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Transcript
```Some Economic applications
of one variable functions.
Martin Fajkus
Faculty of applied informatics
Tomas Bata University in Zlin
A: Small motivation
How to fence a garden
!
S = 𝑚𝑎𝑥
c = 100
S = 5 · 90 = 450
S = 30 · 40 = 1200
S = 40 · 20 = 800
A: Small motivation
How to fence a garden
!
S = 𝑚𝑎𝑥
c = 100
S = 𝑎. 𝑏
c = 2𝑎 + 𝑏 = 100
𝑏 = 100 − 2𝑎
S = 𝑎. (100 − 2𝑎)
S = 100𝑎 − 2𝑎2
!
S ´ = 100 − 4𝑎 = 0
𝑎 = 25
𝑏 = 100 − 2.25
𝑏 = 50
Smax = 25·50 = 1250
B: Economic applications
I. Basic functions of economic analysis
I. A. – utility function
I. Basic functions of economic analysis
I. A. – utility function; surplus
Consumer surplus
I. Basic functions of economic analysis
Co-ordinate axes
x-axis ⟷ x (or q) – QUANTITY
y-axis ⟷ p
– PRICE
I. B. – demand and supply
Demand
p = d(x)
⟷
Supply
x = D(p)
Usually decreasing:
With higher price people want to buy less.
p = s(x)
⟷
x = S(p)
Usually increasing:
With higher price producers want to produce more.
Demand function
(copies marginal utility of the buyer)
Market equlibrium; surplus and shortage
supply
demand
I. Basic functions of economic analysis
I. C. – costs, revenue; profit
FIXED
VARIABLE
TOTAL
COSTS
FC
VC(x)
TC(x) = FC + VC(x)
REVENUE
FR
VR(x) = p.x
TR(x) = FR + VR(x)
PROFIT
FP
VP
TP(x) = TR(x) − TC(x)
AVERAGE
𝐴𝐶 =
𝑇𝐶
𝑥
𝐴𝑅 =
𝑇𝑅
𝑥
𝐴𝑃 =
𝑇𝑃
𝑥
```