THE LAW OF DEMAND VERSUS DIMINISHING MARGINAL UTILITY

THE LAW OF DEMAND VERSUS DIMINISHING MARGINAL UTILITY Authors: Bruce R.Beattie and Jeffrey T.La France Review of Agricultural Economics – Volume 28, Number 2 – Pages 263-271 Presented By: Hajah Siti Wardah & Suzilawaty 21 Jan 2008 Microeconomic ECN 5112, Dr.Rusmawati Faculty of Economics And Management

Definitions Authors’ Results - DMU vs CIC - DMU vs DSD Authors’ Conclusion Appraisal on Article Conclusion OVERVIEW

(i) MARGINAL UTILITY (MU) Measures the additional satisfaction obtained from consuming an additional amount of a good. (ii) DIMINISHING MARGINAL UTILITY (DMU) As consumption increases, MU will always fall. Likewise, total utility increases much more slowly as more quantity consumed. (iii) INDIFFERENCE CURVE(IC) Indifference curve shows various possible combinations between two goods (x,y) that will give the consumer the same level of satisfaction. The article refers it as convex indifference curve (CIC). DEFINITION

COMPARISON

Convex indifference curve (CIC) means indifference curve is convex to the origin. This is because of principle of diminishing marginal rate of substitution. This mean that when the demand for good x increases, the consumer has to give up less and less of good y. Quantity of y y1 U1 y2 Quantity of x x2 x1 Utility Curve GRAPHS COMPARISON Price p1 p2 U1 Quantity of x x1 x2 Demand Curve

Beattie & LaFrance’sArticle The authors present their opinion as fact, supported by three results.

Main argument of Authors: Diminishing Marginal Utility (DMU) is not the Cause of Downward-Sloping Demand(DSD).

1st RESULT :DMU is not necessary for negatively sloped CICs.

GRAPHS Figure 1(a) Surface plot for Figure 1(b) Contour plot for From Figure 1(a), MU increases everywhere on utility surface for both and . In figure 1(b), IC become more dense as one moves across the graph parallel to axis increasing while holding constant or vice versa – again reflecting increasing MU.

EXPLANATION : DMU is not necessary for CICs • Upshot: Despite MU for both goods are increasing, ICs are everywhere negatively sloped and convex to the origin. Therefore, the utility function shows that DMU is not necessary for CICs. • Silberberg and Suen “…..convexity of ICs in no way implies or is implied by DMU. DMU and convexity of ICs are two independent concepts. Convexity of IC relates to how marginal evaluations change, holding utility (dependent variable) constant. DMU refers to changes in total utilities i.e. movements from one indifference level to another.”

2nd RESULT: DMU isnot necessaryfor DSD • Again using Stone-Geary utility function used in 1st result, The equation of demand function for q1 obtained from first order conditions of budget-constrained maximization of (1) is given by: • Upshot: ICs are negatively sloped and convex as q1 increases given utility is fixed or constant. Therefore, it is convexity of ICs that is crucial for DSD in this case, not DMU.

1st and 2nd results follow from the fact that utility function is unique only up to monotonic transformation. However, Stone-Geary utility function is non-unique in such a way that “ implied demand functions for 2 goods are similar irrespective of exponent on q1 and q2 in equation 1 as long as they are positive”. In other word, it does not matter MU is decreasing (exponent < 1) , constant (e=1), or increasing (e>1). Therefore, 1st & 2nd results hold true as long as Stone-Geary utility function preserves ordinal utilities. Note that…….

Using utility function that gives rise to linear upward sloping demand for q1 and exhibits DMU for q1 and q2 (La France). 3rd RESULT:DMU is not sufficient for DSD

GRAPHS Figure 2(a) Surface plot for u(q1,q2) Figure 2(b) Contour plot for u(q1,q2)= In figure 2(a), there is DMU for q1 and q2. The curvature of the utility function in both the q1 and q2 direction is concave to the q1q2 plane. And in figure 2(b), the indifference curves become less dense as q1 increases given q2 and vice versa. Also, the indifference curves are negatively sloped and convex to the origin in the regular region.

Upshot : DMU in addition to being unnecessary, is not sufficient for DSD as sometimes alleged. In this example, we have perfectly acceptable (well-behaved) utility function giving rise to an upward-sloping demand function even when MU of that good is diminishing-the long-known Giffen good case (Spiegel). 3rd RESULT : DMU isnot sufficient for DSD

AUTHORS’ CONCLUSION DSD is not dependent on DMU based on two utility functions and the related graphs. DSD is constructed from the assumptions of ordinal utility maximization, (instead of cardinal utility) and the ideas of substitution and income effects.

OUR APPRAISAL

COMPARISON: PARADOX vs AUTHORS’ VIEW • In understanding economics, DSD previously taught to be a result of DMRS (in terms of Adam’s Smith paradox of value by looking at the relationship of demand, total utility & marginal utility). • However, as shown by the authors, in 3D view, the convexity or negative slope of the IC which measures the MRS, in fact is not equivalent to DMU (MRS is the ratio of the marginal utility of x to the marginal utility of y, whereas DMU is movements from one indifference level to another).

Under the paradox, marginal utility is equated with demand and price.

EXPLANATION OF GRAPH • Because of the availability of water, an extra glass provides very little marginal utility. As we drink more glasses of water, the demand for water decreases. • Indeed, the law of diminishing marginal utility is operating in full force with water. • Compare to diamond which has smaller effect of DMU because people are willing to pay more for diamonds than water as they are high value & less available.

CONCLUSION • Paradox of value concept needs to be reviewed. • We agree with the Beattie & LaFrance’s opinion. Bear in mind on difference in definitions of convexity of IC & MU. • Be careful in policy decision making: Beattie & LaFrance’s evidences only valid when the utility functions satisfy axioms of consumer theory.

CONCLUSION The article does challenge our own beliefs and assumptions in economic foundation.

References • Synder, C & Nicholson, W 2008, Microeconomic Theory: Basic principles and extensions, 10th edn, Thomson Southwestern, America. • Beattie BR & LaFrance JT 2006, ‘The Law of Demand versus Diminishing Marginal utility’, Review of Agricultural Economics, vol. 28, no. 2, pp. 263 -271. • Online Business Dictionary n.d., Substitution effect & Income effect. Retrieved Jan 19, 2009, from http:// www.businessdictionary.com/ • Ali, H1999, Comprehensive Economics Guide, 2nd edn, Oxford University Press, Singapore. Macroeconomic ECN 5112, Dr.Rusmawati Faculty of Economics And Management

THANK YOU Microeconomic ECN 5112, Dr.Rusmawati Faculty of Economics And Management

THE LAW OF DEMAND VERSUS DIMINISHING MARGINAL UTILITY