Bicycle-Chain Maker Facing a Loss: Shutdown Point and the MR = MC Rule
A small firm in Ludhiana makes bicycle chains and sells in a perfectly competitive market where the ruling price is ₹190 per chain. Its total fixed cost is ₹300 per day - the rent on a small shed plus a licence fee - and this payment cannot be avoided in the short run. The accountant supplies the following daily total variable costs: 0 units, ₹0; 1 unit, ₹200; 2 units, ₹360; 3 units, ₹480; 4 units, ₹620; 5 units, ₹800; 6 units, ₹1,020. Output cannot be split into fractions and the firm carries no inventory. The owner has read that 'a competitive firm should shut down when it makes a loss' and is ready to close the shed. The bank that lent to the firm wants an assessment of whether closing now is the right decision, and at what price closing would become unavoidable.
1. Construct the total cost, marginal cost and average variable cost schedules for outputs 1 to 6. Find the profit-maximising output at the price of ₹190 and state the resulting profit or loss.
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Schedules (₹ per day).
| Q | TVC | TC = TVC + 300 | MC (ΔTC) | AVC |
|---|---|---|---|---|
| 0 | 0 | 300 | - | - |
| 1 | 200 | 500 | 200 | 200 |
| 2 | 360 | 660 | 160 | 180 |
| 3 | 480 | 780 | 120 | 160 |
| 4 | 620 | 920 | 140 | 155 |
| 5 | 800 | 1100 | 180 | 160 |
| 6 | 1020 | 1320 | 220 | 170 |
Optimum. In perfect competition MR = price = ₹190. Expand while the marginal cost of the next unit is below ₹190: the 5th unit costs ₹180 (< 190), so it is worth producing; the 6th costs ₹220 (> 190), so it is not. Output = 5 units.
Result. TR = 5 × 190 = ₹950; TC = ₹1,100; loss = ₹150 per day.
Check against neighbours: at Q = 4, loss = 920 − 760 = ₹160; at Q = 6, loss = 1,320 − 1,140 = ₹180. Q = 5 is the least-loss output, confirming the MR = MC result.
2. Should the firm close the shed? Justify your answer using total revenue and total variable cost, not the fact that a loss is being made.
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No - it should keep producing in the short run.
The correct comparison is not profit versus zero but loss if it operates versus loss if it shuts down. Fixed cost of ₹300 is unavoidable either way, so closing the shed means losing exactly the whole of it: loss = ₹300.
Producing 5 units gives a loss of ₹150, which is ₹150 smaller. The reason: TR = ₹950 exceeds TVC = ₹800. All variable costs are covered and ₹150 is left over as a contribution towards the ₹300 of fixed cost. Equivalently, price ₹190 exceeds AVC ₹160 at Q = 5.
The owner's rule of thumb wrongly treats any loss as a signal to exit. A loss is a signal to exit only when the firm cannot cover even its variable costs - that is, when price falls below minimum AVC. Here every rupee of revenue above AVC reduces the unavoidable fixed-cost loss. The decision should be revisited in the long run, when the shed lease can be renegotiated and the fixed cost becomes avoidable.
3. At what price would the firm actually shut down, and why must marginal cost be rising at the chosen output rather than falling?
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Shutdown price. The firm exits when price falls below the minimum of AVC, because below that point operating adds to the loss rather than reducing it. From the schedule, AVC is minimised at Q = 4, where AVC = 620/4 = ₹155. So:
- Price ≥ ₹155: produce where MR = MC; loss is smaller than ₹300.
- Price < ₹155: shut down and lose only the ₹300 fixed cost.
Between ₹155 and the minimum of ATC the firm still operates at a loss; the shutdown point is the AVC minimum, not the break-even point.
Why MC must be rising. The optimum occurs where MC cuts MR(=price) from below. If MC were falling at the chosen output, the next unit could be produced more cheaply than the last one and at a cost below the price, so expanding output would add to profit - the firm could not be at an optimum. Hence only the rising portion of MC above minimum AVC is the firm's short-run supply curve; with a horizontal price line, the falling stretch could never satisfy MR = MC from below.