12th June, 2012
MATHEMATICS FOR
ECONOMICS
Sharmini Balachandran, BA Hons (Cantab)
Mathematics For Economics
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Introduction: How important is Mathematics for
Economics?
Economics Interview Questions
How is Mathematics tested in an Economics
interview?
 Interview example questions
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Mathematics required for an Economics Degree
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Mathematics for Microeconomics
Mathematics for Macroeconomics
Econometrics
What can students do to prepare?
How Important is Mathematics for
Economics?
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You cannot avoid Maths in an Economics degree!
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Core elements: Pure Mathematics and Statistics
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Mathematics is part of an economist’s toolkit
Model economic relationships
 Demonstrate well-known empirical results
 Solve for economic equilibrium
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BUT an economist must also be able to interpret
results and evaluate conclusions
ECONOMICS INTERVIEW
QUESTIONS
How Are Maths Skills Tested At
Interview?
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‘On the spot’ mental arithmetic and brain teasers
Problem solving – Calculus with an economic
application
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Graphical interpretation
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Probability questions
‘On The Spot’ Maths
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Simple questions designed to test how quickly
candidates think
‘Curve ball’ questions that can get candidates
flustered
Question 1: What is 49 squared?
‘On The Spot’ Maths
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Solution 1
Look for shortcuts
2
4 9  (5 0  1)
2
 (5 0  1)(5 0  1)
 2 5 0 0  (2  5 0 )  1
 2500  100  1
 2401
Problem Solving – Economic
Applications

Use algebraic techniques and calculus to solve
economics problems
Linear and non-linear functions
 Linear programming
 Differentiation and integration
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Economics applications
Demand and supply analysis
 Profit maximization
 Calculate consumer or producer surplus
 Calculating elasticities

Demand And Supply

Question 2: Firm BA operates in the airline
industry, facing the following demand and supply
curves. p denotes price. q denotes quantity.
Demand:
p  1000  2 q
Supply:
p  200  2 q
Solve for the equilibrium price and quantity in
the airline industry.
Demand And Supply
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Solution 2: Solve using linear programming.
D S
1000  2 q  200  2 q
8 00  4 q
q*  2 0 0
Substituting equilibrium quantity into the
demand curve:
p  1000  (2  200 )
p*  600
Profit Maximisation
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Question 3: A monopolist faces the following
economic relationships:
Total Cost:
Total Revenue:
Demand Curve:
TC (q )  200 q  15 q
TR(q )  1200 q  10 q
p  1200  10 q
What output maximises its profit?
b) What is the profit-maximising price?
c) What is the firm’s maximal profit?
a)
2
2
Profit Maximisation
Solution 3: This is an optimisation problem
a) The monopolist sets MC=MR

M C (q )  TC '(q )  2 0 0  30 q
M R (q )  TR '(q )  1 2 0 0  2 0 q
 200  30 q  1200  20 q
50 q  1 00 0
q*  20
b) Substituting
q* into the demand curve:
p  1200  (10  20 )  1000
Profit Maximisation
c)
Profit is total revenue minus total cost,
therefore:
2
2
TR  TC  1 200 q  10 q  (2 00 q  15 q )
 1 000 q  25 q
2
Substituting in q*
2
 (1 0 0 0  2 0 )  2 5 (2 0 )
 20000  10000
 10000
Graphical Interpretation
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Candidates are given graphs and asked to
identify/describe the economic relationship
Explain or show how an economic relationship
can be modeled with mathematics
Draw the graph of a mathematical function
Total Revenue Curve
q
Graphical Interpretation
Question 4: Describe the relationship between
total revenue and sales (output)?
 What mathematical function would you use to
model this relationship?
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Solution 4: This is a quadratic function
Revenue is an increasing function up to output q and
decreasing thereafter
 Graph is an ‘inverted parabola’  we know that the
quadratic term must be negative
 The general form is:

TR (q )  a  bq  cq
2
Probability Questions
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Probability of multiple events occurring at once
Mutually exclusive events
 Independent events
 Conditional probability
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Expected values
Question 5: Firm ABC is a monopoly in the
electricity industry. The economy can be in a
‘boom’ phase or ‘recession’. The probability of a
boom is 0.4. ABC charges a price of £2 per watt in
a boom and charges £1 in a recession. What is the
expected price per watt of electricity?
Probability Questions
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Solution 5: The expected price is the probability
weighted mean of the price in the two scenarios
‘boom’ and recession.
E ( p )  (0.4  £2 )  (0.6  £1)  £1.40
MATHEMATICS REQUIRED
FOR AN ECONOMICS DEGREE
Mathematics for Microeconomics
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Consumer Theory
Indifference curves and budgetary constrainsts –
maximise utility with respect to a budget
 Intertemporal consumption decisions – allocating
consumption between time periods
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Producer Theory
Pricing and output decisions – profit maximisation
 Constant, increasing & decreasing returns to scale
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Mathematics For Macroeconomics
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Aggregate Supply & Demand
IS-LM framework – solve for equilibrium
 Intertemporal aggregate consumption
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Fiscal Policy
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Intertemporal government spending decisions
Monetary Policy
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Money demand and supply equilibrium
Econometrics
Descriptive statistics
 Linear Regression
 Time Series
 Hypothesis Testing
 Confidence Intervals
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What Can Students Do To Prepare?
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Choose the right A-Levels – too much Maths and
Statistics is never a bad thing!
Be comfortable with calculus
Preliminary reading in Mathematics before the
course starts is a must
Resources
Introductory Text
 ‘Mathematics for Economics and Finance –
Methods and Modelling’ – Anthony & Biggs
1st Year:
 ‘Mathematics for Economists – An introductory
textbook’ – Pemberton & Rau
2nd Year:
 ‘Mathematical Statistics with Applications’ –
Miller & Miller
 ‘Mathematics for Economists’ – Simon & Blume
(advanced)