Pricing, loyalty and investment at Qormi Bakery
Qormi Bakery sells 2,000 loaves a week at €1.20. Variable cost is €0.70 a loaf and fixed costs are €900 a week. A supermarket has opened nearby with an own-brand loaf at €1.10. The owner estimates the own-price elasticity of demand is -0.9 over the relevant range, based on three months of local sales. Two options are on the table. Option A raises the price to €1.35. Option B keeps €1.20 but introduces a loyalty card: every tenth loaf is free, and administration costs €120 a week; the owner expects cardholders to buy 8% more loaves. The bank has also offered a loan for a second oven that would cut variable cost to €0.58 but add €250 a week in fixed cost. The owner asks whether price, loyalty or investment is the safer commercial judgement.
1. Calculate weekly profit under the current arrangement and under Option A using the elasticity estimate. Comment on the assumptions behind your answer.
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Current profit = 2,000 × (€1.20 − €0.70) − €900 = €2,400 − €1,400 − €900 = €100 a week. Option A raises price by €0.15, or 12.5%. With elasticity −0.9, quantity changes by −0.9 × 12.5% = −11.25%, so Q = 1,775 loaves. Revenue = 1,775 × €1.35 = €2,396.25; variable cost = 1,775 × €0.70 = €1,242.50; profit = €2,396.25 − €1,242.50 − €900 = €253.75. Profit rises by €153.75 because demand is inelastic in this range. The assumptions are important: the elasticity is constant, rivals do not react, fixed costs do not change and there is no waste. The supermarket at €1.10 may make actual demand more elastic, and if elasticity were below −1 the price rise would reduce revenue. The owner should test the price for four weeks before treating the calculation as reliable.
2. Evaluate Option B, the loyalty card. Include a calculation and explain why the owner might still prefer it despite the profit figure.
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If 2,000 loaves are bought and every tenth is free, 1,800 are paid for. Revenue = 1,800 × €1.20 = €2,160; variable cost is incurred on all 2,000 loaves = €1,400; fixed cost €900; administration €120. Profit = €2,160 − €1,400 − €900 − €120 = −€260. With the expected 8% increase, Q = 2,160; paid loaves = 1,944; revenue = €2,332.80; variable cost = 2,160 × €0.70 = €1,512; profit = €2,332.80 − €1,512 − €900 − €120 = −€199.20. To break even with full redemption, contribution per 10 loaves is 9 × €1.20 − 10 × €0.70 = €3.80, so required output is (€1,020 ÷ €3.80) × 10 = 2,684 loaves, 34% above current volume. The owner might still prefer the card if it builds habit, captures customer data and reduces search, but at current costs it is not a safe profit move. A smaller reward such as every twentieth loaf, or a paid membership, would reduce the cost.
3. Assess the second-oven investment. Should the owner take the loan before or after changing price?
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At current volume of 2,000, the new oven gives profit = 2,000 × (€1.20 − €0.58) − €900 − €250 = €1,240 − €1,150 = €90, slightly below the current €100. Break-even output is €1,150 ÷ €0.62 = 1,855 loaves. So the oven is only safe if demand is above about 1,855 loaves a week, or if the owner can use spare capacity for wholesale. If Option A is also imposed, Q = 1,775 and profit = 1,775 × €0.62 − €1,150 = −€49.50. The oven raises operating leverage: lower variable cost but higher fixed cost, so it magnifies the effect of a demand fall. Given supermarket competition and uncertain elasticity, the safer sequence is to test Option A first, monitor volume, and defer the loan until a wholesale contract or volume above 1,855 is secure.