Buttons at ₹40: Output, Loss and the Shutdown Decision
A small firm in the garment-buttons trade of a Karnataka industrial estate sells at the ruling market price of ₹40 per unit. More than 200 identical firms sell the same product, and no single firm can move the price. The firm's total cost schedule (₹ per day) is: 0 units → 60; 1 → 110; 2 → 140; 3 → 165; 4 → 205; 5 → 260; 6 → 340. Of the ₹60 fixed cost, ₹40 is a machine lease that cannot be cancelled this month and ₹20 is insurance. The manager is currently producing 5 units a day, arguing that 'more output spreads the fixed cost over more units'. A trade journal forecasts that falling export demand may pull the market price down to ₹32 next month, and the manager wants to know whether to keep the machines running or lock the shed.
1. Compute marginal cost at each output, find the profit-maximising output at ₹40, and show the profit or loss.
Read the worked answer
MC = change in TC: 1st unit 50, 2nd 30, 3rd 25, 4th 40, 5th 55, 6th 80.
Under perfect competition P = MR = ₹40 and the firm cannot influence price, so it produces where MR = MC (MC rising through the price): at 4 units MC = ₹40 = MR, while the 5th unit would cost ₹55 to make and fetch ₹40.
- TR = 4 × 40 = ₹160
- TC = ₹205
- Loss = ₹45
The firm is making a loss, but at 4 units TR ₹160 exceeds TVC ₹145, so ₹15 of fixed cost is being covered. Compare the alternatives: at the manager's 5 units, TR = ₹200 and TC = ₹260, loss = ₹60, exactly the whole fixed cost - the 5th unit adds ₹40 of revenue for ₹55 of cost and destroys the ₹15 contribution. Choosing output by 'spreading fixed cost' throws that contribution away.
2. Should the firm produce or shut down if the price falls to ₹32? Show the shutdown test using average variable cost.
Read the worked answer
TVC = TC − 60: 50, 80, 105, 145, 200, 280. AVC: 50, 40, 35, 36.25, 40, 46.7. Minimum AVC = ₹35 at 3 units.
At P = ₹32, produce where MC is closest below the price: MC is ₹30 at 2 units, ₹40 at 3 units and ₹25 at 3 units? Checking in order - MC of the 1st = 50, 2nd = 30, 3rd = 25, 4th = 40. Price ₹32 lies below MC of the 3rd (₹40) but above ₹30, so the best the firm can do is 2 units: TR = ₹64, TVC = ₹80, so the firm does not even cover its variable cost.
Shutdown test: P = ₹32 < minimum AVC = ₹35, so every unit sold adds to the loss. Producing 2 units loses ₹140 − ₹64 = ₹76; shutting down loses only the fixed cost of ₹60. Shut down (and do not renew the machine lease when it expires). The rule: operate in the short run only if price ≥ minimum AVC.
3. Explain the long-run adjustment if the price stays at ₹32, and correct the manager's reasoning about fixed cost.
Read the worked answer
At ₹32, price is below minimum AVC and so far below average total cost that every firm in the trade is losing. In the long run the ₹40 machine lease is avoidable, so firms exit; the market supply curve shifts left; the price rises until the remaining firms earn only normal profit, at the minimum of long-run average cost. The firm's long-run output is at minimum LAC, not at the short-run MR = MC point, and the number of firms is smaller.
The manager's error is a confusion between average and marginal. Spreading fixed cost over more units does lower AFC, but AFC is not a decision variable: the fixed cost is the same whether output is 4 or 5, so it cannot justify the 5th unit. Output is chosen by comparing the extra cost of a unit with the extra revenue it brings. Here the extra unit costs ₹55 and earns ₹40 - the fact that it also lowers average fixed cost is irrelevant.