What it means
A producer cannot use the same scarce labour, machines and land for two purposes at once. A production possibilities frontier, or PPF, shows the combinations of two outputs feasible with current resources and technology.
Moving along that frontier means producing more of one output and less of the other, and MRT measures the local output trade-off. Suppose a factory can increase production of desks by ten if it gives up twenty chairs.
Around that operating point, its MRT is two chairs per desk. A different point may have a different rate because the people and tools best suited to desks are used first, so as desk production expands the factory may divert resources better suited to chairs, raising the number of chairs sacrificed for each additional desk.
OpenStax presents the slope of the production possibilities frontier as the opportunity cost of increasing one output, and economists call the local slope's magnitude the MRT. The frontier is usually drawn as curved when resources are not equally suited to every use.
A straight frontier would instead imply a constant trade-off. Managers can use the concept when capacity is tight.
If a delivery fleet handles both grocery and pharmaceutical orders, taking one more urgent contract may displace several routine orders. The relevant cost is not only cash spent on the new order; it includes the foregone contribution from what the same drivers and vehicles could have delivered.
MRT is about physical possibility, while the decision about which output mix earns the most depends on prices and customer demand as well. In a simplified efficient allocation, the output trade-off is compared with the price ratio or consumers' willingness to substitute.
It differs from the marginal rate of substitution, which concerns a consumer's preferences between goods at a fixed satisfaction level. The frontier itself can shift.
Better equipment or a larger workforce raises feasible output, so yesterday's MRT may no longer describe today's options.
In practice
Real-world examples.
Example
A small factory can use a shift to make ten extra desks only by giving up twenty chairs. Near the current plan, its MRT is two chairs for each extra desk.
Example
A farm reallocates its best vineyard land first, giving up a little grain for more grapes. After expansion reaches land better suited to grain, the grain sacrifice per extra grape harvest rises.
Example
A logistics company accepts a new urgent route and loses capacity for three regular routes. The owner prices the urgent work against the contribution from the displaced work, not only its fuel and wages.
Formula
Calculation
MRT of good X for good Y = the positive magnitude of change in Y / change in X along a production possibilities frontier, locally approximated by -dY/dX. If ten extra desks require giving up twenty chairs, MRT = 20 / 10 = 2 chairs per desk at that operating range.
Worked example. At a busier operating point, the same invented factory finds that ten more desks require giving up 35 chairs.
- MRT = 35 / 10 = 3.5 chairs per desk, higher than the 2 chairs per desk at the quieter point.
- Suppose a desk sells for $300 and a chair for $100, so the price ratio is $300 / $100 = 3 chairs per desk. At the busy point one more desk costs 3.5 chairs, worth 3.5 x $100 = $350, which is more than the $300 the desk earns, so shifting further towards desks no longer pays.Case study
Seen in the real world.
Fictional example: Alder Foods, a fictional producer of frozen meals and baked snacks, received a large order for extra meals. Sales staff used the meal's positive unit margin to argue for immediate acceptance. The plant manager mapped the shared packing line and found that the order would displace almost twice as many snack packs during peak shifts as during quiet shifts. At the busy operating point, the MRT made the meal order less attractive than it first appeared.
Alder negotiated a later delivery schedule that used quiet shifts and preserved snack commitments. It then ran a pilot with a new packing attachment that reduced changeover time, shifting its feasible frontier outward. The following quarter the same meal order was worthwhile without displacing snacks. The board learned to measure the output sacrificed at the current capacity point and revisit that cost when technology changes.
Watch out
Common mistakes.
- Treating the trade-off as a fixed rate even when resources are better suited to one output than another.
- Ignoring the displaced output when pricing new work under a shared capacity constraint.
- Confusing the production trade-off between outputs with a consumer's preference trade-off or an input-substitution rate.
Questions
People also ask.
What does MRT measure?
It measures the amount of one output sacrificed for an additional unit of another along the current production frontier. It is a local opportunity cost in output units.
Why does it often rise as output expands?
Resources differ in suitability. After the most appropriate people and machines are moved first, further expansion may require giving up more of the other product.
Can a firm lower its MRT?
Technology, training and added capacity can change the feasible trade-offs. Measure the new frontier rather than assume the old sacrifice rate still applies.
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