The marginal rate of technical substitution (MRTS) can be defined as, keeping constant the total output, how much input 1 have to decrease if input 2 increases by one extra unit. In other words, it shows the relation between inputs, and the trade-offs amongst them, without changing the level of total output. When using common inputs such as capital (K) and labour (L), the MRTS can be obtained using the following formula:
The MRTS is equal to the slope of isoquants. In the adjacent figure you can see three of the most common kinds of isoquants.
The first one has a MRTS that changes along the curve, and will tend to zero when diminishing the quantity of L and to infinite when diminishing the quantity of K.
In the second graph, both inputs are perfect substitutes, since the lines are parallel and the MRTS = 1, that is the slope has an angle of 45º with each axis. When considering different substitutes inputs, the slope will be different and the MRTS can be defined as a fraction, such as 1/2 ,1/3, and so on. For perfect substitutes, the MRTS will remain constant.
Lastly, the third graph represents complementary inputs. In this case the horizontal fragment of each indifference curve has a MRTS = 0 and the vertical fractions a MRTS = ∞.