The Cuttack Furniture Unit: Shut Down or Sell at ₹470?
A furniture unit near Cuttack employs five carpenters and rents a shed for ₹40,000 a month; the salaries of a supervisor and a clerk add ₹20,000, so total fixed cost is ₹60,000 a month. Each chair sells for ₹600. At the present output of 300 chairs a month, total variable cost - wood, varnish, wages and power - is ₹1,50,000. The owner is considering hiring a sixth carpenter at ₹9,000 a month; output is expected to rise to only 320 chairs, because the shed and machines are already fully used and the extra worker will often wait for the saw. A large retailer has offered to buy any number of chairs at ₹470 each, well below the present price; the owner is tempted to close the unit for a few months instead of selling at such a low price, but the five carpenters are trained and hard to replace.
1. Calculate total cost, average fixed cost, average variable cost and average total cost at 300 chairs, and the monthly profit or loss at ₹600. Should the owner accept the retailer's offer of ₹470? Show your reasoning.
Read the worked answer
| Item | Calculation | Value |
|---|---|---|
| TFC | 40,000 + 20,000 | ₹60,000 |
| TVC | given | ₹1,50,000 |
| TC | TFC + TVC | ₹2,10,000 |
| AFC | 60,000 ÷ 300 | ₹200 |
| AVC | 1,50,000 ÷ 300 | ₹500 |
| AC | 2,10,000 ÷ 300 | ₹700 |
| TR at ₹600 | 300 × 600 | ₹1,80,000 |
| Profit/loss | 1,80,000 − 2,10,000 | loss of ₹30,000 |
The ₹470 offer. The shut-down rule compares price with average variable cost, not with average total cost. At ₹470, P < AVC (₹500): every chair sold brings in ₹470 but adds ₹500 of variable cost, so each sale widens the loss by ₹30. Producing 300 chairs at ₹470 gives TR ₹1,41,000 against TVC ₹1,50,000 - a loss of ₹69,000 including fixed cost, against a loss of only ₹60,000 (the fixed cost) if the unit closes.
Decision: reject the offer and suspend production rather than sell at ₹470, provided the shut-down is genuinely short and the carpenters can be recalled. That proviso matters: if closing destroys the trained team or the retail goodwill, the owner is comparing a money loss with a future-capability loss. The extra-unit version is the same: since AVC is already ₹500 and rising, extra chairs at ₹470 do not pay either.
2. Evaluate the proposal to hire the sixth carpenter. Use marginal product, marginal cost and marginal revenue, and state the general rule the owner should follow in adding workers.
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Step 1 - marginal product. MP of the sixth carpenter = 320 − 300 = 20 chairs a month.
Step 2 - marginal cost of those chairs. MC = extra wage ÷ extra output = ₹9,000 ÷ 20 = ₹450 per chair, because the shed and machines are fixed and only labour is added.
Step 3 - compare with marginal revenue. MR = price = ₹600. Since MR (₹600) > MC (₹450), the 20 extra chairs add 20 × ₹600 = ₹12,000 to revenue and ₹9,000 to cost, improving the result by ₹3,000 a month.
Check with averages. New TC = 2,10,000 + 9,000 = ₹2,19,000; new AC = 2,19,000 ÷ 320 = ₹684.4 (down from ₹700); new loss = ₹1,92,000 − ₹2,19,000 = ₹27,000, against ₹30,000 before. Hiring helps, but the unit still makes a loss.
General rule. Hire while MP ≥ wage ÷ price. Here the threshold is 9,000 ÷ 600 = 15 chairs. Because the shed and machines are fixed, the law of variable proportions implies the seventh worker's MP will be lower and MC higher; stop when MC reaches ₹600.
3. Calculate the break-even quantity at the present price of ₹600. Given that the unit now makes 300 chairs, suggest two realistic ways of reaching break-even and comment on each.
Read the worked answer
Break-even means TR = TC, i.e. P × Q = TFC + AVC × Q, or Q = TFC ÷ (P − AVC). Contribution per chair = ₹600 − ₹500 = ₹100. Break-even Q = 60,000 ÷ 100 = 600 chairs a month - exactly double the present output.
Route 1 - cut fixed cost. Halving rent-plus-salaries to ₹30,000 (share the shed, drop the clerk, move to a smaller premises) gives Q = 30,000 ÷ 100 = 300 chairs, i.e. break-even at present output. This is arithmetically clean but may reduce capacity and supervision.
Route 2 - raise the price. To break even at 300 chairs, price must equal AC, i.e. ₹700 (a rise of ₹100, about 17%). But at a higher price quantity sold will fall, since chairs sold in a competitive local market have close substitutes; the unit may end up at a lower point on its demand curve, so this route needs a demand estimate, not just a cost calculation.
Route 3 (worth stating). Reduce AVC - bulk timber purchase, less wastage, better jigs. A ₹20 cut in AVC raises contribution to ₹120 and lowers break-even to 500 chairs. The ₹470 offer, by contrast, reduces contribution below zero and cannot help break-even at all.