General Overview about Quantitative techniques application in Economic.

1. USE OF QUANTITATIVE
TECHNIQUES IN
ECONOMICS
Mr. P. Balaji

2. Topics
 Comparative static Analysis
 Linear Programming
 Game theory

3. 1. Comparative static analysis
 It used to compare various points of equilibrium when
certain factors change.
 It used to compare two different economic outcomes,
before and after a change in some underlying
exogenous parameter
 A form of sensitivity or what-if analysis.

4. Market equilibrium

5. Market equilibrium
• Assume all variables are
constant except demand.
• If demand shift upper, then
market will reach high
equilibrium price and
quantity.
• What happen if demand
decreases ?
• How it reach new
equilibrium point?

6. Market equilibrium
• Assume all variables are constant
except supply.
• If supply increases, then market
will reach new equilibrium price
and quantity.
• What happen if supply
decreases ?
• How it reach new equilibrium
point? And where it reaches?

7. What if
What happens if
 New sellers may enter a market
 Existing sellers may exit from a market
Comparative static analysis (How?)

8. Comparative Static Analysis
 Step 1: Model the system by using system of
equations.
System
Input Output
Exogenous
Variables (Ex:
Price of Product)
Endogenous
Variables (Ex:
Demand of
product)
System of
equations

9. Comparative Static Analysis
 If exogenous variables changes, the endogenous
variables will change
 Comparative static analysis examines how these
changes occur.

10. Example : Market for Product
 A market is one whereby parties engage in exchange.
 First step is to develop a system of equation for market.
 First develop an system of an equation to describe the
behavior of buyers.
 Second develop an system of an equation to describe the
behavior of sellers.
 Finally Develop an system of an equation to describe the
interaction of buyers and sellers.

11. Buyers
 Many factors affect willingness of buyer to buy a product but consider only
two; price of product(P) and income of buyer(Y).
D= aY-bP ,a>0, b>0 (derived from theory)
 D denote the demand for the product (i.e., the amount of the product which
buyers wish to buy.
 a and b are sensitive parameters (Constants).
 a measures sensitivity of demand to change in income.
 b measures sensitivity of demand to change in price.

12.  Let Y = 100, P = 3, a = .5, and b = 2. then D =
(.5)(100) - (2)(3) = 44.
 Now, note that if Y increases by 1 (from 100 to 101)
then D increases by a = .5 (from 44 to 44.5),
 while if P increases by 1 (from 3 to 4) then D
decreases by b = 2 (from 44 to 42).
 If a gets larger, demand becomes more responsive to a
change in income.
 If b gets larger, demand becomes more responsive to a
change in price.

13. (ii)Sellers, (iii) Interaction between seller
and buyer
S= cP, c>0
 S denote the supply of the product (i.e., the amount
of the product which sellers wish to sell)
S* = D*

14. Second step: Classify the variables
 Identify the endogenous variables in model. The
number of endogenous variables should be equal to
the number of independent (or nonequivalent)
equations in the model. (output)
 Classify the remaining variables as exogenous
variables

15. Variables
 Endogenous variables
 Demand (it depends on income and price)
 Supply (it depends on price)
 Price ( In eq 3, at equilibrium condition together with
demand and supply, determine price P*)
 Exogenous variables
 Y, a, b, c ( doesn‟t depends on anything)

16. Third step: Isolate endogenous variables
on one side
 Solve the model by starting with equilibrium point
Substitute P value in Demand equation

17. Fourth step: Find Comparative static
multiplier
 It gives the change in a chosen endogenous variable when a chosen
exogenous variable increases by one unit.
 It indicates one unit increase in income leads to increase in P of (a/b + c).
 If a = .5, b = 3, and c = 2 result would indicate that, one rupees increase in
income leads to increase the product price of .1 rupees.

18. As Y increases from Y1 to Y2, the equilibrium price level increases from P1 to
P2.
• A total of 12 comparative static
multipliers can be calculated.
• 4 endogenous and 3 exogenous
variable, so 12 comparative static
multiplier we can calculate and
interpret.

19. 2. Linear Programming
 Management decisions in many organizations involve trying
to make most effective use of resources (machinery, labor,
money, time, warehouse space, and raw materials) in order
to produce products or provide services.
 Ex: A firm want to maximize its profit. But workers and
resources are limited.
 Linear programming offers algorithm to compute optimum
way to allocate resource such that output gets maximized or
minimized.

20. Basic Steps to Solve LP Problems
Formulation
 Process of translating problem scenario into simple LP model framework with a
set of mathematical relationships.
Solution
 Mathematical relationships resulting from formulation process are solved to
identify optimal solution.
Interpretation and What-if Analysis
 Problem solver or analyst works with the manager to Interpret results and
implications of problem solution.
 Investigate changes in input parameters and model variables and impact on
problem solution results.

21. Problem
 How many bowls and mugs should be produced to
maximize profits given labor and materials constraints?
 Product resource requirements and unit profit:
 Total labor hours available is 40 hours and total clay is
120 lb.

22. Formulation
Maximize Z = 40X1 + 50X2
subject to:
1X1 + 2X2 ≥ 40
4X1 + 3X2 ≥ 120
X1, X2 ≥ 0

23. Solution
 Graphical Approach
 Simplex Algorithm

24. Optimal point
 Optimal solution is the point in feasible region that produces
highest profit
 There are many possible solution points in region.
 How do we go about selecting the best one, one yielding
highest profit?
 Let objective function (that is, $$40x1 + $50x2) guide one
towards optimal point in feasible region.
 Plot line representing objective function on graph as a
straight line.

25. Optimal Points
 It is a very important property of Linear Programming
problems: This property states optimal solution to LP problem
will always occur at a corner point.
 It is possible to do what if analysis: what
happen if you increases bowls and mugs
prices.

26. 3. Game theory
The analysis of competitive situations (or situations of
conflict) using mathematical models
Economist use it for auctions, bargaining, merger pricing,
oligopolies etc.

27. Key ingredients of Game theory
 One or more players – participants, each may be an individual, a group or
organisation, a machine, and so on.
 One or more moves (or choices) – where a move is an action carried out
during the game, including chance moves (when “nature plays a hand”) as in
the toss of a coin.
 A set of outcomes – where an outcome is the result of the completion of one
or more moves
[e.g. game of chess may end in checkmate or a draw]
 Payoff – an amount received for a given outcome.
 Finally, a set of rules which specify the conditions for the players, moves,
outcomes and payoffs.

28. Game theory
What is it about?
 Fundamentally about the study of decision-making
 Investigations are concerned more with choices and
strategies than „best‟ solutions.
It seeks to answer the questions:
 What strategies are there?
 What kinds of solutions are there?

29. Defining Games
 Two ways of representation
 Matrix form: List what payoffs get as a function of their
actions
 It is as if players moved simultaneously
 Extensive Form: Includes timing of moves
 Players move sequentially, represented as a tree
 Chess: white player moves, then black player can see white‟s move
and react...
 Keeps track of what each player knows when he or she makes
each decision

30. Example 1: Matching Pennies
 Two player game. One player want to match, other
want to mismatch
(1,-1) (-1,1)
(-1,1) (1,-1)
Head Tail
Player 1
Player 2

31. Coordination Game
(1,1) (0,0)
(0,0) (1,1)
Left Right
Player 2
Player 1
Which side of the road you take?
Both players have same interest

32. Battle of Sexes
 Cooperation and Competition
(2,1) (0,0)
(0,0) (1,2)
Boy Friend
Girl Friend
Immortal Titanic