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Introduction and the Role of Mathematics in
Economics
Is Economics a Science?
Mathematics is for Describing Human Behavior in Economics
Is Economics a Science?
Physics: Descriptive science
Galileo: How and How much
Economics: Descriptive part Normative part
What ought to be: how things should be Assumptions about what is “rightright”
Deontological Teleological
Is Economics a Science?
Physics: Descriptive science
Galileo: How and How much
Economics: Descriptive part Normative part
What ought to be: how things should be Assumptions about what is “rightright”
Deontological Teleological
Lionel Robbins 1932. An Essay on the Nature and Significance of Economic Science.
“The economist is not concerned with ends as such. He is concerned with the way in which the attainment of ends is limited. The ends may be noble or they may be base. They may be “material” or” immaterial” –if ends can be so described. But if the attainment of one set of ends involves the sacrifice of others, then it has an economic aspect” (Robbins, 1932, p. 25).
The Difference between Economics and Management Economics
“The economist is not concerned with ends as such. He is concerned with the way in which the attainment of ends is limited. The ends may be noble or they may be base. They may be “material” or” immaterial” –if ends can be so described. But if the attainment of one set of ends involves the sacrifice of others, then it has an economic aspect” (Robbins, 1932, p. 25).
Management Ends:
Profit Share of consumers Prestige
Case Behavior 2:
A student has 500€ for her monthly expenditures
200
150
€
Room
Food
150
Others
Cleanliness
Clothes
Entertainment
Toothpaste, Soap, Dish cleaning, … 20€
1 T-shirt (20€), 1 trousers (20€), 1 pullover (20€) 60€
2*movie (30€), 3*Shamrock (40€) 70€
52€
VWL-Book
30€
Friend’s Happy B
How to manage the budget?
A Comparison
1 2
2
x
# Sheep
Clothes: 3 1 Save 40€
Movie: 2 1 Save 15€
Shamrock: 3 1 Save 25€
Food: 150€ 140€ Save 10€
=
P( ) =
P( ) P( )
1 2
Similarities ScarcityScarcity
European lacks sheep, African lacks tobacco The student doesn’t have enough money
Allocation and ReallocationAllocation and Reallocation Two sticks less for one sheep One sheep less for two sticks The student tries to reallocate the goods acquired with money
SatisfactionSatisfaction The European feels better with one sheep and two less sticks The African feels better with one sheep less but two sticks The student tries to preserve her level of satisfaction with small
changes. She reduces just marginally the levels of consumption of some
goods.
Decisions at the Margin and Satisfaction Exchange at the Margin
The European has many tobacco sticks and is willing to give two sticks.
The African has some sheep and is willing to give one sheep.
Reallocation at the Margin
The student is willing to reduce to some extent the consumption of some goods for other uses of money.
Satisfaction
The European and the African try to increase their levels of satisfaction with a marginal exchange.
The student tries to maintain her level of satisfaction with a marginal decrease of the consumption of some goods.
Decisions at the Margin and Mathematical Language (Exchange)
Exchange Scarcity Allocation Max. Satisfaction
U(Eur)
A B
U(A)
U(B)
Sheep
U(Goods) U(B) = U(A) + ƒ * (B - A)
U(B) - U(A) = ƒ * (B - A)
U(B) - U(A)(B - A)ƒ =
U(B) - U(A)
B - A
Decisions at the Margin and Mathematical Language (Exchange)
A more general (and formal) approach Given that U (the function of satisfaction) has a form (equation), what
is the marginal increase in the satisfaction at any given point of U?
I.e. what is the form of the function ƒ for any point A?
U(Eur)
A B
U(A)
U(B)
Sheep
U(Goods)
U(B) - U(A)(B - A)ƒ =
U(B) - U(A)
B - A
ƒ is a tangent!
Decisions at the Margin and Mathematical Language (Exchange)
ƒ is more than a tangent
U(B) - U(A)(B - A)ƒ =
A
U
The process of decreasing the horizontal distance in order to find the right value of the tangent is represented by a limit.
Lim B A
“Limit when B tends to A of ƒ”
U(B) - U(A)(B - A)ƒ = = U’
ƒ is the derivative of U
Decisions at the margin are represented by derivatives
Calculus is the mathematical language of Economics
Decisions at the Margin and Mathematical Language (Reallocation)
Scarcity (re)allocation max. satisfaction
xx
yy
xk
yk
x1
y1
The reallocation of EntertainmentEntertainment
Let denote xx = units of movie, yy = units of party
The Problem:Given an initial allocation (x1,y1) for party and movie, find the set (x2,y2) that less decreases the current level of satisfaction. (x1,y1)
U1U0
U1>U0
U2
U2>U1