A Fifth Worker at a Coir Rope Unit
A coir rope unit near Pollachi runs a single motorised spinning machine in a rented shed. The rent is ₹1,500 a day, fixed by an annual agreement. Coir fibre costs ₹6 for every kilogram of rope produced, and rope sells at ₹16 a kilogram in a wholesale market where this unit is one of many sellers. With four workers at ₹400 a day each, the unit produces 240 kg a day. The owner, who is deciding next month's staffing, has collected these output estimates: a fifth worker would raise output to 275 kg, a sixth to 300 kg, and a seventh to 310 kg. Meanwhile the shed owner has given notice that the rent will rise to ₹1,800 a day from next month. The accountant says the firm is already making a loss and should consider closing; the owner believes that as long as each kilogram earns something above the fibre cost, more workers can only help.
1. Calculate the marginal product and average product of labour from four to seven workers, and identify the stage of the law of variable proportions in which the unit is operating.
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| Workers (L) | Total product (kg) | Marginal product (kg) | Average product (kg) |
|---|---|---|---|
| 4 | 240 | - | 60.0 |
| 5 | 275 | 35 | 55.0 |
| 6 | 300 | 25 | 50.0 |
| 7 | 310 | 10 | 44.3 |
MP = change in total product from one more worker; AP = total product ÷ number of workers.
Reading the table. From the fifth worker onward both MP and AP fall (35 → 25 → 10 and 60 → 55 → 50 → 44.3), and MP lies below AP throughout, which is why AP is falling. MP is still positive, so total product still rises, but at a diminishing rate.
Stage identification. This is Stage II - the stage of diminishing returns. Stage I ends where AP is at its maximum (at four workers, where MP would equal AP); Stage III begins where MP turns negative, which is not reached even at seven workers. A rational producer operates in Stage II: output per worker is falling but the extra worker still adds something. The important point for the owner is that diminishing marginal product is not the same as negative marginal product - Stage II is still a sensible place to operate, but the question is how far into it to go.
2. Should the owner have hired the fifth worker? Use marginal reasoning, and separately state whether the unit should shut down.
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The hiring decision (marginal reasoning)
Each kilogram earns ₹16 and uses ₹6 of fibre, so the net contribution of a kilogram is ₹10. The marginal revenue product of a worker is therefore MP × ₹10.
- MRP of the 5th worker = 35 × ₹10 = ₹350; wage = ₹400
- MRP < wage by ₹50 a day → the fifth worker reduces profit.
Rule: hire additional units of a factor while MRP ≥ factor price, and stop before MRP < factor price. So on the estimates given, four workers - not five - is the profit-maximising level.
Check by totals
- 4 workers: revenue 240 × 16 = ₹3,840; fibre 240 × 6 = ₹1,440; wages ₹1,600; rent ₹1,500; total cost ₹4,540; loss ₹700
- 5 workers: revenue 275 × 16 = ₹4,400; fibre ₹1,650; wages ₹2,000; rent ₹1,500; total cost ₹5,150; loss ₹750
The two calculations agree. The owner's intuition - "anything above fibre cost helps" - is right about the shutdown question but wrong about the hiring question; the wage has to be covered too.
Shutdown decision
AVC at five workers = (1,650 + 2,000) ÷ 275 = ₹13.27, which is below the price of ₹16. The unit covers its variable costs and contributes about ₹2.73 per kg, in total ₹750, towards rent. So it should continue producing in the short run, even though it makes a loss, because shutting down would cost the full ₹1,500 rent.
3. The rent rises to ₹1,800 a day. Explain whether this changes (a) the number of workers to be employed and (b) the decision to continue production.
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Rent is a fixed cost - it does not vary with output and therefore does not enter marginal cost.
(a) Hiring decision: unchanged. The MRP of the fifth worker (35 × ₹10 = ₹350) and the wage (₹400) are both untouched by rent. The comparison MRP vs wage is therefore unchanged, and four workers remain the right number.
(b) Shutdown decision: also unchanged in the short run. The shutdown rule compares price with average variable cost, and AVC contains only fibre and wages. At P = ₹16 and AVC = ₹13.27 the unit still covers variable cost and makes a positive contribution to fixed cost, so it keeps producing.
What does change is profit.
- With 4 workers: total cost rises from ₹4,540 to ₹4,840; loss rises from ₹700 to ₹1,000.
- With 5 workers: loss rises from ₹750 to ₹1,050.
The long-run point. Average cost at four workers with the higher rent = 4,840 ÷ 240 = ₹20.17, far above the price of ₹16. Because price does not cover average cost, the unit cannot survive in the long run and exit becomes the rational response once the rent agreement expires. The general principle to state in the answer: fixed costs affect the size of profit and the long-run entry/exit decision, but not short-run output and employment, which depend on marginal and variable costs only.