## What is the 'Marginal Rate of Transformation'

The marginal rate of transformation (MRT) is the rate at which one good must be sacrificed in order to produce a single extra unit (or marginal unit) of another good, assuming that both goods require the same scarce inputs.

Marginal rate of transformation can also be referred to as the opportunity cost.

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## BREAKING DOWN 'Marginal Rate of Transformation'

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. 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.

The marginal rate of transformationÂ can be defined as the number of units of good xÂ that will be foregone in order to produce an extra unit of good y,Â while keeping constant the use of production factors and the technology being used. MRT is the absolute value of the slope of the production possibilities frontier. For each point on the frontier,Â which is displayed as a curved line, there is a different marginal rate of transformation, based on the economics of producing each product individually.

The marginal rate of transformation 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. 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.

## Determining the Marginal Rate of Transformation

MRT can be determined using the following formula:

The formula indicates the rate at which a small amount of xÂ can be foregone for a small amount of y.Â 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. 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. For perfect substituteÂ goods, the MRT will equal 1 and remain constant.

As another example, consider a student who faces a trade-off that involves giving up some free time to get better grades in class by studying more. The MRT is the rate at which the studentâ€™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.

## MRT vs. MRS

While the marginal rate of transformation is similar to the marginal rate of substitution (MRS), these two concepts are not the same. The marginal rate of substitutionÂ focuses on demand, while MRT focuses on supply. The marginal rate of substitution highlights how many units of x would be consideredÂ by a given consumer groupÂ to be compensation for one less unit of y. For example, a consumer who prefers oranges to applesÂ may only find equal satisfaction if she receives three apples instead of one orange.

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