CU Mathematics for Economists Discussion

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This is part B containing 30% of the marks. Your assignment must be submitted by 22nd 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.
This is part B containing 30% of the marks. Your assignment must be submitted by 22nd 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 10 questions from lessons 5 to 8, do proper online research and use lecture notes to
answer them.
PART B (30%)
1. An annuity will pay £8,000 at the end of each year for 5 successive years, the first
payment being 12 months from the initial purchase date. What is the maximum price any
rational investor would pay for such an annuity if the opportunity cost of capital is 10%?
2. There are limited world reserves of mineral M. The current rate of extraction is 45
million tonnes a year, with all mined material being used up by manufacturing industry.
This extraction rate is expected to increase at 3% per annum. Total estimated reserves are
1,200 million tonnes. When will they be expected to run out if this 3% growth rate
continues?
3. A developing country currently produces 3,600 million units of food per annum and this
rate of production is expected to increase by 4% a year. Its population is currently 2.5
million and expected to grow by 6% per annum. The minimum recommended average
intake of food is 1,200 units of food per person per year. Assuming no changes in
production or population growth rates, no imports and exports and no foreign aid, when
will food production fall below the subsistence level?
4. A retailer has to order stock of a particular summer seasonal product in one batch at the
start of the season. The first week’s sales are expected to be 200 units. Past years’ sales
suggest that demand will then grow by 5% a week for the next 14 weeks and then fall by
10% a week for the remaining 10 weeks of the season. How much stock needs to be
ordered to meet the anticipated sales for the whole 25-week season?
5. In a basic Keynesian macroeconomic model it is assumed that Y = C + I where I = 250
and C = 0.75Y. What is the equilibrium level of Y? What increase in I would be needed
to cause Y to increase to 1,200?
6. A firm uses 200,000 units of a component in a year, with demand evenly spread over the
year. In addition to the purchase price, each order placed for a batch of components costs
£80. Each unit held in stock over a year costs £8. What is the optimum order size?
7. In a Keynesian macroeconomic system, the following relationships and values hold:
Y=C+I+G+X?M
C = 0.8Yd
M = 0.2Yd
Yd = (1 ? t)Y
t = 0.2
G = 400
I = 300
X = 288
What is the equilibrium level of Y? What increase in G would be necessary to increase Y
to 2,500? If this increased expenditure takes place, what will happen to
(i)
the government’s budget surplus/deficit, and
(ii)
The balance of payments?
8. A firm produces goods A and B which are complements. Derive marginal revenue
functions for the two goods if the relevant demand schedules are
qA = 850 ? 12.5pA ? 3.8pB
qB = 936 ? 4.8pA ? 24pB
9. For the production function Q = 32K0.5 L0.25 R0.4 derive all the second-order and cross
partial derivatives and show that the cross partial derivatives with respect to each possible
pair of independent variables will be equal to each other.
10. A firm produces two products which are sold in two separate markets with the demand
schedules
p1 = 600 ? 0.3q1 p2 = 500 ? 0.2q2
Production costs are related and the firm faces the total cost function
TC = 16 + 1.2q1 + 1.5q2 + 0.2q1q2
If the firm wishes to maximize total profits, how much of each product should it sell?
What will the maximum profit level be?

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