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Revealed preference theory.docx

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Satya Narayana

(1) Revealed preference theory, pioneered by Paul Samuelson, analyzes consumer choice and behavior based on actual choices made between bundles rather than assumed utility functions. (2) It establishes that a consumer's preferences are rational if they satisfy the weak axiom of revealed preference (WARP) and its strengthened version, the strong axiom of revealed preference (SARP). (3) Consumer surplus measures the difference between the maximum price consumers would be willing to pay for a good or service and the actual market price, representing the extra satisfaction consumers receive from purchasing the good.

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SEMINAR TOPIC:- REVEALED PREFERENCE THEORY & CONSUMER SURPLUS Submitted to:- Dr. Anandamoy Mondal Miss A. Sanyal Submitted by:- Satyanarayana Boda 1st year MFSc F.E.C 501 Dept.of fisheries economics and statistics 9/15/2015Dept.ofF.E.S,F.F.SC,W.B.U.A.F.S
REVEALED PREFERENCE Pioneered by American economist Paul Samuelson. Used analyze choice made by consumer. Policies on consumer behavior. Preference depend on habits. ORIGIN OF THE THEORY. Older theories depends on diminishing marginal rate of substitution (MRS). Means to reconcile demand theory by defining utility functions by observing behaviour.9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
(x1, x2) is chosen when (y1, y2) could have been chosen: p1x1+p2x2p1y1+p2y2 (x1, x2) is directly revealed preferred to (y1, y2).9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Suppose there is a unique optimal bundle for each budget set; Suppose the consumer always chooses the most preferred bundle he/she can afford; Suppose the consumer has chosen (x1, x2) when faced by (p1, p2); Suppose p1x1+p2x2p1y1+p2y2; we must have 1 2 1 2( , ) ( , )x x y y 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Contd. Suppose the consumer has chosen (y1, y2) when faced by (q1, q2); Suppose q1y1+q2y2q1z1+q2z2; Then we know that 1 2 1 2 1 2 1 2( , ) ( , ) and ( , ) ( , )x x y y y y z z From transitivity we can conclude that: 1 2 1 2( , ) ( , )x x z z (x1, x2) is indirectly revealed preferred to (z1, z2). 1 2 1 2 1 2 1 2( , ) ( , ) and ( , ) ( , )x x y y y y z z 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
(x1, x2) is indirectly revealed preferred to (z1, z2). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
WARP: If (x1, x2) is directly revealed preferred to (y1, y2); and (x1, x2)(y1, y2); Then (y1, y2) cannot be directly revealed preferred to (x1, x2). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
SATISFACTION OF WARP Example of coke and Pepsi. conclusion Consumer should have consistent preferences. (Y1, Y2 ) & (Z1, Z2 ) non profit maximizing consumers. If (Y1, Y2 ) RP to (Z1, Z2 ) & (Y1, Y2 ) (Z1, Z2 ) then it cant happen that (Z1, Z2 ) RP to (Y1, Y2 ). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
MATHEMATICAL EXPRESSION OF WARP At price p1 & p2 ( P1 Y1 + P2 Y2 ) > or = (P1 Z1 + P2 Z2 ) At price Q1 &Q2 if (Z1, Z2 ) bundle is chosen then it cant be the case that (Q1 Z1 + Q2 Z2 ) > or = (Q1 Y1 + Q2 Y2 ) 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Checking on WARP Assume that Bundles Price X={2,2,2} P={2,2,2} X={3,1,2} P={1,3,2} X={4,1,1.5} P={2,1.5,5} B/W X &X PX=12 PX=12 PX=12 PX=10 So PX<PX WARP is satisfied X is p X B/W X &X PX=10 PX=17.5 PX=10 PX=17 So PX<PX WARP is satisfied X IS P X 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
B/W X &X PX=17 PX=13 PX=17 PX=12 SO PX<PX WARP is satisfied X Is P X Finally XPXPXPX it is violating WARP and transitivity law. XPX &XPX = XPX To come up this problem SARP is formulated. CONTD.. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
SARP: If (x1, x2) is (directly or indirectly) revealed preferred to (y1, y2); and (y1, y2)(x1, x2); Then (y1, y2) cannot be (directly or indirectly) revealed preferred to (x1, x2). SARP is both necessary and sufficient for rational consumer behavior. For any finite set of bundles x1,x2,x3........... xn-1xn if x1 RP x2 x2 RP x3 ........ xn-1 RP xn then xn is not RP x1. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Excess of the price which a consumer would be willing to pay rather that go without a thing over that which he actually does pay, is the economic measure of surplus satisfaction. (Marshall) Important to implement policies like 1.Taxation. 2.Price policy by monopolist. This is the extra satisfaction for same price. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Derived from law of diminishing marginal utility. Consumers surplus = What a consumer is prepared to pay - What he actually pays. = Sum of marginal utility - (Price x No. of units purchased). Consumers Surplus =Total Utility (Number of Units of a Commodity Purchased * Price of the Commodity). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
PRICE (IN RS/KG.) NO.OF BUYERS QUANTITY DEMANDED(KG) 100 1 1 80 2 2 60 3 3 40 4 4 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
MATHEMATICAL EXPRESSION Calculate consumer surplus at price 40. C.S of 1st buyer = 100 40= 60. C.S of 2nd buyer = 80 40= 40. C.S of 3rd buyer = 60 40= 20. Total C.S = 60+40+20=120. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
Importance of Consumers Surplus 1) Distinction between value- in-use and value-in-exchange. 2) Helpful to monopolist in price fixation. 3) Helpful to policy makers. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S

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Revealed preference theory.docx

  • 1. SEMINAR TOPIC:- REVEALED PREFERENCE THEORY & CONSUMER SURPLUS Submitted to:- Dr. Anandamoy Mondal Miss A. Sanyal Submitted by:- Satyanarayana Boda 1st year MFSc F.E.C 501 Dept.of fisheries economics and statistics 9/15/2015Dept.ofF.E.S,F.F.SC,W.B.U.A.F.S
  • 2. REVEALED PREFERENCE Pioneered by American economist Paul Samuelson. Used analyze choice made by consumer. Policies on consumer behavior. Preference depend on habits. ORIGIN OF THE THEORY. Older theories depends on diminishing marginal rate of substitution (MRS). Means to reconcile demand theory by defining utility functions by observing behaviour.9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 3. (x1, x2) is chosen when (y1, y2) could have been chosen: p1x1+p2x2p1y1+p2y2 (x1, x2) is directly revealed preferred to (y1, y2).9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 4. Suppose there is a unique optimal bundle for each budget set; Suppose the consumer always chooses the most preferred bundle he/she can afford; Suppose the consumer has chosen (x1, x2) when faced by (p1, p2); Suppose p1x1+p2x2p1y1+p2y2; we must have 1 2 1 2( , ) ( , )x x y y 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 5. Contd. Suppose the consumer has chosen (y1, y2) when faced by (q1, q2); Suppose q1y1+q2y2q1z1+q2z2; Then we know that 1 2 1 2 1 2 1 2( , ) ( , ) and ( , ) ( , )x x y y y y z z From transitivity we can conclude that: 1 2 1 2( , ) ( , )x x z z (x1, x2) is indirectly revealed preferred to (z1, z2). 1 2 1 2 1 2 1 2( , ) ( , ) and ( , ) ( , )x x y y y y z z 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 6. (x1, x2) is indirectly revealed preferred to (z1, z2). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 7. WARP: If (x1, x2) is directly revealed preferred to (y1, y2); and (x1, x2)(y1, y2); Then (y1, y2) cannot be directly revealed preferred to (x1, x2). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 8. SATISFACTION OF WARP Example of coke and Pepsi. conclusion Consumer should have consistent preferences. (Y1, Y2 ) & (Z1, Z2 ) non profit maximizing consumers. If (Y1, Y2 ) RP to (Z1, Z2 ) & (Y1, Y2 ) (Z1, Z2 ) then it cant happen that (Z1, Z2 ) RP to (Y1, Y2 ). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 9. MATHEMATICAL EXPRESSION OF WARP At price p1 & p2 ( P1 Y1 + P2 Y2 ) > or = (P1 Z1 + P2 Z2 ) At price Q1 &Q2 if (Z1, Z2 ) bundle is chosen then it cant be the case that (Q1 Z1 + Q2 Z2 ) > or = (Q1 Y1 + Q2 Y2 ) 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 10. Checking on WARP Assume that Bundles Price X={2,2,2} P={2,2,2} X={3,1,2} P={1,3,2} X={4,1,1.5} P={2,1.5,5} B/W X &X PX=12 PX=12 PX=12 PX=10 So PX<PX WARP is satisfied X is p X B/W X &X PX=10 PX=17.5 PX=10 PX=17 So PX<PX WARP is satisfied X IS P X 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 11. B/W X &X PX=17 PX=13 PX=17 PX=12 SO PX<PX WARP is satisfied X Is P X Finally XPXPXPX it is violating WARP and transitivity law. XPX &XPX = XPX To come up this problem SARP is formulated. CONTD.. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 12. SARP: If (x1, x2) is (directly or indirectly) revealed preferred to (y1, y2); and (y1, y2)(x1, x2); Then (y1, y2) cannot be (directly or indirectly) revealed preferred to (x1, x2). SARP is both necessary and sufficient for rational consumer behavior. For any finite set of bundles x1,x2,x3........... xn-1xn if x1 RP x2 x2 RP x3 ........ xn-1 RP xn then xn is not RP x1. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 13. Excess of the price which a consumer would be willing to pay rather that go without a thing over that which he actually does pay, is the economic measure of surplus satisfaction. (Marshall) Important to implement policies like 1.Taxation. 2.Price policy by monopolist. This is the extra satisfaction for same price. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 14. Derived from law of diminishing marginal utility. Consumers surplus = What a consumer is prepared to pay - What he actually pays. = Sum of marginal utility - (Price x No. of units purchased). Consumers Surplus =Total Utility (Number of Units of a Commodity Purchased * Price of the Commodity). 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 15. PRICE (IN RS/KG.) NO.OF BUYERS QUANTITY DEMANDED(KG) 100 1 1 80 2 2 60 3 3 40 4 4 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 16. MATHEMATICAL EXPRESSION Calculate consumer surplus at price 40. C.S of 1st buyer = 100 40= 60. C.S of 2nd buyer = 80 40= 40. C.S of 3rd buyer = 60 40= 20. Total C.S = 60+40+20=120. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 17. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 18. Importance of Consumers Surplus 1) Distinction between value- in-use and value-in-exchange. 2) Helpful to monopolist in price fixation. 3) Helpful to policy makers. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S
  • 19. 9/15/2015 Dept. of F.E.S, F.F.SC, W.B.U.A.F.S