# Предельная ставка замещения – Marginal rate of substitution – qaz.wiki

Marginal rate of substitution is the amount of a good a consumer is willing to consume in relation to another good, as long as it is equally satisfying.

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## As the slope of indifference curve

Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve (more precisely, to the slope multiplied by −1) passing through the consumption bundle in question, at that point: mathematically, it is the implicit derivative. MRS of X for Y is the amount of Y which a consumer can exchange for one unit of X locally. The MRS is different at each point along the indifference curve thus it is important to keep locus in the definition. Further on this assumption, or otherwise on the assumption that utility is quantified, the marginal rate of substitution of good or service X for good or service Y (MRSxy) is also equivalent to the marginal utility of X over the marginal utility of Y. Formally,

M R S x y = − m i n d i f = − ( d y / d x ) {displaystyle MRS_{xy}=-m_{mathrm {indif} }=-(dy/dx),} M R S x y = M U x / M U y {displaystyle MRS_{xy}=MU_{x}/MU_{y},} It is important to note that when comparing bundles of goods X and Y that give a constant utility (points along an indifference curve), the marginal utility of X is measured in terms of units of Y that is being given up.

For example, if the MRSxy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X.

As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases). This is known as the law of diminishing marginal rate of substitution.

Since the indifference curve is convex with respect to the origin and we have defined the MRS as the negative slope of the indifference curve,

M R S x y ≥ 0 {displaystyle MRS_{xy}geq 0} ## What Is the Marginal Rate of Substitution (MRS)?

In economics, the marginal rate of substitution (MRS) is the amount of a good that a consumer is willing to consume in relation to another good, as long as the new good is equally satisfying. It’s used in indifference theory to analyze consumer behavior. The marginal rate of substitution is calculated between two goods placed on an indifference curve, displaying a frontier of utility for each combination of “good X” and “good Y.”

#### Marginal Rate of Substitution

• Marginal concepts
• Marginal rate of technical substitution (the same concept on production side)
• Indifference curves
• Consumer theory
• Convex preferences
• Implicit differentiation

## Смотрите также

• Маргинальные концепции
• Предельная норма технического замещения (та же концепция со стороны производства)
• Кривые безразличия
• Теория потребления
• Выпуклые предпочтения
• Неявное дифференцирование

## References

• Krugman, Paul; Wells, Robin (2008). Microeconomics (2nd ed.). Palgrave. ISBN 978-0-7167-7159-3.
• Pindyck, Robert S.; Rubinfeld, Daniel L. (2005). Microeconomics (6th ed.). Pearson Prentice Hall. ISBN 0-13-008461-1.
• Dorfman, R. (2008). “Marginal Productivity Theory”. In Palgrave Macmillan (ed.). The New Palgrave Dictionary of Economics. London: Palgrave Macmillan. doi:10.1057/978-1-349-95121-5_988-2. ISBN 978-1-349-95121-5 – via SpringerLink.

## Limitations of Marginal Rate of Substitution

The marginal rate of substitution does not examine a combination of goods that a consumer would prefer more or less than another combination. This generally limits the analysis of MRS to two variables. Also, MRS does not necessarily examine marginal utility since it treats the utility of both comparable goods equally though in actuality they may have varying utility.

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