Question

The demand for ice cream is given by Q D = 20 – 2P, measured in gallons of ice cream. The

supply of ice cream is given by Q S = 4P – 10. Suppose that the government legislates a $1 tax on

a gallon of ice cream, to be collected from the seller.

a) As a result of the tax, what is the price paid by buyers?

b) What is the price received by sellers?

Hint: You need to determine the consumer and producer burden of the tax. First find equilibrium price

and quantity. Then, determine the elasticity of demand and supply. Then, use the share of the tax formula

provided to you to determine the burdens. After, that you add the consumer burden to the equilibrium

price to find buyer price. Subtract the producer burden from equilibrium price to find seller price.

Answer 1

At equilibrium,

Qd=Qs

Or, 20 - 2P = 4P - 10

Or, 6P = 30

or, P = 5

And, at this price, Qd = Qs = 10

The equilibrium price is $5 and equilibrium quantity is 10 units.

Now we need to calculate elasticity of demand and elasticity of supply.

Demand equation is given by,

Qd = 20 - 2P

Or, d(Qd)/dP = - 2

And at equilibrium,where P=5 and Q=10,

elasticity of demand (E_d)= -2(5/10) = - 1

Or, | E_d | = 1

Supply equation is given by,

Qs= 4P - 10

Or, d(Qs)/dP = 4

At equilibrium, elasticity of supply ( E_s)= 4(5/10) = 2

Now we'll have to calculate Tax burden on Consumer and on producer.

Tax burden on Consumer = E_s /(E_d + E_s) = 2/(1+2) = 2/3

Tax burden on producer = E_d /(E_d + E_s) = 1/(1+2) = 1/3

Now, to find the buyers price we have to add consumer burden to the equilibrium price and to find Sellers price we have to substract producers burden from equilibrium price.

Answer- A) Price paid by buyers = $(5+(2/3)) = $ 5.67

B) Price received by sellers = $(5 - (1/3)) = $4.67

Tax=( Price paid by buyers - Price received by sellers)

= $(5.67 - 4.67) = $1