Coir Pith Unit in Alappuzha: When to Shut Down
A small coir pith block unit in Alappuzha sells its output in a wholesale market where many identical units compete and no single seller can influence the price. The prevailing market price is ₹60 per block. The unit's total fixed cost is ₹100 per day. Its total cost at different daily outputs is: 0 blocks ₹100; 1 block ₹160; 2 blocks ₹210; 3 blocks ₹255; 4 blocks ₹310; 5 blocks ₹380; 6 blocks ₹470. The owner currently produces 5 blocks because 'more output means more sales'. A neighbouring unit has already stopped production, and the owner wonders whether to continue. The owner has no debt and can restart easily. The local industries officer asks for a short-run analysis of profit, loss and the shutdown decision, and wants to know what would happen if the market price fell to ₹48.
1. Prepare a table showing TFC, TVC, MC, TR and profit at each output. Identify the profit-maximising output and the profit or loss at that output.
Read the worked answer
TFC is ₹100 at every output; TVC = TC − TFC; MC = change in TC; TR = ₹60 × Q; profit = TR − TC.
| Q | TC | TFC | TVC | MC | TR | Profit |
|---|---|---|---|---|---|---|
| 0 | 100 | 100 | 0 | - | 0 | −100 |
| 1 | 160 | 100 | 60 | 60 | 60 | −100 |
| 2 | 210 | 100 | 110 | 50 | 120 | −90 |
| 3 | 255 | 100 | 155 | 45 | 180 | −75 |
| 4 | 310 | 100 | 210 | 55 | 240 | −70 |
| 5 | 380 | 100 | 280 | 70 | 300 | −80 |
| 6 | 470 | 100 | 370 | 90 | 360 | −110 |
The firm is a price taker, so MR = P = ₹60. Profit is maximised where MC is closest to MR from below, provided the firm covers variable cost. MC is ₹55 at Q = 4 and ₹70 at Q = 5, so the best output is 4 blocks. At Q = 4, TR = ₹240 and TC = ₹310, giving a loss of ₹70. Producing 5 blocks would give a loss of ₹80, so the owner's current output is not the best choice.
2. Find the shutdown price. Should the owner continue producing at ₹60? What should the owner do if the market price falls to ₹48?
Read the worked answer
AVC = TVC / Q:
| Q | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| AVC | 60.00 | 55.00 | 51.67 | 52.50 | 56.00 | 61.67 |
Minimum AVC is about ₹51.67 at Q = 3, so the shutdown price is approximately ₹51.67. At a price of ₹60, the firm should continue in the short run because 60 > 51.67 and the loss at the best output (₹70) is less than TFC (₹100). Shutting down immediately would give a loss of ₹100, which is worse.
At a price of ₹48, the price is below minimum AVC. Operating at Q = 3 gives TR = ₹144 and TVC = ₹155, a loss of ₹111 before fixed cost, which is worse than the ₹100 fixed-cost loss from shutting down. The owner should stop production in the short run and lose only TFC. The owner should restart only if the price rises above minimum AVC.
3. Explain why this firm's short-run supply curve is its MC curve above minimum AVC, and how the market supply curve is obtained from individual firms.
Read the worked answer
For any price above minimum AVC, the firm chooses output where P = MC and MC is rising. If price rises, the intersection with MC moves to a higher output, so the quantity supplied increases. If price falls below minimum AVC, the firm supplies zero because it cannot cover even variable costs. Therefore the individual firm's short-run supply curve is the rising part of its MC curve above minimum AVC, with zero supply below that price.
The market supply curve is the horizontal sum of the individual firms' supply curves: at each price, add the quantities supplied by all active firms. In the short run the number of firms is fixed. In the long run, positive profits attract entry and losses cause exit, shifting market supply and pushing price toward minimum long-run average cost. This is why the coir pith market price tends to be outside any single unit's control.