The Bakery's Fifth Worker and the Shutdown Decision
A bakery has one fixed oven and hires workers by the day. The daily wage is ₹600. Cakes sell for ₹100 each, and the bakery can sell all it produces at that price. Fixed costs (oven, rent) are ₹800 a day. Output with successive workers is: 0 workers: 0 cakes; 1: 8; 2: 20; 3: 30; 4: 36; 5: 40; 6: 42. The owner currently employs 4 workers and is under pressure to hire a fifth because 'more workers always mean more output and more profit'. The bakery cannot change the oven in the short run. Workers are identical and each works the same day. The owner asks whether the fifth worker should be hired and whether the bakery should continue production at all if the cake price falls to ₹50.
1. Compute marginal product and marginal revenue product for each worker at a cake price of ₹100. Identify the profit-maximising number of workers and compare profit at 4 and 5 workers.
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Marginal product (MP) is the change in total product from adding one worker. Marginal revenue product (MRP) = MP × price = MP × ₹100.
| Workers | Total product | MP | MRP at ₹100 |
|---|---|---|---|
| 1 | 8 | 8 | ₹800 |
| 2 | 20 | 12 | ₹1,200 |
| 3 | 30 | 10 | ₹1,000 |
| 4 | 36 | 6 | ₹600 |
| 5 | 40 | 4 | ₹400 |
| 6 | 42 | 2 | ₹200 |
Hire workers as long as MRP is at least the wage of ₹600. The 4th worker's MRP is exactly ₹600, so 4 workers is the profit-maximising choice. The 5th worker's MRP is only ₹400, which is less than the ₹600 wage.
At 4 workers: revenue = 36 × ₹100 = ₹3,600; variable cost = 4 × ₹600 = ₹2,400; fixed cost = ₹800; profit = ₹400.
At 5 workers: revenue = 40 × ₹100 = ₹4,000; variable cost = 5 × ₹600 = ₹3,000; fixed cost = ₹800; profit = ₹200.
The fifth worker adds ₹400 of revenue but ₹600 of cost, so profit falls by ₹200. The owner should not hire the fifth worker on profit grounds.
2. The owner argues that the fifth worker still adds 4 cakes, so the worker must be profitable. Explain the error using marginal analysis and the stages of the law of variable proportions.
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The owner is looking at marginal product, not marginal profit. A positive MP means total output rises, but it does not mean the extra output is worth more than the extra cost. The correct comparison is MRP with the wage.
With one fixed oven, the bakery is subject to the law of variable proportions. MP rises at first, reaches a maximum at the 2nd worker, and then diminishes: 12, 10, 6, 4, 2. The 5th worker is in the stage of diminishing returns, where MP is positive but falling. That is still a rational stage to operate in, but not every worker in it is profitable. The bakery should stop hiring where MRP = wage. At the 5th worker, MRP = ₹400 < ₹600, so the worker reduces profit even though output rises.
The same logic explains why 'more output' is not the objective. The objective is profit, and the marginal worker must cover the marginal cost of hiring.
3. If the cake price falls to ₹50, recalculate the optimal number of workers conditional on producing. Should the bakery shut down in the short run? Use the fixed cost of ₹800.
Read the worked answer
At ₹50 per cake, MRP = MP × ₹50:
| Workers | MP | MRP at ₹50 |
|---|---|---|
| 1 | 8 | ₹400 |
| 2 | 12 | ₹600 |
| 3 | 10 | ₹500 |
| 4 | 6 | ₹300 |
| 5 | 4 | ₹200 |
| 6 | 2 | ₹100 |
Compare MRP with the ₹600 wage. The 1st worker gives ₹400 < ₹600; the 2nd gives ₹600 = ₹600; the 3rd gives ₹500 < ₹600. Conditional on producing, the bakery should employ 2 workers.
At 2 workers, output = 20 cakes. Revenue = 20 × ₹50 = ₹1,000. Variable cost = 2 × ₹600 = ₹1,200. Contribution = ₹1,000 − ₹1,200 = −₹200. With fixed cost of ₹800, total loss = −₹1,000.
If the bakery shuts down, it avoids variable cost but still pays fixed cost, so loss = ₹800. Since ₹1,000 > ₹800, producing at 2 workers is worse than shutting down. On the profit criterion, the bakery should shut down in the short run. It should reopen only if the price recovers enough for revenue to cover variable cost and make a positive contribution.