4.4 The Marginal Rate of Technical Substitution: the Slope of an Isoquant

Fundamentally, the isoquant illustrates a tradeoff. Suppose Chuck needs to catch 20 fish a day to survive, and he’s currently using some amount of labor and capital $(L,K)$. He might consider fashioning a stronger spear in order to have to spend a bit less time fishing, while keeping his output at 20 fish. To do so, he would need to figure out how much more capital he would need ($\Delta K$) to reduce his time fishing by some amount ($\Delta L$). The rate of additional capital needed per labor reduced, $\Delta K / \Delta L$, is called his marginal rate of technical substitution between labor and capital. (Note: Some textbooks refer to this as the “Technical Rate of Substitution.”)

Visually, the MRTS is represented by the magnitude of the slope of an isoquant:

[ See interactive graph online at https://www.econgraphs.org/graphs/firm/technology/mrts ]

On Friday, we’ll go into the mathematics of how to calculate the MRTS.

Different functional forms

So far we’ve analyzed the features of a production function: given $f(L,K)$, we can find the marginal products, plot the isoquants, and calculate the MRTS. We now face our first modeling choice: which production function best suits a particular production process? While there are an infinite number of possible functional forms, let’s look at two that are commonly used to model production technologies: linear and Cobb-Douglas production functions.