Basic Mathematics for Economists - Rosser - Chapter 14 pps

... your forecast for price when t is 8? 14. 10 Continuous adjustment in a Keynesian macroeconomic model In a basic Keynesian macroeconomic model, with no foreign trade and no government sec- tor, ... constant. © 1993, 2003 Mike Rosser Example 14. 3 An economy is forecast to grow continuously at an annual rate of 2.5%. If its GNP is currently e56 billion, what will the forecast for GNP...

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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 ... -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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... 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 0 914. 99 Example 7.30 A firm has ... £) PV = 2,000(1 .14) −1 +2,000(1 .14) −2 +2,000(1 .14) −3 +2,000(1 .14) −4 +2,000(1 .14) −5 In this example the annual payment R = 2,000, i = 0 .14 and...

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... constraint, when the first-order conditions for optimization of the relevant Lagrange equation are met. For the purpose of answering the problems in this Chapter, and for most constrained maximization problems ... Lagrangian for this problem is therefore G = 24K 0.6 L 0.3 + λ(50,000 − 18K − 8L) Partially differentiating to find the stationary points of G gives ∂G ∂K = 14. 4K −0.4 L 0....

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... rule. Assume, for example, that you wish to find an expression for the slope of the non-linear demand function p = (150 − 0.2q) 0.5 (1) ThebasicrulesfordifferentiationexplainedinChapter8cannotcopewiththissortof function. ... =−0.1644 < 0 Therefore, the second-order condition for a maximum is satisfied when t = 66.67. Maximum tax revenue is raised when the per-unit tax is £66.67. © 1993...

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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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... by calculating y for a few selected values of x: x 1234567 y 8141 820201 814 These figures show that y first increases and then decreases in value as x is increased and so there is no inverse for this non-monotonic ... Rosser TestYourself,Exercise4.10 Fortheproductionfunctionsbelow,assumefractionsofaunitofKandLcanbe used,and (a)deriveafunctionfortheisoquantrepresentingthespecifiedoutputle...

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