Information about Marginal Rate Of Substitution
In economics, the marginal rate of substitution (MRS) is the least-favorable rate at which an agent is willing to exchange units of one good or service for units of another. The MRS measures the value that the consumer places on one extra unit of a good or service, where the opportunity cost is quantified by amount of another sacrificed.
Textbook Definition: The rate at which a customer is ready to give up a product A in exchange for product B , total satisfaction remaining the same is termed marginal rate of substitution of B for A
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,
, where U is consumer utility, x and y are goods.
Also, note that:
where MUx is the marginal utility with respect to good x and MUy is the marginal utility with respect to good y.
By taking the total differential of the utility function equation, we obtain the following results:
The marginal rate of substitution is defined by minus the slope of the indifference curve at whichever commodity bundle quantities are of interest. That turns out to equal the ratio of the marginal utilities:
When consumers maximize utility with respect to a budget constraint, the indifference curve is tangent to the budget line, therefore, with m representing slope:
Therefore, when the consumer is choosing his utility maximized market basket on his budget line,
This important result tells us that utility is maximized when the consumer's budget is allocated so that the marginal utility to price ratio is equal for each good.
Textbook Definition: The rate at which a customer is ready to give up a product A in exchange for product B , total satisfaction remaining the same is termed marginal rate of substitution of B for A
Marginal rate of substitution 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 endowment in question, at that endowment. 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,
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,
Simple mathematical analysis
Assume the consumer utility function is defined by, where U is consumer utility, x and y are goods.
Also, note that:
where MUx is the marginal utility with respect to good x and MUy is the marginal utility with respect to good y.
By taking the total differential of the utility function equation, we obtain the following results:
, or substituting from above,
, or without, loss of generality,
, that is,
.
- :
, or rearranging
The marginal rate of substitution is defined by minus the slope of the indifference curve at whichever commodity bundle quantities are of interest. That turns out to equal the ratio of the marginal utilities:
.
When consumers maximize utility with respect to a budget constraint, the indifference curve is tangent to the budget line, therefore, with m representing slope:
Therefore, when the consumer is choosing his utility maximized market basket on his budget line,
This important result tells us that utility is maximized when the consumer's budget is allocated so that the marginal utility to price ratio is equal for each good.
References
- Microeconomics (2005, 6th Edition) by Pindyck, and Rubinfeld. ISBN 9780130084613.
See also
Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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In economics, opportunity cost, or economic cost, is the cost of something in terms of an opportunity forgone (and the benefits which could be received from that opportunity), or the most valuable forgone alternative (or highest-valued option forgone), i.e.
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Neoclassical economics refers to a general approach in economics focusing on the determination of prices, outputs, and income distributions in markets through supply and demand.
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An indifference curve in microeconomic theory is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another.
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In mathematics the concept of a measure generalizes notions such as "length", "area", and "volume" (but not all of its applications have to do with physical sizes). Informally, given some base set, a "measure" is any consistent assignment of "sizes" to (some of) the subsets of the
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The introduction to this article may be too long. Please help improve the introduction by moving some material from it into the body of the article according to the suggestions at Wikipedia's .
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In mathematics (more precisely in differential calculus), the term total derivative has a number of closely related meanings.
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- The total derivative of a function of several variables, with respect to one of its variables, is, in contrast to the partial derivative, a
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A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.
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In economics, marginal concepts refer to the effect of producing or consuming one more of a good, i.e. at the edge, or margin, of the total produced/consumed.
For example, marginal cost refers to the cost of producing one more unit of some good.
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For example, marginal cost refers to the cost of producing one more unit of some good.
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An indifference curve in microeconomic theory is a graph showing different bundles of goods, each measured as to quantity, between which a consumer is indifferent. That is, at each point on the curve, the consumer has no preference for one bundle over another.
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Consumer theory is a theory of economics. It relates preferences (through indifference curves and budget constraints) to consumer demand curves. The models that make up consumer theory are used to represent prospectively observable demand patterns for an individual
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Convex preferences refer to a property of utility functions commonly represented in an indifference curve as a bulge toward the origin for normal goods (for unwanted goods, the curve bulges away from the origin).
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Microeconomics (or price theory) is a branch of economics that studies how individuals, households, and firms make decisions to allocate limited resources,[1] typically in markets where goods or services are being bought and sold.
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