Six Tailors, Four Machines: Hiring Where MRP Meets the Wage
A garment unit in Bommanahalli, Bengaluru, has four sewing machines, one cutting table and a supervisor - all fixed in the short run. The owner hires tailors by the day at ₹2,000 each and sells every shirt at ₹300. Daily output is: 1 tailor → 10 shirts; 2 → 24; 3 → 39; 4 → 52; 5 → 60; 6 → 64; 7 → 64; 8 → 60, because tailors then wait for machines and crowd the cutting table. The owner is employing 6 tailors on the principle that 'more hands mean more shirts', and is losing money. A buyer offers a large order if daily output can be raised. Meanwhile the owner's cousin, quoting these shirt figures, argues that doubling the whole unit - eight machines, twice the tailors, a bigger shed - cannot possibly double output, because 'adding labour always yields less and less'.
1. Compute marginal product and average product for each tailor, identify the three stages of the law of variable proportions, and state which stage is the rational one to operate in.
Read the worked answer
MP (shirts per extra tailor): 10, 14, 15, 13, 8, 4, 0, −4. AP (shirts per tailor): 10, 12, 13, 13, 12, 10.7, 9.1, 7.5.
- Stage I: tailors 1–4. AP is rising and MP > AP; AP peaks at 4, where MP = AP (13 = 13).
- Stage II: tailors 4–7. AP is falling, MP is positive but below AP, and MP reaches zero at the 7th tailor (total product peaks at 64).
- Stage III: beyond 7. MP is negative and total product actually falls to 60.
A rational producer operates in Stage II. He will not stop in Stage I, because each additional tailor still raises average productivity; and he will never enter Stage III, because the 8th tailor adds output that is negative - he is paid ₹2,000 to destroy 4 shirts.
2. Using marginal revenue product, decide how many tailors the owner should employ, and quantify the daily error in employing 6 instead of the correct number.
Read the worked answer
MRP = MP × ₹300 per shirt: 3,000; 4,200; 4,500; 3,900; 2,400; 1,200; 0; −1,200.
The rule is to keep adding a tailor while MRP ≥ wage of ₹2,000:
- 5th tailor: MRP ₹2,400 ≥ ₹2,000 → hire.
- 6th tailor: MRP ₹1,200 < ₹2,000 → do not hire.
Profit-maximising employment is 5 tailors. The 6th adds only 4 shirts (₹1,200 of revenue) against a ₹2,000 wage, so each day the owner loses ₹800 net on that tailor alone. Total product is higher with 6 tailors than with 5, which is exactly why 'more hands mean more shirts' is the wrong test - the question is whether the extra shirts cover the extra wage, not whether output rises.
3. Explain the error in the cousin's argument about doubling the whole unit.
Read the worked answer
The cousin is reading a short-run law of returns to a variable factor as if it were a statement about returns to scale. The shirt figures hold capital fixed at four machines; diminishing marginal product appears because each extra tailor has less machinery and table space to work with. That says nothing about what happens when machines, shed, supervisor and tailors are all doubled.
Doubling every input is a long-run change of scale, which may show increasing returns to scale (specialisation, indivisible machinery), constant returns, or decreasing returns (management overload). The observed fall from 15 to 4 to 0 shirts per extra tailor is caused by the fixed factor - it is not evidence about scale at all.
The test the cousin needs is a different one: double all inputs and compare output with the doubled figure. His conclusion may even be right, but the data he quotes cannot establish it.