School Bag Unit Facing a Price Fall
A small unit in Jalandhar stitching school bags has a monthly fixed cost of ₹10,000 for rent and salaried supervision. Its variable cost schedule is: at 100 bags, ₹15,000; at 150 bags, ₹27,000; at 200 bags, ₹45,000; at 250 bags, ₹75,000. The wholesale market price of a bag is ₹200. The owner currently produces 150 bags but is losing money. A large retailer offers to buy any quantity at ₹200, but a competing supplier has begun selling imported bags, and the owner fears the price may fall to ₹140 next month. The unit cannot instantly change its fixed commitment, and shutting down would still leave the rent and supervision contracts to be paid for the month. The owner asks whether to raise output to 200 bags to “spread the fixed cost”, or to cut back, or to shut down temporarily.
1. Compute total cost, average variable cost and marginal cost at each output level. What law explains the pattern of marginal cost?
Read the worked answer
| Output | TVC (₹) | TC = TVC + 10,000 (₹) | AVC (₹) | MC (₹) |
|---|---|---|---|---|
| 100 | 15,000 | 25,000 | 150 | 150 (first 100 units) |
| 150 | 27,000 | 37,000 | 180 | (27,000−15,000)/50 = 240 |
| 200 | 45,000 | 55,000 | 225 | (45,000−27,000)/50 = 360 |
| 250 | 75,000 | 85,000 | 300 | (75,000−45,000)/50 = 600 |
Marginal cost rises sharply as output expands. This is the law of variable proportions: with fixed rent and supervision, adding more variable inputs eventually yields diminishing marginal returns, so extra bags cost progressively more.
2. At a price of ₹200, calculate profit or loss at each output and identify the loss-minimising output. Should the owner produce 200 bags to spread fixed cost? Explain.
Read the worked answer
Profit/loss = (₹200 × quantity) − TC:
- 100 bags: 20,000 − 25,000 = −₹5,000
- 150 bags: 30,000 − 37,000 = −₹7,000
- 200 bags: 40,000 − 55,000 = −₹15,000
- 250 bags: 50,000 − 85,000 = −₹35,000
The loss is smallest at 100 bags. Producing 200 bags to “spread fixed cost” is wrong because the marginal cost of the extra units (₹240 and ₹360) exceeds the price of ₹200. Each extra bag adds more to cost than to revenue. From 100 to 150 bags, revenue rises by ₹10,000 but cost rises by ₹12,000, so the loss worsens by ₹2,000. The owner should produce 100 bags, provided price covers average variable cost, which it does (₹200 > ₹150).
3. If the price falls to ₹140, should the unit shut down in the short run? What if the price is ₹160? Use the shutdown rule and calculate.
Read the worked answer
The short-run shutdown rule is: shut down if price falls below minimum average variable cost.
At ₹140: at 100 bags, TR = ₹14,000 and TC = ₹25,000, so loss = ₹11,000. Shutting down would leave the fixed cost of ₹10,000 as the loss. Since ₹11,000 > ₹10,000, producing is worse than shutting down. AVC at 100 bags is ₹150, which exceeds ₹140, so each bag fails to cover its variable cost. The unit should shut down temporarily.
At ₹160: at 100 bags, TR = ₹16,000, loss = ₹9,000. This is less than the shutdown loss of ₹10,000, and price exceeds AVC (₹160 > ₹150). The unit should continue at 100 bags. At 150 bags, the loss would be ₹13,000, so 100 bags remains the best choice.