The Price Cap on Winter Heating
A regional market for home heating fuel has demand that is highly inelastic in winter: at $2.00 per liter, households buy 10 million liters per month; at $2.60, they still buy 9.4 million liters. Supply is more responsive: at $2.00, suppliers offer 10 million liters; at $2.60, they offer 12 million liters. A cold snap raises input costs, and the wholesale price would settle near $2.60. Worried about vulnerable households, the regional government imposes a cap of $2.00 per liter and promises to review it in 90 days. Within weeks, reports emerge of queues at depots, informal resale at $3.10, and suppliers diverting tankers to neighboring regions.
1. Using the numbers given, quantify the shortage created by the cap and explain the mechanism. Is the cap binding?
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The cap is binding because it sits below the market-clearing price. To see the equilibrium, compare the two price points:
- At $2.00: quantity demanded = 10.0 million L; quantity supplied = 10.0 million L.
- At $2.60: quantity demanded = 9.4 million L; quantity supplied = 12.0 million L.
Demand falls only 0.6 million L (6%) for a 30% price rise, so demand is inelastic. Supply rises 2.0 million L for the same rise, so supply is more elastic. The unregulated equilibrium lies between $2.00 and $2.60, where the two curves cross.
At the $2.00 cap, suppliers will not offer the 12 million L they would at $2.60; they offer roughly 10 million L (or less, once input costs rise). Meanwhile demand at $2.00 stays at 10 million L and may rise as the cap removes the incentive to conserve. Any upward shift in cost makes the gap larger. The shortage is the horizontal distance between quantity demanded and quantity supplied at the cap - small on paper, but it widens as costs rise and as suppliers divert stock to unregulated regions.
The queues and the $3.10 informal price are the market's way of rationing: the cap does not eliminate the higher price, it moves it into non-price forms (waiting, search, black-market premia).
2. The government wants to protect low-income households without creating a shortage. Recommend an alternative and explain why it is likely to work better, noting any trade-offs.
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Because demand is inelastic, a universal price cap is a blunt instrument: it suppresses the price signal that would otherwise trigger conservation and attract supply, while the benefit is spread across all households, including those who can easily pay.
A better design is targeted income support with the price left to clear the market:
- Let the price rise to its market level so suppliers keep stock in the region and households face an incentive to conserve.
- Send direct transfers (a rebate or voucher) to low-income households, sized to cover the higher cost of a basic consumption level. A household consuming 100 L/month faces about $60 extra at $2.60 versus $2.00; a transfer of that size protects them.
- Fund it from general revenue, which spreads the cost broadly rather than hiding it in shortages.
Why it works better: transfers preserve the price signal (so supply is not diverted and queues disappear) while shielding the vulnerable. The trade-offs are real: identifying eligible households has administrative cost and error (exclusion and inclusion mistakes), transfers may arrive with a lag, and politically a visible price rise is harder to defend than a visible cap. There is also a fiscal cost that must be met from somewhere. But compared with a cap that produces queues, black markets at $3.10, and regional diversion, targeted support dominates on both efficiency and equity.