Basic Mathematics for Economists - Rosser - Chapter 10 potx

... rationale for all the second-order conditions is not quite so straightforward. We shall therefore just state these second-order conditions here and give a brief intuitive explanation for the two-variable ... case before looking at some applications. The second-order conditions for the optimization of multi-variable functions with more than two variablesareexplainedinChapter15usingmatrix...

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... in a format such as ‘1 in 10 , meaning that the road rose vertically by 1 foot for every 10 feet travelled in a horizontal direction. Now the European format is used and so instead of ‘1 in 10 ... Mike Rosser TestYourself,Exercise4 .10 Fortheproductionfunctionsbelow,assumefractionsofaunitofKandLcanbe used,and (a)deriveafunctionfortheisoquantrepresentingthespecifiedoutputlevelinthe for...

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... that 10 divided by 3 is 3.3333333 recurring, it is difficult for basic calculators to store this number accurately in decimal form. Although modern computers have a vast memory they still perform ... 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, whichareexplainedinChap...

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... operations to solve for x and y. 10x + 3y = 250 (1) 5x + y = 100 (2) Solution Multiplying (2) by 3 15x + 3y = 300 Subtracting (1) 10x + 3y = 250 Gives 5x = 50 x = 10 © 1993, 2003 Mike Rosser Note that ... input 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 for...

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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 -6 6...

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... 12152.86 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 ... Interest rate= 15% 2 3 YEAR RETURN PV 4 0 -2 5000 -2 5000 5 1 5000 4347.83 6 2 6000 4536.86 7 3 100 00 6575.16 8 4 100 00 5717.53 9 5 100 0...

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... expression for the slope of the 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 ... for the demand function q = 400 − 0.1p. Solution Given q = 400 − 0.1p 10q = 4,000 −p p = 4,000 − 10q Using this inverse demand function we can now derive TR = pq = (4,000 − 10q)q = 4,000q...

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... between 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 minimum ... inflexion (asinFigure9.2(b))whenitsslopeiszerowehavetoconsiderwhatareknownasthesecond- order conditions. (The first-order condition for any of the three forms of stationary point is that th...

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