MARGINAL RATE OF SUBSTITUTION: HOW IT IS CALCULATED AND EXAMPLE - ECONOMY - 2025

The marginal rate of substitution (TMS) is the quantity of a product that the consumer is willing to give up for another product, provided that the new good is satisfactory in the same way. It is used in the theory of indifference to study consumer behavior.

It can be defined as the number of units of a product X that must be abandoned to obtain an additional unit of a product Y, while maintaining the same level of utility or satisfaction. Therefore, it involves the exchange of goods to change the allocation of products combined in different packages.

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An indifference curve is a graph of the different packages of two products to which a consumer is indifferent to choosing. That is, it has no preference for one package over another.

If the units of one product are decreased, the consumer must be compensated with more units of the other product to maintain the condition of indifference. The marginal rate of substitution is the rate at which a decrease in one product must be offset by an increase in the other product.

What is the marginal rate of substitution?

The marginal rate of substitution is an economic term that refers to the point at which one product is substitutable for another.

This rate forms a downward sloping curve, called the indifference curve. Each point along it represents the amounts of product X and product Y that would be suitable substituting one for the other.

It is always changing for some given point on the curve, mathematically representing the slope of the curve at that point. At any given point along an indifference curve, the marginal rate of substitution is the slope of the indifference curve at that point.

If the marginal rate of substitution of X by Y or Y by X decreases, the indifference curve must be convex at the origin.

On the other hand, if it is constant, the indifference curve will be a straight line sloping down to the right at an angle of 45 ° for each axis. If the marginal rate of substitution increases, the indifference curve will be concave at the origin.

Principle of decrease in the marginal rate of substitution

The TMS of product X with respect to product Y decreases as more of product X is replaced by product Y. In other words, as the consumer has more and more of product X, he is prepared to give up less and less product. AND.

The rate at which the consumer substitutes product X for product Y is higher initially. However, as the substitution process continues, the substitution rate begins to decline.

Limitations

The marginal rate of substitution does not examine which combination of products a consumer would prefer more or less than another mixture, but rather examines which combinations of products the consumer would likewise prefer.

Nor does it explore marginal utility, which is how better or worse a consumer would be with one combination of products rather than another, because along the indifference curve all combinations of products are valued in the same way by the consumer.

How is it calculated?

The law of diminishing marginal utility states that marginal utility, which is the additional utility for each new unit of a product, will be less than the marginal utility of the preceding unit.

That is, the first unit of a product has the highest utility, the second unit has the second highest utility, and so on.

Now, if a consumer substitutes a product X for another product Y, he must be compensated with the highest number of units of Y for the first unit of X, the second highest number of units of Y for the second unit of X, and so on continuously.

This shows that the marginal rate of substitution changes continuously as you move along an indifference curve.

For very small changes in a product, the marginal rate of substitution approximates the slope of the indifference curve, which is equal to the change in Y divided by the change in X.

Formula

The marginal rate of substitution (TMS) is calculated between two products placed on an indifference curve, showing a point of equal utility for each combination of "product X" and "product Y". The formula for the marginal rate of substitution is:

TMSxy = - (Y1 - Y0) / (X1 - X0) = dy / dx, where:

- "X" and "Y" each represent a different product.

- dy / dx refers to the derivative of y with respect to x.

On the other hand, TMSxy and TMSyx are not the same. In fact, they are reciprocal of each other, that is, TMSyx = 1 / TMSxy.

It can be shown that the marginal rate of substitution of y for x is equal to the price of x divided by y. This is equal to the marginal utility of x divided by the marginal utility of y, that is, TMSxy = MUx / MUy

The indifference curve becomes more horizontal as it moves from the y-axis to the x-axis. It is because as y becomes scarce and x becomes abundant, the marginal rate of substitution of x with y decreases. This is known as the diminishing marginal rate of substitution.

Example

For example, a consumer must choose between hamburgers and hot dogs. To determine the marginal rate of substitution, the consumer is asked which combinations of hamburgers and hot dogs provide the same level of satisfaction.

When these combinations are graphed, the slope of the resulting line is negative.

This means that the consumer faces a decreasing marginal substitution rate. As long as you have more hamburgers relative to hot dogs, the consumer will be willing to give up fewer hot dogs for more hamburgers.

In the graph, at point A, it can be seen that the consumer is ready to substitute (14-11) = 3 units of hot dogs for (25-20) = 5 extra units of hamburgers. Therefore, at this stage, the consumer's marginal rate of substitution of hot dogs for hamburgers is 5/3 = 1.67.

However, at point B, the consumer to substitute other (11-7) = 4 units of hot dogs would need (40-25) = 15 extra units of hamburgers, being in this stage his TMS of 15/4 = 3, 75.

Any of the three combinations on the graph are assumed to have the same level of utility.

References

1. Adam Hayes (2019). Marginal Rate of Substitution - MRS Definition. Investopedia. Taken from: investopedia.com.
2. Prateek Agarwal (2018). Marginal Rate Of Substitution. Intelligent Economist. Taken from: intelligenteconomist.com.
3. Jan Obaidullah (2018). Marginal Rate of Substitution. Xplaind. Taken from: xplaind.com.
4. Smriti Chand (2019). The Marginal Rate of Substitution (MRS) - Economics. Your Article Library. Taken from: yourarticlelibrary.com.
5. Toppr (2019). Marginal Rate of Substitution. Taken from: toppr.com.