Basic Mathematics for Economists - Rosser - Chapter 13 pptx

... 115 14.25 -2 .25 13 3 92.5 15.38 1 .13 14 4 103.75 14.81 -0 .56 15 5 98.125 15.09 0.28 16 6 100.9375 14.95 -0 .14 17 7 99.53125 15.02 0.07 18 8 100.23438 14.99 -0 .04 19 9 99.882 813 15.01 0.02 ... 100.05859 15.00 -0 .01 © 1993, 2003 Mike Rosser Table 13. 4 A B C D E 1 Ex. LAGGED KEYNESIAN MODEL 2 13. 7 where Yt = Ct + I t 3 Ct = a + bYt-1 4 Parameters 5 a...

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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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... 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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... Rosser (YoucancheckthesesolutionsarethesameasthoseinExample5.14whichhadthesame supplyanddemandfunctions.) Inamodelwithtwodependentvariables,likethissupplyanddemandmodel,oncethe reducedformequationforonedependentvariablehasbeenderivedthenthereducedform equationfortheotherdependentvariablecanbefound.Thisisdonebysubstitutingthe reducedformforthefirstvariableintooneofthefunctionsthatmakeupthemod...

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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 ... 200 11 -4 93 22 -7 02 33 -4 27 5 0.5 158 11.5 -5 13 22.5 -7 00 33.5 -4 03 6 1 117 12 -5 32 2...

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... 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 7.30 A firm has to choose ... 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, 2003 Mike...

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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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