A Price Ceiling on Atta and the Subsidy Alternative
The state government has capped the retail price of atta (wheat flour) at ₹15 per kg after complaints that the open-market price had reached ₹20. Market surveys for a typical day give demand as Qd = 500 - 10P and domestic supply as Qs = 100 + 10P, where Q is in thousand kg per day and P is the price in rupees per kg. Within a week of the cap, retail shops report queues by 7 a.m., a large share of demand going unmet, and informal sales at a premium. Small millers say they are cutting back runs because ₹15 does not cover their costs plus distribution. The food department has two options on the table: keep the cap and pay millers a subsidy per kg, or withdraw the cap and use the money for a transfer to poor households. Officials need a number for the size of the shortage, a view on where the informal premium comes from, and a costing of both options per kg of atta actually delivered to a low-income family.
1. Calculate the equilibrium price and quantity without the cap, and the size of the shortage at ₹15.
Read the worked answer
Equilibrium: set Qd = Qs: 500 - 10P = 100 + 10P → 400 = 20P → P = ₹20 per kg Q = 500 - 10(20) = 300, check 100 + 10(20) = 300, so Q = 300 thousand kg per day.
At the cap of ₹15:
- Qd = 500 - 150 = 350 thousand kg
- Qs = 100 + 150 = 250 thousand kg
- Shortage = 100 thousand kg (1,00,000 kg) per day
The cap is binding because it lies below the equilibrium price; the quantity actually traded is the smaller of the two, that is 250 thousand kg, not the 350 thousand kg that households want.
2. Find the price at which the quantity actually supplied would clear demand, and identify who gains and who loses from the cap.
Read the worked answer
Informal price. Only 250 thousand kg is available. The demand price for that quantity is found from 250 = 500 - 10P, giving P = ₹25 per kg - a premium of ₹10 over the cap, which is why informal sales appear.
Gains and losses, per day:
- Households who do obtain the 250 thousand kg pay ₹5 less per kg: gain = 5 × 250 thousand = ₹12.5 lakh.
- Millers receive ₹5 less on the same 250 thousand kg: loss = ₹12.5 lakh unless the state compensates them. The cap is therefore mainly a transfer, not a net gain.
- The 100 thousand kg of demand that is never served is a pure loss: those buyers lose the entire surplus they would have enjoyed.
- Deadweight loss = ½ × (300 - 250) × (25 - 15) = ½ × 50 × 10 = 250 (₹ thousand) = ₹2.5 lakh per day.
Judgement: the allocation is decided by queueing, rationing and connections rather than by willingness to pay, so the ₹12.5 lakh transfer does not reliably reach the poorest household - a household without the time to queue gets nothing.
3. The food department proposes to keep the ₹15 cap and pay millers a subsidy of ₹10 per kg. Evaluate this against a direct transfer to poor households.
Read the worked answer
With a ₹10 subsidy, millers effectively receive ₹15 + ₹10 = ₹25: Qs = 100 + 10(25) = 350, which exactly equals Qd at ₹15 (350). The shortage disappears. Cost to the exchequer = 10 × 350 thousand = ₹35 lakh per day.
With a transfer instead: withdraw the cap, leave the price at ₹20, and give poor households ₹5 per kg. Covering the 300 thousand kg that the market supplies costs 5 × 300 thousand = ₹15 lakh per day - less than half the subsidy bill. The money also goes only to the intended households, not to every buyer.
Judgement: the subsidy is expensive for three reasons. It is paid on every kg including to households that do not need help; supply is inelastic (elasticity = 10 × 20/300 ≈ 0.67), so a large subsidy buys relatively little extra output; and it removes the incentive for consumers to economise. The transfer is cheaper and better targeted, but it needs a beneficiary list and delivery capacity that the state may not have, and it allows the price to rise to ₹20.
Practical answer: withdraw the universal cap, run a targeted transfer, and hold a small buffer stock so that the transition does not produce a price spike.