0.75

Qs''= 9+0.5(P-1.5)=9+0.5P-.75=8.25+0.5P

Qd'=12-(P-0.75)=12.75-P

Qs''=Qd'

8.25+0.5P=12.75-P

New Equilibrium Price P***=4.5/1.5=$3

New Equilibrium quantity Q***=11.25-3=8.25

Final tax burden on consumer= $3-$2.25=$0.75

So the final consumer has risen for consumer