When is MRS Equal to the Ratio of Marginal Effects? Explained

The Marginal Rate of Substitution (MRS) quantifies a consumer's willingness to swap one good for another while maintaining the same satisfaction level. It's calculated as the ratio of the marginal utilities of the two goods. But how does MRS relate to marginal effects, which measure the change in demand for one good due to a price change in another?

Let's break it down:

Marginal Effects: These reflect how much the quantity demanded for one good shifts when the price of another good changes. It's calculated as the derivative of the demand function with respect to the price of the other good.
Substitutes: For substitute goods, an increase in the price of one leads to increased demand for the other. Think coffee and tea - if coffee gets pricier, people might switch to tea. In this case, the marginal effect is positive.
Complements: Conversely, for complement goods, a price increase in one leads to decreased demand for the other. Imagine printers and ink cartridges - if printer prices soar, demand for cartridges might fall. Here, the marginal effect is negative.

Here's the key connection: When dealing with substitute or complement goods, the MRS can indeed be equal to the ratio of the marginal effects.

Let's illustrate:

Substitutes: If the price of good A increases and the demand for good B increases, both the MRS (reflecting the willingness to substitute) and the ratio of marginal effects will be positive.
Complements: If the price of good A increases and the demand for good B decreases, both the MRS and the ratio of marginal effects will be negative.

Important Note: This relationship holds true under specific conditions, primarily when dealing with substitute or complement goods. In more complex scenarios, other factors might influence the relationship between MRS and marginal effects.

When is MRS Equal to the Ratio of Marginal Effects? Explained