Hiring and Shutdown at a Tiruppur Garment Unit
Arun owns a small garment unit in Tiruppur with two cutting machines and a monthly factory rent of ₹30,000, which is fixed under a one-year lease. He hires workers on monthly contracts at ₹4,000 each and can vary their number. The current market price of his standard shirt is ₹200, and he can sell all he produces at that price. His production record for the past six months, with capital fixed, is: 0 workers → 0 shirts; 1 → 30; 2 → 70; 3 → 105; 4 → 130; 5 → 145; 6 → 150. Arun is considering hiring a sixth worker because 'more output always means more sales revenue'. He is also worried because a buyer has offered a lower price of ₹110 per shirt for next month, and he must decide whether to operate or temporarily shut down. The lease cannot be cancelled, and workers can be laid off without penalty at one month's notice.
1. Compute marginal product and average product for each worker. Identify where diminishing returns set in and explain why the sixth worker's marginal product matters for the hiring decision.
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MP = change in TP; AP = TP/L.
| L | TP | MP | AP |
|---|---|---|---|
| 0 | 0 | - | - |
| 1 | 30 | 30 | 30.0 |
| 2 | 70 | 40 | 35.0 |
| 3 | 105 | 35 | 35.0 |
| 4 | 130 | 25 | 32.5 |
| 5 | 145 | 15 | 29.0 |
| 6 | 150 | 5 | 25.0 |
Diminishing returns set in after the second worker: MP rises from 30 to 40, then falls to 35, 25, 15 and 5. The sixth worker adds only 5 shirts, worth ₹1,000 at ₹200, but costs ₹4,000 in wages. The relevant comparison is marginal revenue product with marginal factor cost, not total output. Because MRP (₹1,000) is below the wage (₹4,000), hiring the sixth worker lowers profit even though total output rises. The law of variable proportions is operating because capital is fixed.
2. At a shirt price of ₹200, calculate total revenue, total cost and profit or loss at 4, 5 and 6 workers. Decide the profit-maximising labour input and whether Arun should hire the sixth worker.
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TFC = ₹30,000; TVC = ₹4,000 × L; TC = TFC + TVC; TR = ₹200 × TP.
At L = 4: TR = 200 × 130 = ₹26,000; TVC = ₹16,000; TC = ₹46,000; loss = ₹20,000. At L = 5: TR = 200 × 145 = ₹29,000; TVC = ₹20,000; TC = ₹50,000; loss = ₹21,000. At L = 6: TR = 200 × 150 = ₹30,000; TVC = ₹24,000; TC = ₹54,000; loss = ₹24,000.
The best of these is L = 4, with a loss of ₹20,000. Adding the fifth worker raises revenue by ₹3,000 but raises cost by ₹4,000, so profit falls by ₹1,000. The sixth is worse still. Arun should hire four workers, not six. Even though the sixth worker produces extra shirts, the extra wage exceeds the extra revenue. The lease cost is fixed and unavoidable in the short run, so it should not govern the hiring decision at the margin.
3. If the buyer's offer of ₹110 per shirt is the best available price next month, should Arun operate or temporarily shut down? Use the shutdown rule and show the relevant calculations.
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At a price of ₹110, compare price with minimum average variable cost. AVC at L = 4 is ₹16,000/130 ≈ ₹123.08; at L = 3 it is ₹12,000/105 ≈ ₹114.29; at L = 2 it is ₹8,000/70 ≈ ₹114.29. All available AVC values exceed ₹110, so price is below minimum AVC. If Arun operates at L = 4: TR = 110 × 130 = ₹14,300; TVC = ₹16,000; loss = TR − TVC − TFC = ₹14,300 − ₹16,000 − ₹30,000 = −₹31,700, i.e. a loss of ₹31,700. If he shuts down, he loses only TFC = ₹30,000. Shutting down is cheaper by ₹1,700. The shutdown rule is P < minimum AVC: produce only if revenue covers variable cost and contributes something to fixed cost. Here it does not. He should temporarily shut down, keep the lease, and resume when price rises above minimum AVC (about ₹114.29).