How Many Workers? Marginal Revenue Product at Anand Bakery
Anand Bakery sells a single line of celebration cakes at ₹60 each and hires part-time workers by the day at ₹1,200 a shift. Rent, oven depreciation and licence fees come to ₹3,000 a day and do not change with output. Daily output for different crew sizes is: 1 worker 40 cakes, 2 workers 90, 3 workers 130, 4 workers 160, 5 workers 180 and 6 workers 190. The owner currently hires four workers because 'the fourth one still adds a lot'. The shed is too small for a seventh worker. A festival wholesaler offers to buy unlimited cakes at ₹75 each for a fortnight, but part-time workers would then demand ₹1,600 a shift. In the quiet month that follows, wholesale demand collapses, the cake price falls to ₹30 and the wage returns to ₹1,200. The owner wants to know whether to keep the shop open at all during the quiet month, and does not see why he should pay for workers whose product sells below cost.
1. Compute marginal product and marginal revenue product for each crew size at a price of ₹60 and a wage of ₹1,200. How many workers should Anand hire, and what does the bakery earn at that crew size?
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| Workers | Output | MP | MRP = MP × ₹60 | Total revenue | Wage bill | Profit (after ₹3,000 fixed) |
|---|---|---|---|---|---|---|
| 1 | 40 | 40 | 2,400 | 2,400 | 1,200 | −1,800 |
| 2 | 90 | 50 | 3,000 | 5,400 | 2,400 | 0 |
| 3 | 130 | 40 | 2,400 | 7,800 | 3,600 | 1,200 |
| 4 | 160 | 30 | 1,800 | 9,600 | 4,800 | 1,800 |
| 5 | 180 | 20 | 1,200 | 10,800 | 6,000 | 1,800 |
| 6 | 190 | 10 | 600 | 11,400 | 7,200 | 1,200 |
Rule: hire while MRP ≥ wage. At a wage of ₹1,200 the fifth worker's MRP equals the wage exactly, so the firm is indifferent between four and five workers; both give the maximum profit of ₹1,800 a day. Hiring the sixth destroys ₹600 of contribution and is clearly wrong.
Reasoning to note. The owner's belief that 'the fourth still adds a lot' is loose language: the fourth worker adds 30 cakes worth ₹1,800 against a wage of ₹1,200, so the worker is worth hiring, but the margin is thin and diminishing returns have already set in after the second worker, where MP peaks at 50. The relevant comparison is always marginal revenue product against the wage, never total output or average product. With equal profits at four and five, the tie-break is practical: the smaller crew leaves spare capacity for a demand spike and reduces supervision and wastage risk.
2. During the festival fortnight (price ₹75, wage ₹1,600) and in the quiet month (price ₹30, wage ₹1,200), what is the profit-maximising crew size? In the quiet month, should the bakery shut down instead of producing?
Read the worked answer
Festival fortnight. MRP = MP × ₹75: 3,000; 3,750; 3,000; 2,250; 1,500; 750. Compare with the wage of ₹1,600: the fifth worker's MRP of 1,500 falls short, so hire four workers. Profit = (160 × 75) − (4 × 1,600) − 3,000 = 12,000 − 6,400 − 3,000 = ₹2,600. Checking the neighbours: three workers give ₹1,950 and five give ₹2,500, so four is genuinely the peak. Note the wage rose 33% while the price rose only 25%, which is why the crew does not grow.
Quiet month. MRP = MP × ₹30: 1,200; 1,500; 1,200; 900; 600; 300. Against a wage of ₹1,200, hire three workers (equality at the third). Revenue = 130 × 30 = ₹3,900; wage bill = ₹3,600; contribution = ₹300; loss = 3,900 − 3,600 − 3,000 = −₹2,700, which is better than the −₹3,000 loss from shutting down.
The shut-down test confirms it: minimum average variable cost is 2,400 ÷ 90 = ₹26.67, and the price of ₹30 is above it. Because price exceeds minimum AVC, production covers all variable cost and contributes ₹300 toward fixed cost. The owner's instinct - 'the cakes sell below cost' - confuses total cost (₹3,000 fixed is unavoidable either way) with variable cost. Two workers also happen to give a ₹2,700 loss, so either two or three is defensible; the bakery should reopen fully only when price recovers above ₹26.67 with a margin.