Difficulty: Intermediate | Prerequisites: Basic cost concepts (fixed vs variable), profit calculation
When a firm has idle capacity, it may consider forward integration: making a finished product instead of selling components. The decision hinges on whether revenue from the new product exceeds variable costs, then whether total contribution covers the new fixed costs, and finally whether the opportunity cost of diverting inputs from their best alternative use makes the whole venture uneconomic. Variable-cost profit alone can be misleading if you ignore what you are giving up.
Variable cost (VC)
A cost that changes with the level of output. If you produce zero units, variable costs are zero. In simple terms, these are the per-unit costs that rise as you make more.
Fixed cost (FC)
A cost that does not change with the level of output, at least within the relevant range. Rent on a factory is a fixed cost whether you produce one unit or a million. Think of it as the cost of keeping the lights on regardless of how busy you are.
Explicit cost
A direct, out-of-pocket payment. You write a cheque, you transfer money. Labour wages and raw material purchases are explicit costs.
Implicit cost (opportunity cost of owned resources)
The value of the next-best alternative you forgo when you use a resource in a particular way. No money changes hands, but the cost is real. If you could sell a microchip for $55 but instead use it in your own product, the $55 forgone revenue is an implicit cost.
Sunk cost
A cost that has already been incurred and cannot be recovered regardless of any future decision. In this problem set, the plant lease and interest on the working-capital loan are treated as sunk once committed. Sunk costs should not influence forward-looking decisions, but students often include them where they should not.
Economic cost
The full cost of a decision, combining sunk costs, explicit costs, and implicit costs. Economic cost = Sunk + Explicit + Implicit.
Forward integration
A business strategy where a firm moves "downstream" in the supply chain, producing a finished product rather than just selling components to other manufacturers. Microchip-X considering making control devices instead of only selling chips is forward integration.
Idle capacity
Productive resources (machines, workers, factory space) that are available but not currently being used. Idle capacity creates a temptation to forward-integrate because the variable cost of using those resources appears to be low.
Microchip-X produces microchips at $30 each and sells them for $55 to high-tech manufacturers. Capacity: 1 million chips per year. A strike at its customers' factories drops outside orders to 800,000, leaving 200,000 chips of idle capacity.
The firm considers using those spare chips to build electronic control devices, each requiring two microchips plus $50 in additional labour. A new plant lease costs $2 million per year and a $20 million working-capital loan carries 5% annual interest. Each control device sells for $150.
Revenue per control device: $150
Variable cost per device: 2 microchips at $30 each ($60) + $50 labour = $110
Contribution margin per device: $150 - $110 = $40
This $40 is the profit per unit if you consider only costs that vary with output. It does not include fixed costs or opportunity costs.
200,000 spare chips make 100,000 control devices (two chips each).
Total contribution from devices: 100,000 x $40 = $4,000,000
New fixed costs:
Plant lease: $2,000,000
Interest on loan (5% of $20,000,000): $1,000,000
Total new fixed costs: $3,000,000
Net profit from the new line: $4,000,000 - $3,000,000 = $1,000,000
The answer is yes. The contribution margin exceeds the additional fixed costs by $1 million, so the new product line is worth opening to absorb the idle capacity.
Once the idle chips are used up, every additional control device requires diverting two microchips that could have been sold externally at $55 each. The calculation changes because opportunity cost enters.
Implicit cost of diverting 2 chips: 2 x $55 = $110 (forgone revenue from outside sales)
Explicit cost of additional labour: $50
Economic cost per additional device: $110 (implicit) + $50 (explicit) = $160
Revenue per device: $150
Loss per additional device: $150 - $160 = -$10
The economic cost ($160) exceeds revenue ($150). Microchip-X should not decline any outside orders to produce more control devices. The variable-cost profit of $40 per device was misleading here because it ignored the opportunity cost of diverting chips from a profitable outside sale.
The crucial shift between Step 2 and Step 3 is the opportunity cost of the microchips. Idle chips have zero opportunity cost (they were going unsold anyway), so using them in-house is free at the margin. Chips that have outside buyers carry an opportunity cost equal to the sale price. The same physical input has a different economic cost depending on its next-best use.
Contribution margin per unit
Revenue per unit - Variable cost per unit = Contribution margin
$150 - ($30 x 2 + $50) = $150 - $110 = $40
Net profit from new product line (using idle capacity)
(Units produced x Contribution margin) - Additional fixed costs = Net profit
(100,000 x $40) - $3,000,000 = $1,000,000
Economic cost (full cost including opportunity cost)
Economic cost = Sunk cost + Explicit cost + Implicit cost
= ($2,000,000 + $1,000,000) + $50 + $110 = $160 per additional device (beyond idle capacity)
Decision rule
Produce if Revenue per unit > Economic cost per unit. Here $150 < $160, so do not divert chips from outside sales.
This is the logic behind "make or buy" decisions across industries. An automotive company with spare factory capacity might start producing a component it previously outsourced, but only if the opportunity cost of using that capacity is lower than the revenue the new product generates. Oil companies deciding whether to refine crude themselves or sell it to refiners face the same trade-off.
Students often use the production cost of the microchip ($30) as the opportunity cost when chips have outside buyers. The opportunity cost is the sale price ($55), not the production cost. The $30 is already spent either way.
Some students include sunk costs (the plant lease, the interest) in the per-unit cost calculation when deciding whether to divert chips. Sunk costs are already committed and do not change with the decision to produce one more device.
A common error is concluding that forward integration is always profitable just because the contribution margin per unit is positive. A positive margin means nothing if total contribution does not cover the additional fixed costs.
Students sometimes forget that opportunity cost is zero for idle resources. The whole point of idle capacity is that the resource has no alternative use, so there is nothing to forgo.
The distinction between variable-cost profit and economic profit is a staple exam topic. Expect a question where the per-unit margin looks attractive but the full economic cost (including opportunity cost) makes the venture unprofitable.
Be ready to calculate opportunity cost as forgone revenue, not forgone profit. The opportunity cost of a chip sold at $55 is $55, not $55 - $30 = $25.
"Should the firm decline outside orders?" is a classic follow-up. The answer hinges entirely on whether economic cost exceeds revenue.
Fixed costs matter for the "should we open the line at all" question but not for the "should we produce one more unit" question once the line is open.
True or false: The opportunity cost of using an idle microchip is $30 (its production cost). ___
Fill in the blank: Economic cost = ___ + Explicit cost + ___ cost.
True or false: If contribution margin per unit is positive, the firm should always open the new product line. ___
Fill in the blank: When a chip can be sold externally for $55, the implicit cost of using it in-house is $___ per chip.
True or false: Sunk costs should influence whether to produce one additional unit. ___
Answers: 1. False (it is zero, the chip has no alternative use). 2. Sunk; Implicit. 3. False (total contribution must also exceed additional fixed costs). 4. $55. 5. False.
Q: A firm produces widgets at $20 each and sells them for $45. It has 50,000 units of idle capacity. It could use two widgets to make a gadget that sells for $100, with $15 in additional labour per gadget. What is the variable-cost profit per gadget?
A: Revenue $100 - Variable cost (2 x $20 + $15 = $55) = $45 per gadget.
Q: In the question above, if the firm must lease new space at $500,000/year to produce gadgets, should it go ahead? It can make 25,000 gadgets.
A: Total contribution = 25,000 x $45 = $1,125,000. Fixed cost = $500,000. Net profit = $625,000. Yes, it should proceed.
Q: Continuing the same scenario, suppose the firm can now sell all its widgets externally at $45 each. What is the economic cost of producing one additional gadget beyond idle capacity?
A: Implicit cost (2 x $45 = $90 forgone widget revenue) + Explicit cost ($15 labour) = $105 economic cost per gadget. Since $105 > $100 revenue, the firm should not divert widgets from outside sales.
Q: Why is the opportunity cost of an idle resource zero?
A: An idle resource has no alternative use generating revenue. There is nothing to forgo by putting it to work, so its opportunity cost is zero.
Q: A firm's per-unit contribution margin is $8 and it can produce 10,000 units with idle capacity. Additional fixed costs for the line are $100,000. Should it proceed?
A: Total contribution = 10,000 x $8 = $80,000. This is less than the $100,000 in fixed costs. Net loss = $20,000. The firm should not proceed despite the positive per-unit margin.
This connects to consumer and producer surplus because the same cost concepts (variable, fixed, opportunity) determine where supply curves sit and therefore how surplus is distributed. It also connects to pricing strategy under market power: if Microchip-X had pricing power over the control device, the profit-maximisation problem would shift from a simple cost comparison to setting MR = MC, as explored in Problems 3 and 4 of this set.
forward integration, vertical integration, make or buy decision, opportunity cost, implicit cost, explicit cost, sunk cost, economic cost, variable cost, fixed cost, idle capacity, contribution margin, marginal analysis, cost-benefit analysis, ECON 101, microeconomics, firms and markets, NYU