EC1030 MATHEMATICS
Prof. Patrick Paul Walsh
Room: 2018 Arts Building
www.tcd.ie/economics/staff/ppwalsh
Course Outline
This course reviews basic mathematical concepts and illustrates these concepts with
examples from economics. Lectures are three hours per week for 10 weeks.
A course manual has been prepared for this course, which includes, exercise and
answer sheets covering each topic. It is essential that each student following the
course obtain a copy of this, which can be purchased from 3014, Economics
Department, Arts Building. The primary text for this course is,
I. Jacques, Mathematics for Economics and Business, fifth ed., Addison Wesley,
2006.
Tutorials
Tutorials will be based on the even questions included in the Course Manual (you
only have the solutions to odd questions). Students are expected to do selected even
questions before the tutorial. This is an essential part of the curriculum, 20 % of the
grade for the course. Remaining even questions will be covered in lectures.
Assessment
In addition to the final exam 60 per cent of course, one and a half-hour test will be
held at Easter, 20 per cent of course. Tests and the final exam will be based on
material covered in lectures/tutorials.
Course Outline
Mathematical Functions (Topic 1)
Linear Functions
Quadratic Functions
Linear Economic Models (Topic 2)
Market Equilibrium
Market Equilibrium with Excise Tax
National Income Determination in Macro Economy
Matrices (Topic 3)
Vector and Matrix Notation (from Topic 2 in Manual)
Calculation of a Determinant
Calculation of a cofactor Matrix
Calculation of an Adjoint Matrix
The Inverse Matrix
Sequences and Series (Topic 4)
Indices
Logarithms
Differentiation (Topic 5)
The Slope of a Function
Definition of a Derivative
Rules for Differentiating
Elasticity
Maximisation and Minimisation (Topic 6)
Stationary Points
Second Order Conditions
Integration (Topic 7)
AntiDifferentiation
The Indefinite Integral
Definite Integrals
Consumers’ Surplus
Summation of a Continuous Flow
Discounted Present Value of a Continuous Flow
Functions of Several Variables (Topic 8)
Some Examples
Partial Differentiation
Total Differential
Chain Rule
Partial Elasticities
Optimisation of a Function of Two Variables
Production and Costs (Topic 9)
Production Functions and Marginal Products
Returns to Scale
Homogenous Functions
Profit Maximisation
Cost Minimisation (constrained optimisation)
Cost Curves
Cost Curves and Returns to Scale
Utility and Demand (Topic 10)
Utility Maximisation subject to Budget Constraint
Constrained Optimisation: The Lagrange Multiplier Method
The Linear Expenditure System