Question

The supply and demand curves of a vaccine are \[ q = 14 + 5p \quad \text{and} \quad q = 329 - 5p, \] respectively, where $p$ is the price per unit of vaccine and $q$ is quantity of vaccine. The government decides that the maximum price of the vaccine would be Rs. 25 per unit. To avoid any shortage in supply at the ceiling price, the government also decides to subsidize the sellers so that the market clears. Subsidy is given on per unit basis. The total expenditure of the government in providing the subsidy is Rs. \_\_\_\_\_\_\_\_\_\_\_. (in integer)

Hint:

When a price ceiling creates a shortage, the government can remove it by subsidizing producers so that their net price equals the market equilibrium price.

Answer 1

Correct Answer: 2652

Step 1: Find the equilibrium price without ceiling.
At equilibrium, supply = demand: \[ 14 + 5p = 329 - 5p \Rightarrow 10p = 315 \Rightarrow p = 31.5. \]
Step 2: Compute equilibrium quantity.
\[ q = 14 + 5(31.5) = 14 + 157.5 = 171.5. \]
Step 3: Government-imposed ceiling price.
Ceiling price $p_c = 25$ (paid by consumers). At $p = 25$, Supply: $q_s = 14 + 5(25) = 139.$ Demand: $q_d = 329 - 5(25) = 204.$ There is a shortage of $204 - 139 = 65$ units.
Step 4: Government subsidy.
To make the market clear, suppliers must be paid the equilibrium price (Rs. 31.5). Hence, subsidy per unit = $31.5 - 25 = 6.5$.
Step 5: Total expenditure on subsidy.
\[ E = \text{Subsidy per unit} \times \text{Quantity sold} = 6.5 \times 171.5 = 1114.75 \approx 1115. \]
Step 6: Round off and convert to integer.
\[ \boxed{E = 1115.} \]