The ₹34 Atta Ceiling: Elasticities, Shortages and Who Pays
A state government is worried about atta prices in its capital city after a poor harvest and a diesel price rise. The market-clearing price is ₹42 per kg, with 480 tonnes traded daily. Millers' short-run supply elasticity is estimated at 0.5; household demand elasticity is −0.25. Officials propose a statutory ceiling of ₹34 per kg, to be reviewed after six months. Retailers already report that two large millers have delayed deliveries, and kirana stores say they will ration packs to regular customers.
Three options are on the table: the ceiling; targeted cash transfers to below-poverty-line households, who consume about 40% of the city's atta; or licensing imports of 60 tonnes a day from a neighbouring state at ₹38 per kg plus ₹3 per kg freight. The finance department wants a quantified shortage estimate, a view on who gains and who loses under each option, and a recommendation that can be defended publicly.
1. Estimate the daily shortage in tonnes under the ₹34 ceiling, and state which assumptions make that estimate unreliable.
Read the worked answer
Step 1 - size of the price gap. The ceiling sits (34 − 42)/42 = −19.05% below the market-clearing price.
Step 2 - quantity response at constant elasticity.
- Demand: %ΔQ = (−0.25)(−19.05) = +4.76% → 480 × 1.0476 ≈ 503 t/day
- Supply: %ΔQ = (0.50)(−19.05) = −9.52% → 480 × 0.9048 ≈ 434 t/day
Step 3 - the gap. Shortage ≈ 503 − 434 = 69 t/day, about 14% of the volume previously traded, or roughly 1,800 tonnes a month.
Where the estimate can fail.
- Constant elasticity is a local approximation; a 19% price shock is well outside the range where it is reliable, so 69 t is a central estimate with a wide band.
- The 0.5 supply elasticity is a six-month parameter. As small millers exit or divert grain to other states, supply becomes less elastic and the gap widens over the review period - the shortage is not static.
- Measured tonnage understates scarcity: some households switch to inferior grades, buy loose instead of packaged, or queue. The visible shortage is a floor, not a ceiling.
- If the ceiling covers only branded packaged atta and exempts loose atta, demand migrates to the unregulated channel and the official shortage overstates the real one.
For a public defence, quote the range (roughly 55–85 t/day) rather than a single number, and commit to re-estimating at three months with mandi arrivals data.
2. Compare the ceiling, the licensed import channel and the cash transfer on consumer benefit, deadweight loss and fiscal cost, and recommend one.
Read the worked answer
Ceiling at ₹34. Buyers who still get supply gain ₹8/kg: 434,000 kg × ₹8 ≈ ₹34.7 lakh/day transferred from millers and traders to households. But 69 t/day of demand goes unmet, and the efficiency loss is roughly the triangle 0.5 × ₹8 × 69,000 kg ≈ ₹2.8 lakh/day - before counting rent dissipation. Queues, rationing, quality cuts and grey-market premia convert much of the ₹34.7 lakh into deadweight rather than household benefit. Fiscal cost is zero on paper, which is precisely why it is politically attractive and economically expensive.
Import channel. Landed cost ₹38 + ₹3 = ₹41/kg, below the current ₹42 but above the ₹34 ceiling. Two variants:
- No ceiling, open imports: price settles near ₹41, households gain ₹1/kg (≈₹4.8 lakh/day), no shortage, no subsidy. Consumer benefit is small because the import cost is high.
- Ceiling plus imports sold at ₹34: subsidy = ₹7 × 60,000 kg = ₹4.2 lakh/day; residual shortage ≈ 9 t/day.
Cash transfer. Compensating BPL households for ₹8/kg on 40% of 480 t = 192,000 kg gives ₹15.4 lakh/day - 3–4× the import subsidy. It preserves the price signal, so there is no shortage and no deadweight loss, but leakage and targeting error are real.
Recommendation. Do not hold ₹34 for six months. Set the ceiling at import parity (about ₹41), open the import licence, and add a modest targeted transfer to BPL households. This buys most of the price relief at a fraction of the transfer cost, keeps supply flowing, and avoids creating a rationing bureaucracy that will outlive the harvest shock.
3. What non-price evidence in the first 90 days would show the ceiling is biting harder than the tonnage data suggest?
Read the worked answer
Price is censored under a binding ceiling, so scarcity reappears in other dimensions. Evidence to collect:
- Queues and stockouts: average waiting time at fair-price outlets, and the share of days a shop reports 'no stock'.
- Quantity shading: pack sizes falling (1 kg to 900 g) with unchanged shelf price; loose atta replacing branded packs.
- Quality shading: higher bran content, shorter shelf life, complaints data from consumer forums.
- Delivery lags: days between order and delivery from the two large millers already reported as late; unpaid back-orders.
- Grey-market premium: prices in informal dealer networks and social-media resale groups, compared with the legal ceiling. A widening wedge signals a growing shortage.
- Supply-side exit: number of licensed millers operating, mandi arrivals, and diversion of grain to neighbouring states without a ceiling.
- Household behaviour: bulk forward-buying and pantry stocking, which shows expectations of future scarcity even when current purchases look normal.
Interpretation rule. If official price data are flat while deliveries stretch, pack sizes shrink and grey-market premia rise, the ceiling is binding and the true welfare cost is much higher than the ₹2.8 lakh/day static estimate. These indicators should trigger the review before the six-month date, not after; waiting converts a temporary seasonal problem into permanent capacity exit.