Government Intervention and Inequality: Question 2
Syllabus 3.1, 3.2
A national health agency is concerned that a popular brand of sugary fizzy drink is over-consumed, since consumers do not fully take into account the long-term health costs of high sugar intake. The table below shows, at each price, the quantity of the drink that consumers demand each week, the quantity that producers originally supplied each week, and the quantity producers would supply each week after a specific (per-unit) tax is imposed on them.
| Price ($ per bottle) | Quantity demanded (thousand bottles per week) | Quantity supplied before tax (thousand bottles per week) | Quantity supplied after tax (thousand bottles per week) |
|---|---|---|---|
| 1.00 | 720 | 360 | 0 |
| 1.20 | 660 | 480 | 120 |
| 1.40 | 600 | 600 | 240 |
| 1.60 | 540 | 720 | 360 |
| 1.80 | 480 | 840 | 480 |
| 2.00 | 420 | 960 | 600 |
(a) Using the "quantity supplied before tax" column, state the original equilibrium price and quantity of the drink. [2]
(b) A specific tax of $0.60 per bottle is imposed on producers of the drink. Using the "quantity supplied after tax" column, state the new equilibrium price paid by consumers and the new equilibrium quantity. [2]
(c) Calculate the price received by producers once the tax has been paid, and hence calculate how much of the $0.60 tax is borne by consumers and how much is borne by producers. [4]
(d) Explain, using the figures in the table, why the burden of the tax is not shared equally between consumers and producers. [2]
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Worked solution
Part (a): The original equilibrium
Scanning the “quantity supplied before tax” column for the row where it equals quantity demanded:
| Price | Qd | Qs before tax |
|---|---|---|
| $1.00 | 720 | 360 |
| $1.20 | 660 | 480 |
| $1.40 | 600 | 600 |
| $1.60 | 540 | 720 |
| $1.80 | 480 | 840 |
| $2.00 | 420 | 960 |
Only at $1.40 do the two columns match, both at 600 thousand bottles per week. This is the original equilibrium, before any tax.
Part (b): The new equilibrium after the tax
The specific tax raises the price producers need to receive to be willing to supply any given quantity, which is why the “quantity supplied after tax” column is lower than the original supply column at every price. The new equilibrium occurs where quantity demanded equals this new supply figure:
| Price | Qd | Qs after tax |
|---|---|---|
| $1.00 | 720 | 0 |
| $1.20 | 660 | 120 |
| $1.40 | 600 | 240 |
| $1.60 | 540 | 360 |
| $1.80 | 480 | 480 |
| $2.00 | 420 | 600 |
Only at $1.80 do the two columns match, both at 480 thousand bottles per week. This $1.80 is the price consumers now pay, and 480 (thousand bottles per week) is the new equilibrium quantity. Lower than the original 600, as expected when a tax is imposed.
Part (c): Splitting the $0.60 tax between consumers and producers
Producers do not keep the full $1.80 that consumers pay, the government collects $0.60 of it per bottle as tax. The price producers actually receive, net of tax, is:
So producers receive $1.20 per bottle.
To find each side’s burden, compare each price with the original equilibrium price of $1.40:
Check: , which equals the $0.60 tax. Confirming the split is correct. Consumers bear $0.40 of the tax (paying $0.40 more than before), and producers bear $0.20 of the tax (receiving $0.20 less than before).
Part (d): Why the burden is unequal
The tax burden splits according to how responsive each side is to a change in price. Reading the “before tax” columns across the full price range in the table ($1.00 to $2.00, a rise of $1.00):
- Quantity demanded falls from 720 to 420, a change of only 300.
- Quantity supplied (before tax) rises from 360 to 960, a change of 600, twice as large, for the same $1.00 price range.
This means demand responds less to a change in price than supply does over this range. Demand is relatively less elastic. When a tax is imposed, the side of the market that is less able (or willing) to adjust the quantity it demands or supplies ends up absorbing more of the price change, because it cannot simply “escape” the tax by significantly changing its behaviour. Here, that is the demand side, which is why consumers bear the larger share of the tax ($0.40) while producers bear the smaller share ($0.20).
Final answers
- (a) Original equilibrium: price $1.40, quantity 600 thousand bottles per week.
- (b) New equilibrium after tax: price paid by consumers $1.80, quantity 480 thousand bottles per week.
- (c) Price received by producers $1.20; consumer burden $0.40 per bottle; producer burden $0.20 per bottle.
- (d) Demand is less responsive to price than supply is over this range, so the burden falls more heavily on consumers.