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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... 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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