The Bakery That Cannot Decide How Much to Hire
A neighborhood bakery sells loaves at $4 each in a competitive market and currently employs 5 bakers. Each baker works a fixed 8-hour shift and is paid $120 per day. The owner's production records show: with 4 bakers, 260 loaves per day; with 5 bakers, 300 loaves; with 6 bakers, 330 loaves. Flour and oven costs are $1.50 per loaf and are the only other variable cost; rent is $400 per day. The owner is considering hiring a sixth baker, and separately whether to expand the shop. A neighboring café pays its staff $140 per day for similar work, and one of the bakery's bakers has been approached by the café.
1. Compute the marginal revenue product of the fifth and sixth bakers and decide whether hiring the sixth baker is profitable. What does the pattern of marginal product suggest?
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Marginal product of the 5th baker = 300 − 260 = 40 loaves. MRP = 40 × $4 = $160, which exceeds the $120 wage, so the 5th baker is profitable (marginal profit $40/day).
Marginal product of the 6th baker = 330 − 300 = 30 loaves. MRP = 30 × $4 = $120, exactly equal to the wage. Marginal profit is zero. Hiring the 6th baker neither adds nor subtracts profit at this wage, so the owner is indifferent on strict profit grounds; any wage increase or price dip would make it unprofitable. The decision rule is to hire while MRP ≥ wage, so the 6th is the last profitable-equivalent hire.
The declining marginal product (40, then 30) reflects diminishing returns from a fixed shop and oven. A good answer states the MRP figures, applies the hiring rule, and warns that a 7th baker would likely have MRP below $120 and reduce profit. Note the flour cost does not enter the hiring decision because it is the same per loaf regardless of which baker makes it - only the incremental revenue and wage matter.
2. The café's $140 wage offer threatens to pull a baker away. Analyze the likely effect on the bakery's wage and employment, and whether the owner should match.
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The café's $140 offer sets a reservation wage for the baker. If the bakery pays $120, it risks losing workers to a competing employer paying $20 more per day. If the bakery must match $140, the hiring rule changes: MRP of the 5th baker is $160 ≥ $140, so the 5th is still profitable, but the 6th baker's MRP of $120 < $140, so the 6th would not be hired. Employment would settle at 5 bakers, not 6.
Matching is defensible if the bakery cannot replace the baker at $120 - recruiting and training costs plus lost output from an understaffed shift may exceed the $20/day premium. The owner should compare the cost of matching (about $20/day for each retained baker) with the cost of turnover. If all 5 bakers must be paid $140, the daily wage bill rises from $600 to $700, a $100 increase; the 5th baker's marginal profit falls from $40 to $20 but stays positive.
A strong answer frames this as a factor-market decision: the wage is set by outside opportunities and MRP, not by the owner's preference. The owner should match selectively (retain the most productive bakers) rather than across the board, and should not hire the 6th at $140 because MRP < wage.