Marginal Rate of Substitution

Marginal Rate of Substitution Definition

The marginal rate of substitution (MRS) is the rate at which a person is willing to give up one good for another good while keeping the same level of satisfaction. In simpler terms, it measures the amount of one thing someone is willing to trade for a little more or less of another thing. For instance, how many apples someone is willing to give up for one more orange.

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does not affect their utility.

That is to say that regardless of what combination they choose and the amount of trade-off of one item they exchange for another, it does not affect their overall satisfaction with consumption.

When consumption levels are at equilibrium, marginal rates of substitution are equivalent to one another, and indifference curves are used to determine marginal rates of substitution between commodity bundles.

Marginal Rate of Substitution: Indifference Curve

Your preferences affect the number of goods you consume. You might prefer consuming more pizza than pasta, or you might like drinking more Cola than eating Salad, or vice-versa. When provided with choices between two bundles, an individual will choose based on their preferences.

If the two bundles provide the same level of satisfaction to the customer, we say that the customer is indifferent between the two bundles. The marginal rate of substitution of one good for another is measured by moving along an indifference curve.

Fig 1. - Indifference curve

Figure 1 above shows the indifference curve of an individual consuming coffee and Pepsi. Along the indifference curve, there are many choices an individual makes between specific units of coffee and certain units of Pepsi.

Keep in mind that these combinations between coffee and Pepsi make the consumer equally satisfied. Whether the consumer chooses the combination of coffee and Pepsi at Point 1 or at Point 2, they are equally happy.

But at what rate is the consumer willing to give up coffee for Pepsi? This is measured by the marginal rate of substitution, which is the rate at which an individual changes consumption of good one (coffee) for consuming an additional unit of good two (Pepsi).

The marginal rate of substitution is the slope of the indifference curve.

The indifference curve is not a straight line. That's because the marginal rate of substitution is not equal at all points of the indifference curve.

At some points of the indifference curve, an individual might be willing to give up more coffee in exchange for an additional unit of Pepsi. However, later on, as an individual is already receiving enough units of Pepsi, they are not willing to give up as many units of coffee. The rate at which a consumer is ready to trade coffee for Pepsi depends on the amount of Pepsi and the sugar intake they've already had. Thus, the marginal rate of substitution diminishes as we go down the indifference curve.

Marginal Rate of Substitution Slope

To understand the marginal rate of substitution slope, we will use the indifference curve of an individual that consumes coffee and Pepsi. The individual makes different combinations of coffee and Pepsi to varying points of the indifference curve.

The MRS also measures the value an individual attaches to the consumption of one good in terms of the other. When the MRS is three, the individual clearly values Pepsi more than he values the consumption of coffee.

Fig 2. - Marginal rate of substitution along the indifference curve

Figure 2 above shows the indifference curve of an individual choosing between coffee and Pepsi. Coffee is on the vertical axis, and Pepsi is on the horizontal axis.

Diminishing Marginal Rate of Substitution

Notice that at different points, the MRS begins to drop. Initially, the MRS is 5, meaning five units of coffee per unit of Pepsi. Then the MRS at another point is 3, meaning 3 units of coffee are exchanged per additional unit of Pepsi. Moving down the indifference curve, the marginal rate of substitution declines.

Consumer preferences are affected by a diminishing marginal rate of substitution. That means that throughout the indifference curve, the MRS will fall.

The diminishing marginal rate of substitution is why the indifference curve is convex (bowed inward).

The MRS might be expressed as

\(-\frac{\Delta\hbox{C}}{\Delta\hbox{P}}\)

\(\hbox{Where:}\)

\(\Delta \hbox{C} = \hbox{Change in consumption of coffee}\)

\(\Delta \hbox{P} = \hbox{Change in consumption of Pepsi}\)

Due to the change in consumption of coffee being negative, we add the minus sign to make the MRS positive.

For the indifference curve to be convex, it means that the slope of the MRS should increase. That means that the change in the consumption of coffee becomes less and less negative.

As the consumption of one good in terms of another increase, the magnitude of the slope of the MRS decreases.

Constant Marginal Rate of Substitution

Constant Marginal Rate of Substitution (MRS) describes a situation where the rate at which a consumer is willing to exchange one good for another remains constant, regardless of how much of each good they have. This means that the slope of the indifference curve, which represents the different combinations of goods that yield the same level of satisfaction to the consumer, is represented by a straight line with a constant slope.

Marginal Rate of Substitution Formula

We calculate the marginal rate of substitution by dividing the change of the first good by the change of the second good. The MRS formula is:

\(MRS = -\frac{\Delta\hbox{Good 1}}{\Delta\hbox{Good 2}} \)

The minus sign is added to make the MRS positive. As an individual gives away more of Good 1 to consume Good 2, the difference in Good 1 is always negative.

How to Calculate the Marginal Rate of Substitution?

Let's calculate the marginal rate of substitution by following the example below.

Marginal Rate of Substitution Example

Let's look at a marginal rate of substitution example. The marginal rate of substitution reveals how we choose to consume between different combinations of two goods while keeping the same satisfaction.

Marginal Rate of Substitution Importance

The marginal rate of substitution (MRS) is the rate at which consumers are willing to switch from one item or service to another. The importance of the marginal rate of substitution comes from its ability to reveal and measure whether a consumer would exchange one product or service for another one.

Companies can plot the MRS curve for their consumers, use it to forecast their sales, and accordingly make decisions on production capacity.