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 equilibrium
set is cfw_(2, 6).
If a percentage [of the price]
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 , invested
at r% per annum, we know that after 1 year the bal
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 worked
examples 1.3, 1.4 and 1.5.
The supply and demand se
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 5: Optimisation
Exercise 1. This question is similar to worked examples 8.1 and 8.2 of the Anthony & Biggs book.
(a) We are given the function f (x) = x3 9x2 + 26x 24 and we note tha
[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 wish,
but only your best 4 questions will count towards t
[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 questions
as you wish, 'but only your best 4 questions will co
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. You may attempt as many questions
as you wish, but only
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 as many questions as you wish,
but only your best 4 an
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 6: Partial derivatives
Exercise 1. By now, the rules of differentiation should be more or less known. If not, see sections
6.2 and 6.4 of the Anthony & Biggs book. See also worked ex
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 negative quantity reverses the direction of the inequali
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 the present value of the sale at time t, then we have P
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 price for
points in the supply set. We have
q = 3p 7,
q S
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 have
dy
g
y (x) =
=
dx
x
0
g
2xy 3 18x2 y 2 + 2y
= 2 2
,
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 the set
of points (x, y) where x 0 and y 0. The answers a
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 obtain your answers.
Please write clearly. Dont just use f
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
constraint is p1 x1 + p2 x2 = M . We are asked to find the L
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 on these
days, and 40 days of poor weather with a profit
Summer 2006 examination
MA1 07
Quantitative Methods
(Mathematics)
Half unit
Suitable for all candidates
Instructions to candidates
Time allowed: 2 hours
This paper contains 5 questions. You may attempt as many questions as you wish,
but only your best 4 a