What it means
Every business combines inputs to make its product. A bakery can use more bakers and fewer ovens, or more ovens and fewer bakers, and still produce the same number of loaves.
The MRTS puts a number on that trade-off at a particular point. Technically, it is the ratio of the marginal products of the two inputs.
The marginal product of labour is the extra output from one more unit of labour, and the marginal product of capital is the extra output from one more unit of equipment. If labour adds twice as much output as equipment at the margin, the business can swap two units of equipment for one worker without changing output.
The MRTS usually falls as you substitute more of one input for the other. Replacing machines with workers works well at first, but as machines become scarce, each additional worker adds less, and more workers are needed to make up for each machine given up.
This is called diminishing marginal rate of substitution and is reflected in the curved shape of an isoquant, a line showing all input combinations that produce the same output. The idea becomes practical when paired with prices.
A business minimises cost when the MRTS equals the ratio of the input prices, that is, the wage divided by the cost of a unit of capital. If the MRTS is higher than the price ratio, labour is relatively productive for its cost and the business should use more of it, and if it is lower, the business should use more equipment.
Real decisions are messier. Some inputs cannot be swapped in the short run, workers need training, and technology changes what is possible.
Even so, the MRTS offers a useful way of thinking about automation, outsourcing and staffing levels.
In practice
Real-world examples.
Example
A call centre considers replacing some agents with an automated phone system. Managers calculate how many agent-hours the system replaces and compare the savings with the cost of the software.
Example
A farm weighs hiring seasonal pickers against buying a harvesting machine. It measures the extra crop each option adds and compares the cost of each, to choose the cheaper mix.
Example
A construction firm in a country with low wages uses more labour and less heavy equipment. When wages rise sharply, the MRTS and the price ratio move apart, and the firm shifts towards machines.
Formula
Calculation
MRTS of labour for capital = Marginal product of labour / Marginal product of capital
Cost-minimising condition: MRTS = Wage per hour / Cost per machine hour
A plant makes 1,000 units a day. One more labour hour adds 10 units of output, and one more machine hour adds 5 units, so the MRTS is 10 / 5 = 2, meaning 2 machine hours can be dropped for each extra labour hour without changing output. If labour costs $30 an hour and a machine hour costs $15, the price ratio is $30 / $15 = 2, equal to the MRTS, so the mix is already cost-minimising. If the wage were $20 an hour, the price ratio would be $20 / $15 = 1.33, below the MRTS, so the plant should use more labour and fewer machines.Case study
Seen in the real world.
Lakeview Printing is an illustrative, fictional print shop with a team of binders and a set of folding machines. The owner noticed that one extra binder allowed the shop to leave out two hours of machine time without losing any output.
Binders cost $24 an hour and the machines cost $8 an hour to run, a price ratio of 3. The MRTS was only 2, so the shop was paying more for labour than its productivity justified.
In this illustrative story, the owner moved some work to the machines and reduced overtime, which cut total costs by about 6% at the same output. The lesson was that the cheapest way to produce a given quantity depends on both productivity and input prices.
Watch out
Common mistakes.
- Using the MRTS without considering input prices, when the cheapest mix depends on both productivity and cost.
- Assuming the rate is constant, when it normally changes as the mix of inputs shifts.
- Confusing it with the marginal rate of substitution in consumer theory, which concerns the preferences of buyers.
Questions
People also ask.
What does an MRTS of 2 mean?
Giving up 2 units of one input is exactly offset by adding 1 unit of the other, with output unchanged.
How is it related to the isoquant?
It is the slope of the isoquant at a given point, showing the trade-off between the two inputs.
Can managers use it in practice?
Yes, as a way of comparing automation, outsourcing and staffing options, although real data are usually rougher than the textbook version.
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