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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
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 Eugene F. Fama, Merton H. Miller. The Theory of Finance, Dryden Press, 1971.