A Bhagalpur Powerloom Unit Decides How Many Workers to Hire - and Whether to Keep Producing
A powerloom weaving unit in Bhagalpur has four looms, rented for ₹1,500 a week in total, and hires workers weekly at ₹1,000 each. With the looms fixed, weekly output from successive workers is: 1 worker 20 thaan, 2 workers 46, 3 workers 76, 4 workers 104, 5 workers 126, 6 workers 138. The wholesale price of cloth is ₹60 per thaan and the unit is a price taker. The owner currently employs five workers and makes a modest profit. Then a large mill enters the same market, the wholesale price falls to ₹35 per thaan, and the wage stays at ₹1,000 because of a local agreement. The owner's cousin, who remembers only that fixed costs are already committed, advises him to keep all five workers because "the rent has to be paid anyway, so stopping only wastes it".
1. Compute the marginal product and average product for each number of workers. Where does diminishing returns set in, and how would you use the phases of the law of variable proportions to describe this unit?
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| Workers | Total product (thaan) | MP | AP |
|---|---|---|---|
| 1 | 20 | 20 | 20.00 |
| 2 | 46 | 26 | 23.00 |
| 3 | 76 | 30 | 25.33 |
| 4 | 104 | 28 | 26.00 |
| 5 | 126 | 22 | 25.20 |
| 6 | 138 | 12 | 23.00 |
Diminishing returns to the variable factor set in with the fourth worker: MP rises to 30 at three workers and falls thereafter (28, 22, 12).
Using the phases: as long as MP > AP the average product rises, and when MP < AP the average product falls; AP is maximum where the two cross. Here AP peaks at 4 workers (26) with MP still above it at 28. So Phase I (increasing average returns) runs up to 4 workers, and Phase II (diminishing but positive marginal returns, MP below AP) covers workers 5 and 6. MP never becomes negative in this data, so the third phase is not reached.
The practical point is that a rational producer does not operate in Phase I: with fixed looms, adding workers up to the point where AP is maximum still raises output per worker, so stopping earlier would waste capacity.
2. At a cloth price of ₹60 per thaan, calculate the marginal revenue product of each worker and determine the profit-maximising number of workers. Verify your answer by computing profit at 4, 5 and 6 workers.
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MRP = MP × ₹60: worker 1 = 1,200; 2 = 1,560; 3 = 1,800; 4 = 1,680; 5 = 1,320; 6 = 720.
Hire a worker whenever MRP ≥ wage of ₹1,000. The fifth worker adds ₹1,320, so he is hired; the sixth adds only ₹720, so he is not. Optimum: 5 workers.
Verification (profit = TR − wages − ₹1,500 rent):
- 4 workers: 104 × 60 = 6,240 − 4,000 − 1,500 = ₹740
- 5 workers: 126 × 60 = 7,560 − 5,000 − 1,500 = ₹1,060
- 6 workers: 138 × 60 = 8,280 − 6,000 − 1,500 = ₹780
Five workers give the highest profit. The sixth worker does raise total product (126 → 138) and even adds ₹720 of revenue, but he costs ₹1,000, so output rises while profit falls - the classic confusion between maximising output and maximising profit. The same logic explains why the owner does not stop at four: the fifth worker's marginal revenue product exceeds his wage, adding ₹320 to profit.
3. With the price at ₹35 per thaan, decide whether the unit should keep producing and, if so, with how many workers. Evaluate the cousin's advice using the concepts of sunk cost and the shutdown point.
Read the worked answer
MRP at ₹35: 700; 910; 1,050; 980; 770; 420. The best operating level is 3 workers (third MRP ₹1,050 ≥ ₹1,000; the fourth at ₹980 < ₹1,000).
At 3 workers: TR = 76 × 35 = ₹2,660; TVC = ₹3,000. Revenue does not even cover wages. Loss = 2,660 − 3,000 − 1,500 = ₹1,840.
Shutdown comparison: stop production and lose only the rent, ₹1,500. Average variable cost at 3 workers is 3,000/76 = ₹39.47, which exceeds the price of ₹35, so price is below minimum AVC and the unit is past its shutdown point. The least-loss operating option is actually 1 worker (TR ₹700, TVC ₹1,000, loss ₹1,800), still worse than shutting down.
The cousin is wrong on two counts. The rent is a sunk fixed cost: it must be paid whether or not the looms run, so it cannot justify continuing - only avoidable costs matter for the decision. And continuing to employ five workers would give TR ₹4,410 against TVC ₹5,000, a loss of ₹2,090 after rent. The correct short-run rule is: shut down when price falls below minimum AVC; in the long run, exit if price stays below minimum average total cost.