### What Is Marginal Rate of Transformation (MRT)?

The marginal rate of transformation (MRT) is the number of units or amount of a good that must be forgone in order to create or attain one unit of another good. In particular, it’s defined as the number of units of good X that will be foregone in order to produce an extra unit of good Y, while keeping constant the use of production factors and the technology being used.

### Key Takeaways

• MRT is the number of units that must be forgone in order to create or attain a unit of another good, considered the opportunity cost to produce one extra unit of something.
• MRT is also considered the absolute value of the slope of the production possibilities frontier.
• The marginal rate of substitution focuses on demand, while MRT focuses on supply.

### The Formula for Marginal Rate of Transformation Is

﻿\begin{aligned} &\text{MRT} = \frac{MC_x}{MC_y} \\ &\textbf{where:}\\ &MC_x=\text{money needed to produce another unit of X}\\ &MC_y=\text{rate of increase by cutting production of Y}\\ \end{aligned}﻿

So the ratio tells you how much Y you need to cut in order to produce another X.

### How to Calculate the Marginal Rate of Transformation (MRT)

The marginal rate of transformation (MRT) is calculated as the marginal cost of producing another unit of a good divided by the resources freed up by cutting production of another unit.

### What Does MRT Tell You?

The marginal rate of transformation (MRT) allows economists to analyze the opportunity costs to produce one extra unit of something. In this case, the opportunity cost is represented in the lost production of another specific good. The marginal rate of transformation is tied to the production possibility frontier (PPF), which displays the output potential for two goods using the same resources.

MRT is the absolute value of the slope of the production possibilities frontier. For each point on the frontier, which is displayed as a curved line, there is a different marginal rate of transformation, based on the economics of producing each product individually.

To produce more of one good means producing less of the other because the resources are efficiently allocated. In other words, resources used to produce one good are diverted from other goods, which means less of the other goods will be produced. This tradeoff is measured by the marginal rate of transformation.

Generally speaking, the opportunity cost rises (as does the absolute value of the MRT) as one moves along (down) the PPF. As more of one good is produced, the opportunity cost (in units) of the other good increases.

### Example of How to Use the Marginal Rate of Transformation (MRT)

The MRT is the rate at which a small amount of X can be foregone for a small amount of Y. The rate is the opportunity cost of a unit of each good in terms of another. As the number of units of X relative to Y changes, the rate of transformation may also change. For perfect substitute goods, the MRT will equal 1 and remain constant.

As an example, if baking one less cake frees up enough resources to bake three more loaves of bread, the rate of transformation is 3 to 1 at the margin. Or consider that it costs $3 to make a make a cake. Meanwhile,$1 can be saved by not making a loaf of bread. Thus, the MRT is $3, or$3 divided \$1.

As another example, consider a student who faces a trade-off that involves giving up some free time to get better grades in a particular class by studying more. The MRT is the rate at which the student’s grade increases as free time is given up for studying, which is given by the absolute value of the slope of the production possibility frontier curve.

### The Difference Between MRT and the Marginal Rate of Substitution (MRS)

While the marginal rate of transformation (MRT) is similar to the marginal rate of substitution (MRS), these two concepts are not the same. The marginal rate of substitution focuses on demand, while MRT focuses on supply.

The marginal rate of substitution highlights how many units of X would be considered by a given consumer group to be compensation for one less unit of X. For example, a consumer who prefers oranges to apples may only find equal satisfaction if she receives three apples instead of one orange.

### Limitations of Using MRT

The marginal rate of transformation (MRT) is generally never constant and may need to be recalculated frequently. As well, if MRT doesn’t equal MRS then goods will not be distributed efficiently.