The Bakery's Pricing Dilemma
A small bakery in a competitive market sells 500 loaves of bread per day at $2 each. The owner estimates that if she raises the price to $2.20, she will sell 450 loaves. Her variable cost per loaf is $1.20, and fixed costs are $200 per day. A new competitor is opening nearby, and she expects demand to become more elastic. She is considering a price increase to cover rising ingredient costs.
1. Calculate the price elasticity of demand for the bakery's bread using the initial price and quantity, and the new price and quantity. Is demand elastic or inelastic? Show your work.
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Using the midpoint formula: % change in quantity = (450 - 500) / ((450+500)/2) = -50 / 475 ≈ -0.1053 or -10.53%. % change in price = (2.20 - 2.00) / ((2.20+2.00)/2) = 0.20 / 2.10 ≈ 0.0952 or 9.52%. Elasticity = -10.53 / 9.52 ≈ -1.11. Taking absolute value, elasticity ≈ 1.11 > 1, so demand is elastic. Alternatively, using the initial point: % change in Q = -10%, % change in P = 10%, elasticity = -1.0, unit elastic. The midpoint method gives a more precise estimate, indicating elastic demand. Since demand is elastic, a price increase will decrease total revenue.
2. Based on the elasticity, should the bakery raise its price to $2.20? Calculate total revenue and total cost at both prices, and profit. What other factors should the owner consider?
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At $2.00: Revenue = 500 * $2 = $1000. Variable cost = 500 * $1.20 = $600. Fixed cost = $200. Total cost = $800. Profit = $200. At $2.20: Revenue = 450 * $2.20 = $990. Variable cost = 450 * $1.20 = $540. Fixed cost = $200. Total cost = $740. Profit = $250. Although revenue falls slightly, profit increases because variable costs decrease with lower quantity. However, since demand is elastic, the price increase reduces revenue, but cost savings outweigh. The owner should consider that the new competitor will make demand more elastic, so further price increases may be risky. Also, consider customer goodwill and long-term market share. If ingredient costs are rising, the cost increase may affect both prices; a better strategy might be to seek cost efficiencies or differentiate the product to reduce elasticity.