A Price Ceiling in the Zarqa Bottled-Water Market
In the city of Zarqa the bottled-water market is competitive. At 0.50 dinar per 1.5-litre bottle, sellers offer 40,000 bottles a week and buyers take 40,000. At 0.70 dinar, supply rises to 70,000 bottles while demand falls to 20,000. After complaints about summer pricing, the water authority fixes a legal maximum of 0.40 dinar; at that price suppliers will offer only 25,000 bottles while consumers want 60,000. Meanwhile the largest bottler reports that when it raised its price from 0.50 to 0.55 dinar last year, sales fell by 25%. Two small bottlers have cut a production shift, blaming higher fuel and packaging costs, and vendors are already reselling bottles above the legal ceiling from the backs of vans. The authority argues the ceiling protects low-income families; bottlers reply that their average cost has risen by about 15%.
1. Calculate the price elasticity of demand between 0.50 and 0.70 dinar using the midpoint method, and compare it with the elasticity implied by the largest bottler's own price experiment. What does each result tell the bottler about pricing?
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Market data (midpoint method):
- % change in quantity = (20,000 − 40,000) ÷ 30,000 = −66.7%
- % change in price = (0.70 − 0.50) ÷ 0.60 = +33.3%
- Elasticity = −66.7 ÷ 33.3 = −2.0 (demand is elastic).
Revenue check: 0.50 × 40,000 = 20,000 dinars; 0.70 × 20,000 = 14,000 dinars. A price rise of 40% loses 30% of revenue - consistent with elastic demand.
Bottler's experiment: price +10% (0.50→0.55), quantity −25% → elasticity ≈ −2.5, also elastic but more so, probably because a single brand faces close substitutes while the whole market does not. Revenue falls proportionally more than the price rises.
Interpretation for the bottler: raising price destroys revenue at current prices, so the last thing it wants is a higher price - yet the ceiling forces a lower one. Under a binding ceiling the firm cannot choose price at all; the constraint is quantity (25,000 bottles). Elastic market demand also means consumers will readily switch to substitutes (filtered tap water, larger packs, other brands) if price rises or quality falls, so a price war is not a route to market share either. The profit-maximising lever becomes cost per bottle, not price.
2. Quantify the effect of the 0.40-dinar ceiling and explain at least three consequences that the authority's 'consumer protection' argument ignores.
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Quantities: at 0.40 dinar, quantity demanded is 60,000 and quantity supplied is 25,000 → a shortage of 35,000 bottles per week (58% of demand is unmet). The ceiling is binding because it sits below the equilibrium price of 0.50.
Consequences the authority ignores:
- Non-price rationing. With price frozen, allocation happens by queues, informal seller loyalty or luck. Being willing to pay 0.45 does not get you a bottle; being first in the queue does. The 25,000 bottles go to whoever arrives first, not to those who value them most.
- Black-market and quality erosion. Resale above the ceiling restores part of the price signal, but the premium goes to intermediaries, not to producers, so it funds no new supply. Sellers may also cut service (no chilled stock, no home delivery) to compete on the frozen price.
- Supply-side exit. At 0.40 with costs up 15%, bottlers whose unit cost exceeds 0.40 lose money on every bottle. The two shifted production cuts are the first sign: supply falls further, deepening the shortage.
Who is actually protected? Only the consumers who obtain one of the 25,000 bottles. The 35,000 who cannot buy are worse off than at 0.50, and the poorest are the least likely to win a queue. Total surplus shrinks through deadweight loss; the transfers do not reach the intended group.
3. Recommend a policy package to the water authority that protects low-income households better than the 0.40 ceiling, and explain the trade-offs of your recommendation.
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Diagnosis: the ceiling suppresses price but not cost, so it converts a price problem into a shortage. Policy should keep supply flowing while targeting support.
Recommended package:
- Remove or raise the ceiling toward 0.50 so supply returns to 40,000. The price signal then covers the 15% cost increase and attracts output, including the two bottlers' idled shifts.
- Subsidise the product, not the price. A per-bottle production subsidy of, say, 0.08 dinar lowers the effective supply price so market price settles near 0.42–0.45 while bottlers still cover costs. Cost: 0.08 × ~35,000 bottles/week ≈ 2,800 dinars a week - transparent in the budget, unlike the hidden cost of queues.
- Target households directly. Vouchers or cash transfers to registered low-income families let them buy at market price and choose among substitutes. This reaches the 35,000 who currently get nothing and does not distort the production decision.
- Enforce competition rules so the price rise reflects cost, not collusion; monitor the resale market to see where shortages bite.
Trade-offs: subsidies carry a fiscal cost and may be captured by non-poor buyers through lower prices; vouchers need a registry and can leak; a price rise is politically visible even when net welfare improves. Sequencing matters: remove the ceiling only after the subsidy or voucher is in place, otherwise the first visible effect is a price jump.