An isoquant shows the different combinations of K and L that produce a certain amount of a good or service. Mathematically, an isoquant shows:

*f (K,L) = q _{0}*

Graphically, the shape of an isoquant will depend on the type of good or service we are looking at. The shape of isoquants is also in close relation with the terms *marginal rate of technical substitution* (MRTS) and *returns to scale*.

The first example of isoquant map showed in the adjacent graph is the most common representation. It shows four convex isoquants (green), showing each curve what amount of capital K the producer can stop applying when increasing the amount of labour L, while maintaining the quantity of output produced constant. This relation gives us the MRTS between these inputs, which is the slope of the curve in each of its points.

Our second example is an isoquant map with four parallel lines (cyan). This is the case for inputs which are perfect substitutes, since the lines are parallel and MRTS = 1, that is the slope has an angle of 45º with each axis. It can also be the case for inputs that are perfect substitutes but in different proportions. In that case, 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.

Our third example shows an isoquants map with four isoquants (red) that represent perfect complementary inputs. This is, there will not be an increase on the amount produced unless both inputs increase in the required proportion. The best example of complementary inputs are shovels and diggers, since the amount of holes will not increase when there are extra shovels without diggers. Notice that the elbows are collinear, and the line crossing them defines the proportion in which each input needs to increase in order to have an increase in the production. In this case the horizontal fragment of each isoquant has a MRTS = 0 and the vertical fractions a MRTS = ∞.

Isoclines are lines which ‘join up’ the different *production regions*. Having defined and decided the optimal levels of K and L we need to produce the different quantities, the line that passes through these optimal levels is an isocline (cyan). In other words, it is the line that joins points where the MRTS of each isoquant is constant:

**Video – Isoquants:**