Basic Mathematics for Economists - Rosser - Chapter 15 doc

... multiplication. © 1993, 2003 Mike Rosser 15 Matrix algebra Learning objectives After completing this chapter students should be able to: • Formulate multi-variable economic models in matrix format. • Add and ... units that sold them. A =  12 30 815  If each item sells for £4, derive a matrix for total sales revenue for this retailer for these two shop units over this two-wee...

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... equal I ? © 1993, 2003 Mike Rosser Example 8.2 Find a formula that gives the slope of the function y = 6x 3 for any value of x. Solution Slope = dy dx = 3 × 6x 3−1 = 18x 2 for any value of x. Example ... function y = 52x 3 . 5. Make up your own single-term function and then differentiate it. 8.2 Rules for differentiation The rule for differentiation can be formally stated as: If y =...

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... order you perform the calculations and the type of calculator you use. There are set rules for the order in which basic arithmetic operations should be performed, whichareexplainedinChapter2.Nowadays,theseareprogrammedintomostcalculators but ... quantification of economic predictions requires the use of mathematics. Although non-mathematical economic analysis may sometimes be useful for...

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... Rosser TestYourself,Exercise4.10 Fortheproductionfunctionsbelow,assumefractionsofaunitofKandLcanbe used,and (a)deriveafunctionfortheisoquantrepresentingthespecifiedoutputlevelinthe formK=f(L) (b)findthelevelofKrequiredtoachievethegivenoutputlevelifL=100,and (c)saywhattypeofreturnstoscalearepresent. 1.Q=9K 0.5 L 0.5 ,Q=36 2.Q=0.3K 0.4 L 0.6 ,Q=24 3.Q=25K 0.6 L 0.6 ,Q=800 4.Q=42K 0.6 L 0.75 ,Q=...

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... equations 10x + 10y = 150 (2) 15x + 6y = 180 (4) Using (3) again to substitute for x in (4), 15( 15 − y) + 6y = 180 225 − 15y + 6y = 180 45 = 9y 5 = y Substituting this value of y into (3) x = 15 − 5 = 10 Thus, ... requirements are 10 units of K plus 30 units of L for each unit of A 25 units of K plus 15 units of L for each unit of B If the per-unit profit is £80 for A and £30 f...

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... 24.5 -6 82 35.5 -2 97 10 3 -3 7 14 -5 98 25 -6 75 36 -2 68 11 3.5 -7 3 14.5 -6 12 25.5 -6 67 36.5 -2 38 12 4 -1 08 15 -6 25 26 -6 58 37 -2 07 13 4.5 -1 42 15. 5 -6 37 26.5 -6 48 37.5 -1 75 14 5 -1 75 16 -6 48 ... -6 48 27 -6 37 38 -1 42 15 5.5 -2 07 16.5 -6 58 27.5 -6 25 38.5 -1 08 16 6 -2 38 17 -...

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... 1 2152 .86 10 6 12000 10% 9563.64 11 11% 7090.04 12 IRR = 14.14% 12% 4725.54 13 13% 2464.06 14 14% 299.94 15 15% -1 772.14 16 16% -3 757.14 17 17% -5 659.71 18 18% -7 484.20 19 19% -9 234.68 20 20% -1 0914.99 Example ... investment. Example 7.39 What would you pay for an annuity that promises to pay £450 a year for the next 10 years given an interest rate of 8%? © 1993...

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... function will be zero at a stationary point. Therefore dy dx = 60 − 0.4x = 0 (1) x = 150 Therefore the first-order condition for a maximum is met when x is 150 . To get the rate of change of the slope ... 0% and 100%. Therefore c will take a value between 0 and 1 and so the second-order condition for a maximum will be met. © 1993, 2003 Mike Rosser The second-order condition for a mi...

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