Summary

Summary Quantitative Modelling 1 Department of Decision Sciences 2023 This is the only study guide for DSC1520

1 purchase

Course
DSC1520

Institution
DSC1520

Quantitative Modelling 1 Department of Decision Sciences 2023 This is the only study guide for DSC1520

[Show more]

Preview 4 out of 210 pages

View example

Uploaded on September 1, 2023
Number of pages 210
Written in 2023/2024
Type Summary

quantitative modelling 1
semesters 1 and 2
department of decision sciences
this is the only study guide for dsc1520

Institution DSC1520
Course DSC1520

ConvenientLearning Member since 4 year 210 documents sold

$19.99

Add to cart

Add to wishlist

100% satisfaction guarantee
Immediately available after payment
Both online and in PDF
No strings attached

DSC1520/001/4/2023

SG001/4/2023

Quantitative Modelling 1
DSC1520

Semesters 1 and 2

Department of Decision Sciences

This is the only study guide for DSC1520.

Bar code

,Contents

1 Introduction 1

1.1 The module ............................................................................................................................................ 1

1.1.1 Knowledge assumed to be in place .......................................................................................... 1

1.1.2 Notation ...................................................................................................................................... 2

1.1.3 Software ...................................................................................................................................... 2

1.1.4 Activities.....................................................................................................................................2

1.2 Modelling ................................................................................................................................................ 3

1.2.1 Development of a mathematical model ................................................................................... 3

I Linear functions 5

2 Applications of linear functions 6

2.1 Revenue, cost and profit ....................................................................................................................... 6

2.1.1 Cost ............................................................................................................................................. 6

2.1.2 Revenue....................................................................................................................................... 7

2.1.3 Profit ........................................................................................................................................... 7

2.2 Demand and supply ............................................................................................................................... 9

2.2.1 Demand ..................................................................................................................................... 10

2.2.2 Supply .......................................................................................................................................11

2.3 Price elasticity of demand and supply ................................................................................................ 13

2.3.1 Price elasticity of demand ....................................................................................................... 14

2.3.2 Price elasticity of supply .......................................................................................................... 16

ii

3 Applications of simultaneous functions 17

, 3.1 Equilibrium ..........................................................................................................................................17
3.1.1 Equilibrium in the goods market ............................................................................................ 17
3.1.2 Equilibrium in the labour market............................................................................................ 18
3.1.3 Price controls and government intervention in markets ....................................................... 19
3.1.4 Complementary and substitute goods .................................................................................... 22
3.1.5 Taxes and subsidies ................................................................................................................. 24
3.2 Break-even analysis.............................................................................................................................. 27
3.3 Consumer and producer surplus ......................................................................................................... 28
3.3.1 Consumer surplus .................................................................................................................... 28
3.3.2 Producer surplus ...................................................................................................................... 29
3.3.3 Total surplus ............................................................................................................................. 30
3.4 Linear programming ............................................................................................................................. 31

II Non-linear functions 39

4 Applications of non-linear functions 40
4.1 Non-linear functions in economics ..................................................................................................... 40
4.2 Quadratic functions ............................................................................................................................. 41
4.2.1 Optimising quadratic revenue, profit and cost functions ...................................................... 42
4.2.2 Market equilibrium .................................................................................................................. 45
4.2.3 Break-even analysis.................................................................................................................. 46
4.3 Cubic functions ..................................................................................................................................... 48
4.4 Exponential and logarithmic functions ............................................................................................... 49
4.4.1 Unlimited growth ..................................................................................................................... 50
4.4.2 Limited growth ......................................................................................................................... 51
4.4.3 Logistic growth ......................................................................................................................... 51
4.5 Hyperbolic functions ............................................................................................................................ 53

III Differentiation 56

5 Differentiation theory 57
5.1 Slope of a curve and differentiation ................................................................................................... 57
5.2 Differentiation rules ............................................................................................................................. 59
5.2.1 The power rule for differentiation .......................................................................................... 60

5.2.2 Exponential and natural logarithmic functions ...................................................................63
5.2.3 The chain rule .......................................................................................................................... 63

, 5.2.4 The product rule ...................................................................................................................... 65
5.2.5 The quotient rule ..................................................................................................................... 67
5.3 Higher derivatives ................................................................................................................................ 69
5.4 Optimisation of functions in one variable .......................................................................................... 70
5.4.1 The nature of stationary points .............................................................................................. 72
5.4.2 Intervals along which a function is increasing or decreasing ................................................ 73
5.4.3 Sketching functions using differentiation ............................................................................... 75

6 Applications of differentiation 77
6.1 Marginal and average functions ......................................................................................................... 77
6.1.1 Marginal revenue ...................................................................................................................... 78
6.1.2 Marginal cost............................................................................................................................ 78
6.1.3 Average revenue and cost functions ...................................................................................... 79
6.1.4 Production functions ................................................................................................................ 82
6.2 Optimisation of economic functions ..................................................................................................... 83
6.3 Elasticity of demand – non-linear demand functions ........................................................................ 89

IV Integration 92

7 Integration theory 93
7.1 Integration as the reverse of differentiation ...................................................................................... 93
7.2 Integration rules ................................................................................................................................... 94
7.2.1 The power rule for integration ............................................................................................... 94
7.2.2 Integration by substitution ...................................................................................................... 96
7.3 The definite integral and the area under a curve............................................................................ 100

8 Applications of integration 105
8.1 From marginal to total functions ...................................................................................................... 105
8.1.1 Total cost from marginal cost ............................................................................................... 105
8.1.2 Total revenue from marginal revenue .................................................................................. 106
8.1.3 Rate of change to total quantity........................................................................................... 106
8.2 Consumer and producer surplus ....................................................................................................... 109
8.2.1 Consumer surplus .................................................................................................................. 109

8.2.2 Producer surplus .................................................................................................................... 111

8.2.3 Total surplus ........................................................................................................................... 112

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller ConvenientLearning. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $19.99. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

69252 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 15 years now

Start selling

Summary

Summary Quantitative Modelling 1 Department of Decision Sciences 2023 This is the only study guide for DSC1520

Document information

Subjects

Written for

Seller

Reviews received

Content preview