MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 4: The cobweb model and derivatives
Exercise 1. See worked example 4.3 of the Anthony & Biggs book. Given a principal, P , inve
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 3: Recurrence equations and limits
Exercise 1. Excise tax is discussed in section 1.4 of the Anthony & Biggs book. See also wor
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 2: Recurrence equations and limits
Extra Exercise 1. The supply and demand sets are sketched in Figure 1(a) and the equilib
MA107: Quantitative Methods (Mathematics) 201516
Solutions to sample examination question 1
(a) The recurrence equation
2yt 3yt1 + 1 = 0
and to solve this, because a =
which is given by
3
2
can be rew
MA107: Quantitative Methods (Mathematics) 201516
Exercises 9: Linear equations and inverse matrices
For all homeworks in this course please note that no marks will be given for answers only. Always
sh
MA107: Quantitative Methods (Mathematics) 201516
Exercises 10: Integration and Differential equations
For all homeworks in this course please note that no marks will be given for answers only. Always
MA107: Quantitative Methods (Mathematics) 201516
Sample examination question 1
Advice: Read the question, take a look at your notes and then, having put your notes away, do the
question. To get maximu
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 8: Consumer choice; vectors and matrices
Exercise 1. For information about contours and their gradients see section 12.3 of the
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 6: Partial derivatives
Exercise 1. By now, the rules of dierentiation should be more or less known. If not, see sections
6.2 an
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Extra Exercises 7: Stationary points and Lagrangeans
Extra Exercise 1. The first-order partial derivatives of the function are
fx = 9x2 +
MA107: Quantitative Methods (Mathematics) 201516
Answers for Exercises 9: Linear equations and inverse matrices
Exercise 1. Information about matrix operations and how to solve systems of linear equat
MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2016)
Question 1.
(a) As supply is determined by the equation p 3q = 2 we have
q S (p) =
p2
3
and
pS (q) = 2 + 3q,
whereas since
[SE
2000 examination
MA107
Quantitative Methods (Mathematics)
(Half Unit)
Instructions to candidates
Time allowed: 2 hours.
This paper contains 5 questions. You may attempt as many questions as you wi
[SE
2001 examination
MA107
Quantitative Methods (Mathematics)
(Half Unit)
Instructions to candidates
Time allowed: 2 hours.
This examination paper contains 5 questions. You may attempt as many questio
Summer 2003 examination
MA107
Quantitative Methods
(Mathematics)
(Half unit)
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This examination paper contains 5 questions. Y
Summer 2005 examination
MA107
Quantitative Methods (Mathematics)
Half unit
Suitable for all candidates
instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt
MA107: Quantitative Methods (Mathematics) 201516
Answers for Extra Exercises 9: Linear equations and inverses
Extra Exercise 1. The augmented matrix describing the equations is
1
2
1
0
2
3
5
1
5
1
4
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 7: Stationary points and Lagrangeans
Exercise 1. Finding and classifying the stationary (or critical) points of a function of t
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 4: Optimisation
Extra Exercise 1. For (a), interest is compounded continuously with a rate of r = 12.5% = 1/8.
If P (t) is
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 3: The cobweb model and derivatives
Extra Exercise 1. The supply function is obtained by expressing quantity in terms of pr
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 5: Partial derivatives
Extra Exercise 1. Setting
g(x, y) = x2 y 3 6x3 y 2 + 2xy 1,
the equation is g(x, y) = 0, and so we h
MA107: Quantitative Methods (Mathematics) 201415
Answers for Exercises 1: Sets, functions, graphs, equations
Exercise 1. This should be standard. Note that R2+ is the non-negative quadrant which is th
MA107: Quantitative Methods (Mathematics) 201415
Exercises 4: Optimisation
For all homeworks in this course please note that no marks will be given for answers only. Always
show the method used to obt
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 7: Consumer choice
1/4 1/2
Extra Exercise 1. The utility function for two goods is u(x1 , x2 ) = x1 x2 and the budget
const
MA107: Quantitative Methods (Mathematics) 201415
Answers for Extra Exercises 6: Stationary points and Lagrangeans
Extra Exercise 1. The managers expect 60 days of good weather with a profit of 2 y y o
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 1: Revision
Exercise 1. We manipulate inequalities just like equations with the exception that multiplying (or
dividing) by a n
MA107: Quantitative Methods (Mathematics) 201516
Answers for Exercises 10: Integration and Differential equations
Exercise 1. The basic ideas and meaning of integration can be found in chapter 25 of t
MA107: Quantitative Methods (Mathematics) 201516
Answers for Extra Exercises 10: Integration and Differential eqns
Extra Exercise 1. For (a), to show that the required algebraic identity holds, we not
MA107: Quantitative Methods (Mathematics) 201516
Exercises 8: Consumer choice; vectors and matrices
For all homeworks in this course please note that no marks will be given for answers only. Always
sh
MA107: Quantitative Methods (Mathematics) 201516
Exercises 2: Sets, functions, graphs, equations
For all homeworks in this course please note that no marks will be given for answers only. Always
show
MA107: Quantitative Methods (Mathematics) 201516
Exercises 7: Stationary points and Lagrangeans
For all homeworks in this course please note that no marks will be given for answers only. Always
show t