ppt mathematical economics 2014 15
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Mathematical EconomicsTRANSCRIPT
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What is Mathematical Economics? &
How is it different from Econometrics?
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Econometrics deals with the study of empirical observations using statistical methods of estimation and hypothesis testing
Mathematical economics refers to the application of mathematics to the purely theoretical aspect of economics analysis with a little or no concern about such statistical problems as the errors of measurement of the variables under study.
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What are Variables, Constants & Parameters?
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In economic application we may distinguish between three types of equations
1. definitional equation: 𝜋 = 𝑅 − 𝐶
2. behavioral equations: 𝐶 = 75 + 10𝑄
3. equilibrium conditions: 𝑄𝑑 = 𝑄𝑠 or 𝑆 = 𝐼
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Types of Functions 1. Linear
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2. Quadratic
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3. Cubic
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4. Rectangular Hyperbolic
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5. Exponential Function
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Functions with one independent variable: 𝑦 = 𝑓(𝑥)
Functions with two or more independent variables: 𝑦 = 𝑔(𝑥, 𝑦)
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Equilibrium Analysis
It is a constellation of selected interrelated variables so adjusted to one another that no inherent tendency to change prevails in a model which they constitute.
The above mentioned equilibrium has relevance only in the context of the particular set of variables chosen, and if the model is enlarged to include additional variables, the equilibrium state pertaining to the smaller model will no longer apply
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E.g:
Translating a concept into a Mathematical Statement, where a model can be written as:
𝑄𝑑 = 𝑄𝑠
𝑄𝑑 = 𝑎 − 𝑏𝑃 (𝑎, 𝑏 > 0)
𝑄𝑠 = −𝑐 + 𝑑𝑃 (𝑐, 𝑑 > 0)
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The graphical presentation will be
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𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑑𝑦
𝑑𝑥 𝑜𝑓 14𝑥3 = 5𝑥3 + 9𝑥3
𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑑
𝑑𝑥7𝑥4 + 2𝑥3 − 3𝑥 + 37
𝐶 = 𝑄3 − 4𝑄2 + 10𝑄 + 75, 𝐶𝑎𝑙𝑐𝑢𝑙𝑡𝑎 𝑑𝐶
𝑑𝑄
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Product Rule:
Find out the derivative of 2𝑥 + 3 3𝑥2
𝐴𝑛𝑠: 18𝑥2 + 18
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Divisibility Rule
𝑑
𝑑𝑥
2𝑥−3
𝑥+1=
5
𝑥+1 2