Ordinal Approach or The concept of Scale of Preferences or The Indifference Curve Technique: Ordinal Approach or The concept of Scale of Preferences or The Indifference Curve Technique Originated by Francis Ysidro Edgeworth in 1881 and Refined by Pareto in 1906. Application in the demand analysis at the hands of J.R. HICKS and R.G.D .Allen in 1934.
The Ordinal Approach In Utility Theory: The Ordinal Approach In Utility Theory The ordinal theory suggests that utility is only relatively discernible but not quantifiable. U is the level of satisfaction than an amount of satisfaction. Utility is a series of assigned numbers to rank options by the consumer preference. The assigned numbers reveal what is more preferred but cannot tell how much the difference is. Utility can only be ranked by an order or a scale of preference to show the degree of willingness of a consumer. Hicks uses ‘ Significance’ rather than ’ Utility’ . Combinations between Apples and Bananas Level of Satisfaction Derived Ranking Order of Preference 12 Apples + 12 Bananas Highest First 10 Apples + 19 Bananas Lesser than (a) Second 5 Apples + 5 Bananas Lesser than (b) Third
Scale of Preferences - Characteristics: Scale of Preferences - Characteristics Drawn by a consumer in his mind consciously or unconsciously. Based on subjective valuation of goods made by the cust on the basis of his liking, habits, tastes, desires, intensity of wants, etc. Independent of Price and consumer’s income. It represents Ordinal comparison of the level of satisfaction derived by the consumer from different combinations of goods. S of P differs from person to person. S of P considers the significance of the commodity in the context of their stocks.
Slide 4: Indifference Schedule —An Indifference schedule is a list of alternate combination in the stocks of two goods which yield equal satisfaction to the consumer. Indifference Curve- An Indifference curve is the locus of points representing all the different combinations if the two goods (say X and Y) which yield equal utility or satisfaction to the consumer. Indifference Map- An Indifference map is a set of indifference curves.
Hypothetical data for an IC Map: Hypothetical data for an IC Map Combination of Goods (Units) I II III X Y X Y X Y 1 10 2 15 3 20 2 6 4 10 5 14 3 3 6 6 7 7 4 1 8 3 9 7 U1(IC1) U2(IC2) U3(IC3) Third Order Preference Second Order Preference First Order Preference QT of comm Y Y X U1 U3 U2 O QT of comm X d c b a ∙ ∙ ∙ ∙
ASSUMPTIONS: ASSUMPTIONS A consumer is interested in buying two goods in combination. He is able to rank his preferences & give a complete ordering of the scale of preferences. Non-satiation, i.e, the consume always prefers more quantities of goods to lesser quantities. He is rational and his choices are transitive.It means, if he prefers combination a to b and b to c, then he must also prefer a to c. Height of the IC indicates the level of satisfaction. IC are drawn as continuous curves assuming infinitesimal amount of changes in the combination of 2 goods i.e. perfect division of the goods under consideration.
The Indifference Curve Theory: The Indifference Curve Theory Based on these assertions, Edgeworth F. Y. ( 1845 - 1926 ) first suggested the indifference curve to represent the level of preference a consumer has when two goods are consumed with different amount, but each combination of these two goods yields the same level of preference .
The Properties of the Indifference Curve: The Properties of the Indifference Curve IC slope downwards from left to right , i.e. –vely sloped, indicating if X increases in combination X and Y , there should be a decrease in Y amount to be on the same level of satisfaction. They are convex to origin. They can’t intersect each other.
The Marginal Rate of Substitution: The Marginal Rate of Substitution Def: The MRS of Xof Y refers to the amount of Y that must be given up per unit of X gained by the consumer to keep the level if satisfaction unchanged. MRSxy= x/ y, where MRSxy = the MRs of X for Y Y = a small change in the quantity of Y X = a small change in the quantity of X
Slide 10: Comm Y Comm X MRS = x / y 10 25 - 11 20 -5/1=-5 12 16 -4/1=-4 13 13 -3/1=-3 14 11 -2/1=-2 Hicks replaces the law of DMU by the principle of Diminishing Marginal Rate of Substitution . As the consumer increases the quantity of X then its MU decreases and % of substitution will be less as the point moves downwards on the IC curve
Budget Constraint Or Budget Line: Budget Constraint Or Budget Line DEF: The Budget line is the locus of points representing all the different combinations of the two goods that can be purchased by the consumer, given his money income and the prices of the two goods. What a consumer can actually buy depends on the income at his disposal and the prices of goods he wants to buy. I and P are 2 objective factors which form the budgetary constraint of the consumer. The consumption or purchase possibility of the consumer is restricted to the budget constraint. The slope of the budget line is called the marginal rate of substitution in exchange = PX / PY. The concept of relative price is important because a rise in relative price would encourage the producer to put more resources in production. The concept also conveys the market information of relative scarcity of those resources. The budget line rotates when the relative price changes. The shift of the line means that either the income changes or there is a change in the price of both goods.
Alternate Purchase Possibilities: Alternate Purchase Possibilities Units of Y Units of X A 5 0 4 2 3 4 2 6 1 8 B 0 10 Qt of Y s z X O Y b a Qt of x c A B Given income = Rs. 50 If P of Y = Rs 10/ unit If P of X = Rs 5/ unit AB= Budget ( Price, Income) Line
Slide 13: Changes in Income. Px, Py constant X A3 O B3 B1 B2 A1 A2 Comm of Y Comm of X Changes in Price of Y Changes in Price of X Comm of X Comm of X Y A1 O X B3 B1 B2 A2 A1 O B Y Changes in money income, Prices and the BL Comm of Y Comm of Y
Assumptions of the Consumer Equilibrium: Assumptions of the Consumer Equilibrium Consumer Has fixed amount of money income. Intends to buy combination of 2 goods, X and Y. Has definite tastes and preferences. Hence has definite scale of preferences. Expressed through ICM. S of P remains same through out the analysis. Is rational and mazimizes his satisfaction Each of the goods X and Y is homogenous (identical characteristics) and divisible, so various combinations of these goods can be sold.
The consumer Equilibrium: The consumer Equilibrium Point e is the equilibrium point given the Budget line. Satisfaction is max when the MRS of x for y is just equal to the price of x to the price of y. Qt. of comm X Qt. of comm Y b a e M N
Consumer Optimum or Equilibrium: Consumer Optimum or Equilibrium The CE is attained when , given, his budget constraint, the consumer reaches the highest point in the IC. The indifference curve and the budget line together constitute the consumption behaviour. Graphically speaking, the two curves meet at a point where the indifference curve is tangent by the budget line to get an unique or internal solution. This point of tangency represents the highest level of preference obtained by a person given a fixed amount of money income. This point is also the point of optimum condition or utility maximization. In mathematics, the slopes of the indifference curve and the budget line are the same. Slope of the budget line = M R S in exchange = PX / PY Slope of the indifference curve = M R S in consumption = Y / X In equilibrium, PX / PY = Y / X file:///C:/Documents%20and%20Settings/Icbm-Sbe/Desktop/MUlecture.ppt#636,1,Slide 1
Slide 17: Alfred Marshall Sir John R. Hicks Vilfredo Federico Damaso Pareto
Slide 18: Francis Ysidro Edgeworth Sir Roy George Douglas Allen