Question

Suppose that, in the market for soda drinks, demand is given by P= 48 – 0.6Q, and supply is given by P= 0.2Q. Further, suppose that the government decides to impose a $4 per soda drink.

A. On a graph, demonstrate the effect of the tax on the equilibrium price and quantity. (Clearly label the value of each both before and after the tax.)

B. Show on the graph and calculate the tax revenue and deadweight loss that result from the tax.

C. Who bears the greater burden of the tax, producers or consumers? Explain why this is the case.

(You can draw the graph, take a picture and attach it here. Please do *not* take a picture of your hand-written answer, it is much easier for your marker to read typed text)

Answer 1

Conditions before the imposition of tax on soda drinks:

Inverse demand function: P = 48-0.6Q

Supply Function: P = 0.2Q

At the equilibrium, demand is equal to supply i.e.

48-0.6Q = 0.2Q

48 = 0.2Q + 0.6Q

48 = 0.8Q

Q = 48/0.8

Q = 60   

Given the equilibrium quantity before tax be Q = 60, we can find the equilibrium price using either the demand or supply function as:

P = 48-0.6Q

P = 48 – 0.6(60)

P = 48 – 36

P = $12

Or P = 0.2Q = 0.2(60) = $12

Conditions after the imposition of tax on soda drinks:

We when a tax of $4 per soda drink is imposed it shifts the supply curve upwards by $4 units i.e. for each level of quantity the consumer has to pay $4 more.

The demand curve remains the same and the supply curve changes to:

P = 0.2Q + 4

At the new equilibrium, the new supply curve and the old demand curve intersects i.e.

0.2Q + 4 = 48-0.6Q

0.2Q + 0.6Q = 48 – 4

0.8Q = 44

Q = 44/0.8

Q = 55

The equilibrium price that the consumer pays can be calculated using the demand or supply curve as :

0.2Q + 4 = 0.2(55) + 4 = 11 + 4 = $15

Or

48-0.6Q = 48 – 0.6(55) = 48 – 33 = $15

a) Basis the above calculations, the below tables represents the before and after tax situations:

Situation	Equilibrium Price (P)	Equilibrium Quantity (Q)
Before Tax	$12	60
After Tax	$15	55
Direction of change	Increase	Decrease

Plotting the demand and supply curve we get:

Curve	Axis Coordinates
P (Y-axis)	Q (X-axis)
Demand Curve (P = 48-0.6Q)	48	0
0	80
Supply Curve before tax (P = 0.2Q)	0	0
Supply Curve after tax (P = 0.2Q + 4)	4	0

Refer to the below figure which shows the market of soda-drinks. Here, X-axis shows the quantity and Y-axis shows the price. Before tax the demand curve D and the supply curve S intersects at equilibrium point E1, where equilibrium quantity demanded/supplied is 60 and equilibrium price is $12. After the imposition of tax, the supply curve shifts upwards by $4 i.e. the difference between the two supply curve is $4. The equilibrium shifts to point E2, where the new supply curve ST and the demand curve D intersects. Here, equilibrium quantity fall to 55 units and equilibrium price rises to $15.

b) Let the price paid by the consumer be : Pc = 15

Tax Imposed: T = $4

Price Received by the seller (given by the old supply curve): Ps = Pc – T = 15 - 4 = $11

Tax revenue is the shaded area of the box (A + B) = Tax * Quantity after Tax = $4 * 55 = $220

With the imposition of tax the consumers have to pay a higher price thus there is a fall in the consumer surplus and also the producer receives a lower price as before since less units are sold which leads to a fall in producer surplus. This creates leads to a reduction on the overall welfare of the society leading to a net welfare loss.

Deadweight Loss = Area of Triangle ( C + G) = 1/2 * Base * Height

= 1/2 * (60 – 55) * 4

= 1/2 * 5 * 4

= 10

c) Basis the diagram we can find the tax burden on consumer and producers as:

Consumer Burden = Area of Rectangle A = L* B = 55 * (15-12) = 55* 3 = 165

Producer Burden = Area of Rectangle B= L* B = 55 *(12 -11) = 55 * 1 = 55

Consumer burden (A = 165) > Producer Burden ( B = 55), thus most of the tax burden is shared by the consumers.

Tax burden generally falls more on the inelastic side of the market. From the graph we can see, the demand curve is steeper than the supply curve. This means the demand of soda drink is relatively inelastic as compared to its supply. When demand is inelastic the responsiveness of consumers towards price changes is low. With a rise in price due to tax, the fall in quantity demanded is not very significant which means the consumers are addicted to the product. This way, the sellers are able to transfer the tax burden to consumers by charging higher prices without a significant decline in the quantity sold.

PC$) 48 St: P=0.2Q +4 Sip=0.20 1 E2 Pe=15 That с A B a El Ps= 1 d =s 55 60 80