Question

4. Suppose that the supply of bourbon (unit = 1 bottle) is given by P = Q. The (inverse) demand for the product is given by P = 200 – 4Q. Suppose the government introduces a tax on bourbon of $15 per bottle, to be paid to the government by consumers.

a. What is the market quantity and price before the tax goes into effect?

b. What is the new market price and quantity after the tax goes into effect?

c. How much of the tax do the consumers bear? How much do suppliers bear?

d. Who bears the larger burden of this tax? Why?

e. What is the deadweight loss associated with this $15 tax on each bottle of bourbon?

f. Now suppose the government decides to impose the tax on suppliers instead of consumers. How would this affect your answers to (b), (c), (d), and/or (e)?

Answer 1

a.   The market quantity and price (before the tax) of bourbon is given at the point where the market demand and supply curve (before the tax) intersect each other. It is also called the equilibrium price and quantity and is calculated as:

Supply equation: P = Q

Demand equation: P = 200 – 4Q or 4Q = 200 - P

Q = 50 -1/4P

At equilibrium, Demand = supply, so

50 -1/4P = P

Solving it we get,

200 = 5P

P = 40

Putting the quantity in either supply or demand equation gives the equilibrium Quantity.

So, market quantity =40 and market price = 40

Q = 50 -1/4(40) = 50 - 10 =40

b. The new market price and quantity after the tax is obtained from the new demand equation and the supply equation. We get the new demand function as Q = 50 -1/4P -15. It is because as the tax is levied on consumer, so the consumer demand lesser.

The new market price and quantity is calculated as:

demand function as Q = 50 -1/4P -15

Supply function: P = Q

At equilibrium, Demand = supply, therefore,

50 -1/4P -15 = P

Solving it we get,

200 - 60 = 5P

140 = 5P so that P = 28

Putting this value in demand/supply gives quantity:

Q = 50 -1/4(28) -15

Q = 50 - 7 -15 = 28

We find that new price = 28 and new quantity = 28

c.The amount that the consumer bears is shown in the following image.The burden borne by consumer is equal to the area ADGE and the burden borne by producer is equal to the area BGEC. From the diagram we see that area ADGE = area of rectangle AGDF + area of triangle DFE

Also, area BGEC = area of rectangle GFCB + area of triagle FEC

So we find the burden of consumer as:

area of rectangle AGDF = length*breadth

=28 * (88-40) = 28 *48 =1344

area of triangle DFE = 1/2*b*h

= 1/2* (28-40)*(88-40) = 288

So the total burden of the consumer = 288+1344 = 1632

Next we find the burden of producer as:

area of rectangle GFCB = length*breadth

= 28*(40-28) = 336

area of triagle FEC  = 1/2*b*h

= 1/2*(40-28)*(40-28) = 72

So the total burden of the producer = 336+72 = 408

hence we find that the burden borne by consumer is 1632 and by producer is 408.

** Please note that the point A is found by plugging the value of quantity = 28 in original demand curve.

d. From the calculations in previous part it is clear that the consumer bears the higher burden of tax than the supplier. This happens in those cases where consumer demand is less responsive to changes in price (as the tax is levied, a higher price does not bother the consumer a lot). Such a demand is called inelastic demand.

So, when the demand is inelastic and supply is relatively more elastic (as it is, in our example), with the introduction of tax, consumer bears more burden because as the supplier is more responsive to price than the consumers- so the supplier makes instant changes while buyers continue to buy at higher prices, and thereby incresing the burden of tax. Therfore, a higher share of burden is borne by the consumer.