Granola Booth Pricing Decision
A student entrepreneurship class runs a granola booth at a weekly farmers market. At the current price of $6 per bag, the booth sells 100 bags each market day. Fixed costs are $150 per market day for the stall fee and equipment rental, and variable cost is $2.50 per bag. The class surveys 80 customers. In the survey, 78 say they would buy at $7, and 125 say they would buy at $5; the survey reports average intended purchases. The faculty advisor wants to raise the price to $7 to 'increase revenue.' A student notes that the survey is a stated-preference poll of a small, nonrandom sample of customers. The class must decide on a price for the next market day and present a one-page recommendation. They have cost data but no data on competitor prices.
1. Calculate the price elasticity of demand between $6 and $7 using the midpoint method, and interpret the result.
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Use the midpoint formula. The quantity changes from 100 to 78, so the percentage change in quantity is (78 − 100) / ((78 + 100)/2) = −22/89 ≈ −24.7%. The price changes from $6 to $7, so the percentage change in price is (7 − 6) / ((7 + 6)/2) = 1/6.5 ≈ 15.4%. Elasticity is approximately −24.7/15.4 ≈ −1.6. Because the absolute value is greater than 1, demand is elastic over this range: a 1% price increase is associated with about a 1.6% quantity decrease. Revenue confirms the direction: at $6, total revenue is $600; at $7, total revenue is $546, a $54 fall. Profit behaves differently because variable cost falls with fewer bags: at $6, profit is 600 − (100 × 2.50) − 150 = $200; at $7, profit is 546 − (78 × 2.50) − 150 = $201. The advisor's claim about revenue is wrong, although profit could rise by about $1 if the survey is accurate.
2. What price should the class charge next market day? Justify using both quantitative and qualitative evidence.
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The class should not treat the $1 profit difference as decisive. It is well inside the uncertainty created by an 80-person, nonrandom stated-preference survey. The elasticity estimate says the $7 price will reduce revenue, and the profit gain comes only from buying fewer bags, not from higher sales. A defensible recommendation is to test $7 for one market day while counting actual sales, then compare with the $6 baseline. Alternatively, test $6.50 to reduce the risk of alienating regular customers. Because both prices exceed variable cost, the booth covers its contribution margin either way; fixed costs are sunk for the day. The class should also collect competitor prices and note whether customers buy multiple bags, since the survey may overstate price sensitivity. The written recommendation should state the assumption, the calculation, the survey limitation, and a decision rule: keep $7 only if actual quantity stays near 78 and profit is at least as high as the $6 baseline.