This document discusses a short introduction to shadow prices used in cost-benefit analysis for projects and policies. Shadow pricing is important for conducting social cost-benefit analysis and accounts for market distortions.

1. SHADOW PRICE /
REDUCED PRICE
LINEAR PROGRAMMING

2. • J. Tinbergen defines it, “shadow prices are prices indicating the intrinsic or true
value of a factor or product in the sense of equilibrium prices. These prices may
be different for different time periods as well as geographically separate areas
and various occupations (in the case of labor). They may deviate from market
prices.”
Shadow price for resource i (denoted by y*i)
• A shadow price is commonly referred to as a monetary value assigned to
currently unknowable or difficult-to-calculate costs. It is based on the
willingness to pay principle - in the absence of market prices, the most
accurate measure of the value of a good or service is what people are
willing to give up in order to get it. Shadow pricing is often calculated on
certain assumptions and premises

3. Calculating shadow prices
The simplest way to calculate shadow prices for a critical
constraint is as follows:
Step 1: Take the equations of the straight lines that intersect at
the optimal point. Add one unit to the constraint concerned,
while leaving the other critical constraint unchanged.
Step 2: Use simultaneous equations to derive a new optimal
solution
Step 3: Calculate the revised optimal Contribution. The increase
is the shadow price for the constraint under consideration

4. Mini Z=5x1 + x2
s.t 2x1 +x2 ≥ 6
x1 + x2 ≥ 4
2x1 + 10x2≥ 20
Sol:-
Graphically solve the LPP and determine the optimal solution.
Calculate slack/surplus for each constraint.
Suppose x1 and x2 are required to be integers, what will be the optimal solution
be?
2x1+x2≥6
X1 X2
0 6
3 0
x1+x2≥4
X1 X2
0 4
4 0
2x1+10x2≥20
X1 X2
0 2
10 0
(x1,x2) Z=5x1+x2
(0,6) 6
(2,2) 12
(1.5,2.5) 10
(10, 0) 50

5. STANDARD FORM
Z-5x1-x2=0
2x1+x2-s1=6
X1+x2-s2=4
2x1+10x2-s3=20
Substituting the optimal solution
S1=0
S2=2
S3=40
Binding
Non binding
Non binding
Shadow Price In MINI
Dual price= -shadow price
Increase by 1
2x1+x2=7
X1=0, x2=7
Sp1= Z1-Z= 7-6=1
Dp1 =-1
If constraint is non binding, it have 0
shadow price