Government Intervention and Inequality: Question 5
Syllabus 3.1, 3.2
A government believes that locally grown vegetables are a merit good that is currently under-consumed, since many consumers underestimate the long-term health benefits of eating them and instead choose cheaper, less healthy processed food. The table below shows, at each price, the quantity of vegetables (measured in boxes) that consumers demand each week, the quantity that producers originally supplied each week, and the quantity producers would supply each week after receiving a subsidy.
| Price ($ per box) | Quantity demanded (boxes per week) | Quantity supplied before subsidy (boxes per week) | Quantity supplied after subsidy (boxes per week) |
|---|---|---|---|
| 2.50 | 550 | 250 | 350 |
| 3.00 | 500 | 300 | 400 |
| 3.50 | 450 | 350 | 450 |
| 4.00 | 400 | 400 | 500 |
| 4.50 | 350 | 450 | 550 |
(a) Using the "quantity supplied before subsidy" column, state the original equilibrium price and quantity of vegetables. [2]
(b) The government pays producers a subsidy of $1.00 per box to encourage consumption of this merit good. Using the "quantity supplied after subsidy" column, state the new equilibrium price paid by consumers and the new equilibrium quantity. [2]
(c) Calculate the price received by producers once the subsidy has been added, and hence calculate how much of the $1.00 subsidy benefits consumers (through a lower price) and how much benefits producers (through a higher price received). [4]
(d) Explain why, in this case, the benefit of the subsidy is shared equally between consumers and producers. [2]
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Worked solution
Part (a): The original equilibrium
Scanning the “quantity supplied before subsidy” column for the row where it equals quantity demanded:
| Price | Qd | Qs before subsidy |
|---|---|---|
| $2.50 | 550 | 250 |
| $3.00 | 500 | 300 |
| $3.50 | 450 | 350 |
| $4.00 | 400 | 400 |
| $4.50 | 350 | 450 |
Only at $4.00 do the two columns match, both at 400 boxes per week. This is the original equilibrium, before any subsidy.
Part (b): The new equilibrium after the subsidy
A subsidy paid to producers lowers their cost of supplying vegetables, so they are willing to supply more at every price. This is why the “quantity supplied after subsidy” column is higher than the original supply column at every price. The new equilibrium occurs where quantity demanded equals this new, higher supply figure:
| Price | Qd | Qs after subsidy |
|---|---|---|
| $2.50 | 550 | 350 |
| $3.00 | 500 | 400 |
| $3.50 | 450 | 450 |
| $4.00 | 400 | 500 |
| $4.50 | 350 | 550 |
Only at $3.50 do the two columns match, both at 450 boxes per week. This $3.50 is the price consumers now pay (lower than the original $4.00, as expected when a subsidy encourages greater consumption) and 450 (boxes per week) is the new equilibrium quantity, higher than the original 400.
Part (c): Splitting the $1.00 subsidy between consumers and producers
Producers receive more than the $3.50 that consumers pay, the government adds the $1.00 subsidy on top for each box sold. The price producers actually receive is:
So producers receive $4.50 per box.
To find each side’s benefit, compare each price with the original equilibrium price of $4.00:
Check: , which equals the $1.00 subsidy. Confirming the split is correct. Consumers benefit by $0.50 per box (paying $0.50 less than before), and producers benefit by $0.50 per box (receiving $0.50 more than before).
Part (d): Why the benefit is shared equally here
Looking at the “before subsidy” columns as price rises in steps of $0.50 (from $2.50 to $4.50): quantity demanded falls by exactly 50 boxes at every step, and quantity supplied rises by exactly 50 boxes at every step. Demand and supply are therefore equally responsive to a change in price in this market, neither side reacts more strongly than the other. When this is the case, a subsidy’s benefit is shared evenly, because neither consumers nor producers are relatively more “flexible” in adjusting the quantity they demand or supply, so the price change caused by the subsidy divides equally between the price consumers pay and the price producers receive.
Final answers
- (a) Original equilibrium: price $4.00, quantity 400 boxes per week.
- (b) New equilibrium after subsidy: price paid by consumers $3.50, quantity 450 boxes per week.
- (c) Price received by producers $4.50; consumer benefit $0.50 per box; producer benefit $0.50 per box.
- (d) Demand and supply are equally responsive to price in this table, so the $1.00 subsidy’s benefit splits evenly between consumers and producers.