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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 weeks 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 governments 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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