basics of micro economics

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
9/15/2015Dept.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+p2x2≥p1y1+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+p2x2≥p1y1+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+q2y2≥q1z1+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
can’t 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 P’X=12
PX’=12 P’X’=10
So P’X’<P’X WARP is satisfied
 X is p X’
B/W X’ &X”
P’X’=10 P”X’=17.5
P’X”=10 P”X”=17
So P”X”<P”X’ 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”
P”X”=17 PX”=13
P”X=17 PX=12
SO PX<PX” WARP is satisfied
X” Is P X
Finally XPX’PX”PX it is violating WARP and
transitivity law.
XPX’ &X’PX” = 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.
 Consumer’s surplus = What a consumer is prepared to pay -
What he actually pays.
= Sum of marginal utility - (Price x No. of units purchased).
 Consumer’s 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 Consumer’s
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