The Coffee Roaster: A Supermarket Contract Below Average Cost
A regional coffee roaster sells 18,000 kg a month at £14.00/kg. Monthly fixed costs are £54,000, so average fixed cost is £3.00/kg. Average variable cost is £9.20/kg, made up of £6.00 green beans, £1.80 packaging and £1.40 direct labour; total average cost is therefore £12.20/kg. A supermarket chain offers a contract for an additional 4,000 kg a month at £10.50/kg, but only if that price applies to all 5,500 kg it would then buy, including the 1,500 kg it currently buys at £14.00. The extra volume requires a second shift, which would add £8,000 a month in fixed cost and raise direct labour per kg by 15% on the contract volumes because of overtime premia. The owner's accountant advises rejection because £10.50 is below the £12.20 total average cost. Separately, the owner is considering a 5% price rise on the retail range, where demand elasticity is estimated at −1.1.
1. Should the roaster accept the supermarket contract? Show the incremental calculation, then state what the accountant has got wrong and what other factors should enter the decision.
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Incremental analysis. Only the change in revenue and the change in cost matter; existing fixed costs are sunk.
- Additional revenue: 4,000 kg × £10.50 = £42,000
- Revenue given up on the 1,500 kg the chain already buys: 1,500 × (£14.00 − £10.50) = £5,250
- Revised variable cost per kg on contract volume: £6.00 + £1.80 + (£1.40 × 1.15 = £1.61) = £9.41
- Variable cost of 4,000 kg: £37,640
- Extra fixed cost: £8,000
Net effect = 42,000 − 5,250 − 37,640 − 8,000 = −£8,890 per month.
The deal destroys value. Break-even would need the new volume to contribute £13,250 at a margin of £1.09/kg, i.e. about 12,150 kg, roughly three times the volume on offer. Even ignoring the cannibalisation of the existing 1,500 kg, the second-shift fixed cost alone exceeds the contribution, so the answer does not hinge on the disputed allocation.
The accountant's error is comparing price with total average cost, which loads £3.00/kg of existing fixed cost onto incremental units. The correct short-run rule is that extra units are worth producing when price exceeds the incremental cost they cause - here £9.41, plus the step cost of the shift.
Other factors. Whether the overtime premium can be avoided by hiring; whether the £8,000 roaster has an alternative use or could serve retail growth too; whether the chain would delist the 1,500 kg if refused; the strategic risk of a two-tier price list inviting renegotiation from other customers; and whether the contract builds capability or volume-based purchasing discounts on green beans.
2. Evaluate the proposed 5% price rise using the elasticity estimate, and explain why a revenue calculation and a profit calculation can point in different directions.
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Revenue view. With elasticity −1.1, a 5% rise cuts volume by roughly 1.1 × 5% = 5.5%, from 18,000 to 17,010 kg. Revenue moves from 18,000 × £14.00 = £252,000 to 17,010 × £14.70 = £250,047, a fall of about £1,950. Demand is elastic, so a price rise reduces revenue - this is the argument against the rise.
Profit view. What matters is the contribution margin, not revenue. Current margin is £14.00 − £9.20 = £4.80/kg, giving contribution of 18,000 × 4.80 = £86,400. After the rise the margin is £14.70 − £9.20 = £5.50/kg, giving 17,010 × 5.50 = £93,555. Contribution rises by about £7,155, and with fixed costs unchanged, profit rises by the same amount.
The two views diverge because revenue ignores the £9.20 of variable cost that is avoided on the 990 kg no longer sold. The general rule: with constant marginal cost, raising price adds profit whenever the current markup (P − MC)/P exceeds 1/|e|. Here the markup is 4.80/14.00 = 34%, while 1/1.1 = 91%, so price is well below the profit-maximising level.
Caution. Applying a constant-elasticity formula mechanically implies an optimal price of 9.20/(1 − 1/1.1) ≈ £101/kg, which is absurd - a sign that the elasticity is not constant over such a large price change. The estimate is also a retail average and may not hold for the supermarket channel, and rival roasters' reactions are ignored. The defensible conclusion is that a modest rise is likely to raise profit, and that the firm should test it in stages rather than extrapolate.
3. The landlord raises the rent by £12,000 a month. Explain the effect on price, output and the shutdown decision in the short run and the long run, and say whether this changes the answer to the contract question.
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Short run. Rent is a fixed cost: it does not vary with output, so it does not enter marginal cost. The profit-maximising price and output are unchanged, because the firm still sets marginal revenue equal to marginal cost. What changes is profit: it falls by £12,000 a month. On the current retail business, contribution is £86,400 and fixed costs rise from £54,000 to £66,000, so profit falls from £32,400 to £20,400.
Shutdown rule. The firm should keep producing as long as price covers average variable cost and the business covers its avoidable fixed costs. At £14.00 against AVC of £9.20 there is no question of shutting down; the relevant question is whether the lease should be renewed.
Long run. All costs are variable. If the rent rise is permanent and cannot be passed on, the firm will exit when the lease expires unless the market price rises to cover the new average cost. In a competitive market, exits reduce supply, price rises, and a new zero-rent equilibrium is reached at a smaller number of larger roasters. The firm's own long-run price must cover 54,000 + 12,000 = £66,000 of fixed cost per month, i.e. average cost of £12.87/kg at 18,000 kg.
Effect on the contract decision. It makes acceptance more attractive relative to rejection, because any contribution towards overheads is now worth more - the firm has £12,000 more fixed cost to cover. But it does not make this contract worthwhile: the deal still yields −£8,890, i.e. negative contribution after its own step cost, so it fails the basic test of covering the costs it causes. The rent would have to fall by more than £12,000 to change the sign, which is not on the table.