Solve the following exercises:
1.
Simplify each of the following expressions, where possible: (a) 2 + 6 − +
3 (b) 5 + 2 − 5 + 4 (c) 4 + 3 − 43 (d) 8 + 4 − 6 − 3 − 3 +
7 (e) 2 + 5 − 2 − 9 (f) 3 + 6 (g)
−
2.
Solve each of the following equations. Leave your answer as a fraction, if
necessary. (a) 4 + 1 = 25 (b) 4 + 5 = 5 − 7 (c) 3(3 − 2 ) + 2( − 1) = 10
(d)
= 5 (e) =
3.
Which one of the following algebraic fractions can be simplified? Explain why
the other two fractions cannot be simplified.
,
,
.
4.
The demand and supply functions of a good are given by = −4 + 120
and =
+ 29, respectively, where ,
and
denote the price, quantity
demanded and quantity supplied respectively. (a) Calculate the equilibrium price and
quantity (b) Calculate the new equilibrium price and quantity after the imposition of a
fixed tax of £13 per good. Who pays the tax?
5.
The demand and supply functions for two independent commodities are given
by
= 40 − 5 −
= 50 − 2 − 4
= −3 + 4
= −7 + 3
where
,
,
denote the quantity demanded, quantity supplied and price of good
( = 1,2 ) respectively. Determine the equilibrium price and quantity for this
two-quantity model. Are these goods substitutable or complementary?
where , ,
6.
The demand function of a good is = 100 − + 2 +
and
denote quantity demanded, price, income and advertising expenditure
respectively. (1) Calculate the demand where = 10, = 40 and = 6. Assuming
that price and income are fixed, calculate the additional advertising expenditure needed
to raise demand to 179 units. (b) Is the good inferior or superior?
7.
If the consumption function is given by = 0.7 + 40 state the values of (a)
autonomous consumption (b) marginal propensity to consume. Transpose this formula
to express in terms of and hence find the value of when = 110.
1. Briefing
Coursework Assignments
The two pieces of coursework assignment are to be released via Blackboard in due course.
They are also attached to end of this Handbook. For this module there are two individual
assignments each worth 25% (50% in total, 2 x 25%).
Coursework Details
The two pieces of coursework are to be drawn from materials in lectures and seminars. They
shall require numerical evaluation via application of mathematical rules as well as
computational exposition using the “Excel” programme. Students are expected to work
independently and individually, as there is no collaboration allowed.
Key Marking criteria will include:
·
Clarification, completeness, and explanation of answers
·
Details of derivations
·
Ability to prove accumulated knowledge
·
Quality/level of analytical mathematical skill demonstrated
·
Explanation of the findings and conclusions drawn, for the underlying problem