Sachet Water Pricing after a Cost Increase
Mrs Okafor sells sachet water in a competitive market. She currently sells 10,000 sachets a month at ₦50 each. Her variable cost is ₦35 per sachet, and her fixed costs are ₦80,000 a month. A supplier raises the price of packaging, adding ₦5 to the variable cost of every sachet. Mrs Okafor considers raising her price to ₦60. She estimates that monthly sales would fall to 8,500 sachets, partly because two nearby sellers would keep their price at ₦50. She cannot differentiate her product, has no storage for a large stock, and must decide within one week. A customers' association argues that the price rise is exploitative because water is a necessity. Mrs Okafor says she is barely covering costs. She asks for advice on whether to raise the price, keep it at ₦50, or stop selling. She also wants to know how a government excise tax of ₦3 per sachet would affect her decision if the tax were imposed on sellers.
1. Calculate Mrs Okafor's price elasticity of demand between ₦50 and ₦60 using the midpoint formula. Is demand elastic or inelastic? What does that imply for revenue?
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Using the midpoint formula:
- % change in quantity = (8,500 − 10,000) ÷ [(10,000 + 8,500) ÷ 2] = −1,500 ÷ 9,250 = −0.1622
- % change in price = (60 − 50) ÷ [(50 + 60) ÷ 2] = 10 ÷ 55 = 0.1818
- PED = −0.1622 ÷ 0.1818 = −0.892, so |PED| = 0.89
Demand is inelastic because |PED| < 1. Revenue at ₦50 is 10,000 × ₦50 = ₦500,000. At ₦60 it is 8,500 × ₦60 = ₦510,000. Revenue rises slightly, which is consistent with inelastic demand. But revenue is not profit: the cost increase must be included before advising.
2. With the new variable cost of ₦40 per sachet and fixed costs of ₦80,000, compare monthly profit at ₦50 (10,000 sachets) and at ₦60 (8,500 sachets). Which price should she choose on profit grounds alone?
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New variable cost = ₦35 + ₦5 = ₦40. Fixed cost = ₦80,000.
- At ₦50: contribution per sachet = ₦10; total contribution = 10,000 × ₦10 = ₦100,000; profit = ₦100,000 − ₦80,000 = ₦20,000.
- At ₦60: contribution = ₦20; total contribution = 8,500 × ₦20 = ₦170,000; profit = ₦170,000 − ₦80,000 = ₦90,000.
On profit grounds alone, ₦60 is better by ₦70,000. The estimate is uncertain, however, and two competitors may react. She should raise the price if she trusts the 8,500 estimate; if sales fall further, profit could vanish. She should also try to negotiate packaging costs before deciding.
3. If government imposes a ₦3 excise tax per sachet on sellers, how would that change the decision? Discuss incidence, assuming demand is inelastic and supply is competitive.
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The ₦3 tax raises effective variable cost to ₦43. At ₦50, contribution is ₦7 and profit is (10,000 × ₦7) − ₦80,000 = −₦10,000, a loss. At ₦60, contribution is ₦17 and profit is (8,500 × ₦17) − ₦80,000 = ₦64,500. So ₦60 remains preferable to ₦50, but the tax reduces profit sharply. Because demand is inelastic, much of the tax can be passed to consumers through higher prices; the incidence falls more on buyers than sellers. In a competitive market, however, she can pass it on only if rivals also raise prices. If the market absorbs the tax, she may need a further price rise; if not, she should consider exit.