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Substitution Marginal Rate and Its Usage in the Marginal Preference Calculation
Dali Magrakvelidze
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DOI:10.17265/2159-5291/2014.12.007
Associate professor, Computational Mathematics, Georgian Technical University, Kostava St. 77, Tbilisi Georgia 0175.
The slope of indifference curve is known as a marginal rate of
substitution (MRS). MRS defining ratio always describes slope of indifferent
curve. i.e. MRS matches the module of indifferent curves slope. Utility function 
is used to calculate marginal rate of
substitution (MRS), because MRS gives the slope of appropriate indifference
curve, it can be interpreted as a norm, in which costumer is ready to
substitute good 1 by small amount of good 2. The word “marginal” in economic means “differential”. Here we have
partial differentiation, because in time of calculation of good 1`s marginal
utility the amount of good 2 remains the same. We can calculate MRS in two ways using differential and function. In the
first case consider change (
) during which utility is unchanged. For the second
method let the curve of indifference present by 
function. The
function shows how many of 
is needed for
each unit of 
to stay on this concrete curve of
indifference. We obtain two equations for the term of MRS and budget constraint
and two 
and variables. To define the optimal choice of and as a function of the price and income, we need to solve those two
equations. The problem of maximization can be solved by using differential.
Marginal rate of substitution, problem of maximization, indifference curve
[1] Hall R. Varian, Intermediate Microeconomics. W. W. Norton & Company. 1993.
[2] Eugene F. Fama, Merton H. Miller. The Theory of Finance, Dryden Press, 1971.