# Basic Mathematics for Economists

Language: English

Pages: 528

ISBN: 0415267846

Format: PDF / Kindle (mobi) / ePub

Economics students will welcome the new edition of this excellent textbook. Mathematics is an integral part of economics and understanding basic concepts is vital. Many students come into economics courses without having studied mathematics for a number of years. This clearly written book will help to develop quantitative skills in even the least numerate student up to the required level for a general Economics or Business Studies course. This second edition features new sections on subjects such as:

matrix algebra

part year investment

financial mathematics

Improved pedagogical features, such as learning objectives and end of chapter questions, along with the use of Microsoft Excel and the overall example-led style of the book means that it will be a sure fire hit with both students and their lecturers.

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value of m is known then equilibrium price and quantity can easily be found. For example, if m is £270 then qd = 160 − 0 . 5 p + 0 . 1 m = 160 − 0 . 5 p + 0 . 1 ( 270 ) = 187 − 0 . 5 p In equilibrium qs = qd and so −20 + 0 . 4 p = 187 − 0 . 5 p 0 . 9 p = 207 p = 230 Substituting this value for p into the supply function to get equilibrium quantity gives q = −20 + 0 . 4 p = −20 + 0 . 4 ( 230 ) = −20 + 92 = 72 If factors outside this model cause the value of m to alter, then the

diagram to ensure that the relative magnitudes of the answer correspond to those read off the graph. In this type of problem it is easy to get mixed up in the various stages of the calculation. From Figure 5.5, we can see that p 1 should be greater than p 2 which checks out with the above answers. Not all price discrimination models involve the horizontal summation of demand schedules. In first-degree (perfect) price discrimination each individual unit is sold at a different price. Because

0.009 F = A(1 + i) n = 100(1.009)12 = 100(1.1135) = £111.35 This final sum of £111.35 after investing £100 for one year corresponds to an annual rate of interest of 11.35%. This is greater than 12 times the monthly rate of 0.9%, since 12 × 0.9% = 10.8% The calculations in the above example that tell us that the ratio of the final sum to the initial sum invested is (1.009)12. Using the same principle, the corresponding AER for any given monthly rate of interest i m can be found using the

2,257.90 − 2,000 = £257.90 NPV of project C = 4,800(1.1)−5 − 3,000 = 2,980.42 − 3,000 = −£19.58 Project B has the largest NPV and is therefore the best investment. Project C has a negative NPV and so would not be worthwhile even if there was no competition. The investment examples considered so far have only involved a single return payment at some given time in the future. However, most real investment projects involve a stream of returns occurring over several time periods. The same

which MC = MR? Which is the profit-maximizing output? 2. If a firm faces the demand schedule p = 120 − 3 q and the total cost schedule TC = 120 + 36 q + 1 . 2 q 2 what output levels, if any, will (a) maximize profit, and (b) minimize profit? 3. Explain why a firm which is a monopoly seller in a market with the demand schedule p = 66 . 8 − 0 . 4 q and which faces the total cost schedule TC = 220 + 120 q − 12 q 2 + 0 . 5 q can never make a positive profit. 4. What is the maximum