Marginal Rate of Substitution

The inverse relationship between goods along the downward-sloping indifference curve means that the absolute value of the slope of an indifference curve equals what is called the Marginal Rate of Substitution (MRS) . The MRS is the rate at which a con-sumer is willing to substitute one good for another with no change in total utility. Begin at A and move to B along the curve. The slope and MRS of the curve is 2/1, or simply 2, when the minus sign is removed to give the absolute value. This is the Indifference curve A curve showing the differ-ent combinations of two products that yield the same satisfaction or total utility to a consumer. Marginal Rate of Substitution (MRS) The rate at which a con-sumer is willing to substitute one good for another without a change in total utility. The MRS equals the slope of the indifference curve at any point on the curve. 168 Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. consumer ’ s subjective willingness to substitute A for B . At point A , the consumer has a substantial amount of steak and relatively little lobster. Therefore, the consumer is willing to forgo or “ substitute ” 2 ounces of steak to get 1 more ounce of lobster. In other words, the marginal utility of losing each ounce of steak between A and B is low compared to the marginal utility of gaining each ounce of lobster. EXHIBIT A-1 A Consumer ’ s Indifference Curve Points A , B , C , D , and each point along the curve represent a combination of steak and lobster that yields equal total utility for a given consumer.

This is equivalent to saying that, the farmer’s ability to substitute paddy for maize increases as more and more substitution takes place. So, MRPS PM states that, ‘the Marginal Rate of Substitution of paddy for maize increases, as the output of paddy increases and output of maize decreases ’. MRPS is, otherwise, defined as ‘the rate at which the farmer must gives up output of one enterprise (maize) in order to produce more of an additional output of other enterprise (paddy) for a given level of resources ’. The reasons for this increasing rate of MRPS of concave shaped PPC are already discussed earlier. This increasing rate of product substitution is more common in agriculture. This ebook is exclusively for this university only. Cannot be resold/distributed. The concept of increasing MRPS between the two products (paddy and maize) is illustrated through the Figure 4.6 . As the farmer moves down the PPC, it indicates the willingness to substitute paddy for maize increases. This means that, as the amount of paddy output is increased by equal amounts, the output of maize diminishes by higher amounts. Thus, the MRPS of paddy for maize MRPS PM is the output of maize that the farmer is willing to give up to gain a marginal increase of output of paddy in the production programme for the given level of resources. This increasing MRPS contributes positive (concave) slope to the PPC. Figure 4.6 : Positively Sloped Production Possibility Curve Showing Increasing MRPS. The concept of MRPS is explained by the following formulae: Similarly, MRPS of maize for paddy is given by, iv. Position of Production Possibility Curve The position of PPC with reference to origin depends upon the level of resources with the farmer. Higher the level of resources, farther away will be the position of PPC from the origin and vice versa .

Indeed, if the marginal utility/price ratio of, say, commodity 2 were greater, which is equivalent to assuming the inequality MU 2 ( x 1 , x 2 ) / p 2 > MU 1 ( x 1 , x 2 ) / p 1 , it would be utility increasing to consume one unit less of good 1. The direct effect of this reduc-tion on utility would be − MU 1 ( x 1 , x 2 ), but it would buy p 1 / p 2 units of good 2 and this indirect effect on utility, ( p 1 / p 2 ) MU 2 ( x 1 , x 2 ), would be greater given the assumed inequality. The equal marginal utility/price ratios, MU 2 ( x 1 , x 2 ) / p 2 = MU 1 ( x 1 , x 2 ) / p 1 , can also be written as follows: MU 1 ( x 1 , x 2 ) / MU 2 ( x 1 , x 2 ) = p 1 / p 2 (3.5) Equation (3.5) states that the Marginal Rate of Substitution equals the price ratio . For the former concept recall equation (2.10). In fact, (3.5) equates the slopes of the indifference curve and of the budget line in Figure 3.1. Indeed, the budget line can be rewritten x 2 = I / p 2 − ( p 1 / p 2 ) x 1 , which reveals its slope, p 1 / p 2 . Sim-ilarly, the indifference curve expression U ( x 1 , x 2 ) = constant implies that x 2 is a function of x 1 , say x 2 = f ( x 1 ). Differentiation of U ( x 1 , f ( x 1 )) = constant yields Utility and expenditures 45 MU 1 ( x 1 , f ( x 1 )) + MU 2 ( x 1 , f ( x 1 )) f ( x 1 ) = 0 so that the slope of the indifference curve, f ( x 1 ), is as in the left-hand side of (3.5). 3.3 Revealed preferences There are many utility functions; the question is, which one is appropriate? So-called constant elasticity of substitution functions are frequently used in microeconomic analysis because they are flexible and encompass both the Leontief and the Cobb–Douglas function. These functions, which will be ana-lyzed in Section 3.4, have the easily verifiable property that an increase in income merely increases all quantities demanded with the same factor.