CU Mathematics for Economists Worksheet
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Your assignment must be submitted by 20th March 2022 via the assignment submission link in the module Canvas site.Please ensure that your student registration number and module code are stated on every page of your assignment (either in the header or footer). An assignment cover sheet should be completed and attached to the front of your assignment. Cover sheets will be available via the module Canvas site.It is the individual responsibility of each student to ensure that their submitted work is free from plagiarism and due acknowledgement is given to all sources.
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Here are basic Mathematics for Economists.
Do proper research and provide clear and well explained answers.
Use Times New Romans Font 12. APA format.
Use very clear sentences while explaining how you solved the problems.
Your assignment must be submitted by 20th March 2022 via the assignment submission link in
the module Canvas site. Please ensure that your student registration number and module code
are stated on every page of your assignment (either in the header or footer). An assignment
cover sheet should be completed and attached to the front of your assignment. Cover sheets will
be available via the module Canvas site. It is the individual responsibility of each student to
ensure that their submitted work is free from plagiarism and due acknowledgement is given to all
sources.
Below are 15 questions from lessons 1 to 5, do proper online research and use lecture notes to
answer them.
PART A (40%)
1. When the price of a product is lowered from £350 to £200 quantity demanded increases
from 600 to 750 units. Calculate the elasticity of demand over this section of its demand
schedule.
2. A businesswoman driving her own car on her employers business gets paid a set fee per
mile travelled for travelling expenses. During one week she records one journey of 234
miles, one of 166 miles and one of 90 miles. Derive an expression for total travelling
expenses.
3. You go into a foreign exchange bureau to buy US dollars for your holiday. You exchange
£200 and receive $343. When you get home you discover that you have lost your receipt.
How can you find out the exchange rate used for your money if you know that the bureau
charges a fixed £4 fee on all transactions?
4. A consumer can buy the two goods A and B at prices per unit of £6 and £4 respectively,
and initially has an income of £120.
(i) Show that a 25% rise in all prices will have a lesser effect on the consumers
purchasing possibilities than would a 25% reduction in money income with prices
unchanged.
(ii) What is the opportunity cost of buying an extra unit of A? (Assume units of A and B
are divisible.)
5. For the production function Q = 4.5K0.4L0.7 derive a function in the form K = f(L) for
the isoquant representing an output of 54.
6. A firm uses the three inputs K, L and R to manufacture its final product. The prices per
unit of these inputs are £20, £4 and £2 respectively. If the other two inputs are held fixed
then the marginal product functions are
MP K = 200 ? 5K
MP L = 60 ? 2L
MP R = 80 ? R
What combination of inputs should the firm use to maximize output if it has a fixed
budget of £390?
7. In a closed economy where the usual assumptions of the basic Keynesian macroeconomic
model apply;
C = £60m + 0.7Y t
Y=C+I+G
Y t = 0.6Y
where C is consumption, Y is national income, Yt is disposable income, I is investment
and G is government expenditure. If the values of I and G are exogenously determined as
£90 million and £140 million respectively, what is the equilibrium level of national
income?
8. A monopoly operates with the marginal cost function MC = 20 + 4q and faces the
demand function p = 400 ? 8q. If a per unit tax t is imposed on its output derive reduced
form equations for the profit maximizing values of p and q in terms of the tax t and use
them to predict the effect of a one unit increase in the tax on price and quantity. Assume
that fixed costs are low enough to allow positive profits to be made.
9. A multiplant monopoly operates two plants whose marginal cost schedules are
MC 1 = 42.5 + 0.5q1 MC 2 = 130 + 2q2
It also sells its product in two separable markets whose demand schedules are
pA = 360 ? qA pB = 280 ? 0.4qB
(Note that the subscripts A and B are used to distinguish quantities sold in the two
markets from the quantities q1 and q2 produced in the two plants.)
Calculate how much it should produce in each plant, how much it should sell in each
market, and how much it should charge in each market.
10. An industry is made up of 100 firms, all with the cost schedules
AC = 40q?1 + 0.4q2 TC = 40 + 0.4q3 MC = 1.2q2.
They sell in a market where the demand schedule is
p = 70 ? 0.08Q
where Q is industry output (and q is an individual firms output).
(i) What will be the short-run price, industry output and profit for each firm?
(ii) What will happen to price, industry output and the number of firms in the long run?
(Assume new entrants have the same cost structure.)
11. A building society account pays interest on a daily basis at an AER of 4.5%. If you
deposited £2,750 in such an account on 1st October how much would you get back if you
closed the account 254 days later?
12. If an annual discount rate of 4 7/8% is quoted for 3-month Treasury Bills, what would it
cost to buy a tranch of these bills with redemption value of £100,000? What would be the
annual equivalent rate of return on the sum paid for them?
13. An investment project requires an initial outlay of £7,500 and will pay back £2,000
at the end of the next 5 years. Is it worthwhile if capital can be invested elsewhere
at 12%?
14. A firm has to choose between projects A and B. Project A involves an initial outlay of
£18,000 and a return in 1 years-time of £20,000. Project B involves an initial outlay of
£2,000 and a return in 1 years- time of £2,500. The interest rate is 6%. Which would be
the better investment?
15. A firms sales revenue is initially £40,000 and then grows by 20% each successive year.
What is the pattern of sales revenue over 5 years? (use geometric series)
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Mathematics for Economists
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