Six workers or seven: a coir unit facing a price collapse
A coir yarn unit near Pollachi has leased four spinning machines for one year at a total lease rent of ₹1,20,000 a month, payable whether or not the machines run. Labour is the only input the owner can vary from month to month, at ₹9,000 per worker. Yarn sells at ₹250 a kg. The engineer's trial run reports total monthly output in kilograms by number of workers: 1 → 120; 2 → 300; 3 → 540; 4 → 720; 5 → 840; 6 → 900; 7 → 930. The owner currently employs four workers and makes a modest profit. A coir exporter now offers a one-year contract at a flat ₹150 a kg and wants an answer within a week. The machine lease cannot be cancelled, the machines have no alternative use, and the owner has no savings to fall back on.
1. Compute marginal product and marginal revenue product for each worker at ₹250 a kg, find the profit-maximising number of workers, and explain the decision rule you used.
Read the worked answer
MP is the change in total product; MRP = MP × ₹250.
| Workers | TP (kg) | MP (kg) | MRP (₹) | Wage (₹) |
|---|---|---|---|---|
| 1 | 120 | 120 | 30,000 | 9,000 |
| 2 | 300 | 180 | 45,000 | 9,000 |
| 3 | 540 | 240 | 60,000 | 9,000 |
| 4 | 720 | 180 | 45,000 | 9,000 |
| 5 | 840 | 120 | 30,000 | 9,000 |
| 6 | 900 | 60 | 15,000 | 9,000 |
| 7 | 930 | 30 | 7,500 | 9,000 |
Rule: hire while MRP ≥ wage. The sixth worker adds 60 kg, worth ₹15,000, against a wage of ₹9,000, so he is worth hiring; the seventh adds only ₹7,500 and would reduce profit. Optimum: six workers. Profit at six = (900 × 250) − (6 × 9,000) − 1,20,000 = ₹2,25,000 − ₹54,000 − ₹1,20,000 = ₹51,000, against ₹24,000 with four workers.
Note the shape of the MP column: it rises to the third worker (better use of the fixed machines, division of labour) and falls from the fourth - the law of variable proportions in its increasing and diminishing returns phases.
2. If the exporter's ₹150 a kg contract is accepted, how many workers should be employed, and should the unit keep operating at all? Show the comparison that drives your answer.
Read the worked answer
Recompute MRP at ₹150: 18,000; 27,000; 36,000; 27,000; 18,000; 9,000; 4,500. Hire while MRP ≥ ₹9,000 - the sixth worker's MRP exactly equals the wage, so five or six workers are equally defensible; the seventh still fails.
Profit check at six workers: (900 × 150) − ₹54,000 − ₹1,20,000 = ₹1,35,000 − ₹1,74,000 = −₹39,000. At five workers: ₹1,26,000 − ₹45,000 − ₹1,20,000 = −₹39,000. At seven: −₹43,500.
Operate or shut down? Shutting down still costs the lease of ₹1,20,000, so the loss would be ₹1,20,000. A loss of ₹39,000 is smaller, so the unit should keep running. The formal test is price versus average variable cost: AVC at six workers = 54,000/900 = ₹60, far below the ₹150 price, so every kg sold covers its variable cost and contributes ₹90 towards the fixed lease. The shut-down point would be reached only if price fell below minimum AVC (about ₹50, at three workers).
Verdict: accept the contract, run six workers, and use the year to renegotiate or shed the machine lease, because ₹150 is far below average total cost of ₹193 at that output.
3. The owner protests: 'With seven workers I produce 930 kg, more than with six. Why stop at six?' Answer him, and say what he should do once the lease year ends if ₹150 persists.
Read the worked answer
Total output is not the objective; profit is. The seventh worker adds 30 kg. At ₹250 that is ₹7,500 of revenue against a ₹9,000 wage, so profit falls by ₹1,500; at ₹150 it adds ₹4,500 and profit falls by ₹4,500. Expanding until marginal revenue product is zero maximises output, not profit - a distinction the marginal-versus-total way of thinking makes clear. Average product also falls (150 kg per worker at six, 132.9 at seven), which tells the same story from the average side.
What changes in the long run: the lease becomes avoidable. Fixed cost is fixed only for the contract period; for a decision about next year it is a variable cost, and the correct comparison is price against minimum long-run average cost. With price at ₹150 and AC around ₹193 on the four-machine set-up, the unit should either exit, or re-plan the plant - lease two machines instead of four, take on job-work for other units in the cluster, or find a buyer paying above ₹200. Closing now would be wrong, because the ₹1,20,000 is sunk for this year; closing at renewal is exactly right if the price does not recover.