Basic Mathematics for Economists - Rosser - Chapter 12 ppsx

... giving d 2 TR dq 2 = 0 + (−975)(−0 .125 ) 0 →+∞ Therefore this second value for q obviously does not satisfy second-order conditions for a maximum. Example 12. 9 AtwhatlevelofKisthefunctionQ=12K 0.4 (160−8K) 0.4 atamaximum?(Thisis Example11.1(reworked)whichwasnotcompletedinthelastchapter.) © ... rule. Assume, for example, that you wish to find an expression for the slope of the non-li...

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... 28.5 These values for y and z can now be substituted into any of the original equations. Thus using (1) we get x + 12( 2) + 3(28.5) = 120 x + 24 + 85.5 = 120 x = 120 −109.5 x = 10.5 Therefore, the solutions ... 240 q 3 = MC 3 − 40 = 160 − 40 = 120 q 4 = 2MC 4 − 120 = 320 − 120 = 200 These total to 700, which checks out with the answer for q above. © 1993, 2003 Mike Rosser Ther...

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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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... 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...

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... 25000 9% 121 52.86 10 6 120 00 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 ... is k = 1 1 + i © 1993, 2003 Mike Rosser Example 7.4 (reworked) £5,000 invested for 2 years at 12% means that A = £5,000 n = 2 i = 12% = 0 .12 F = A(1 + i) n = 5,...

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... Therefore, 3q 2 − 42q + 160 = 184 −8q 3q 2 − 34q − 24 = 0 (q − 12) (3q + 2) = 0 q − 12 = 0or3q + 2 = 0 q = 12 or q =− 2 3 One cannot produce a negative quantity and so the firm must produce 12 units ... Mike Rosser Thus, substituting this result into (1) above, the formula for point elasticity of demand becomes e = (−1) p q 1 dp/dq Example 8.25 What is point elasticity when price is...

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

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