Utility Maximization Steps MPP 801 Fall‚ 2007 The MRS and the Cobb-Douglas Consider a two-good world‚ x and y. Our consumer‚ Skippy‚ wishes to maximize utility‚ denoted U (x‚ y). Her problem is then to Maximize: U = U (x‚ y) subject to the constraint B = p x x + py y Unless there is a Corner Solution‚ the solution will occur where the highest indifference curve is tangent to the budget constraint. Equivalent to that is the statement: The Marginal Rate of Substitution equals the price ratio‚ or px
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Using the recursive least squares method‚ obtain parameter estimates for different model structures. The program is below: clear all close all N=1500; % set lenghth of data y=zeros(1‚N); u=zeros(1‚N); yhat=zeros(1‚N); e=zeros(1‚N); noise=rand(1‚N); % generate noise %ny=2; true value %nu=3; true value %ny=2; good// model with different order :test 1 %nu=4; %ny=3; bad %nu=5; %ny=4; bad %nu=5; %ny=3; good %nu=3; %ny=2; with more numerator terms:test 2 %nu=4; ny=2; %test 3 nu=3; m=ny+nu; P=eye(m‚m)*1000;
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where X is N [µ‚ σ 2 ]. Proposition 4: If X is N [µ‚ σ 2 ] then E(X) = µ and Var(X) = σ 2 . 1 2 Proposition 5: If Y is LN [µ‚ σ 2 ] then E(Y ) = eµ+ 2 σ and 2 2 Var(Y ) = e2µ+σ (eσ − 1). Proposition 6: If X is N [µ‚ σ 2 ] then aX + b is N [aµ + b‚ a2 σ 2 ]. 2 2 Proposition 7: If X is N [µ1 ‚ σ1 ]‚ Y is N [µ2 ‚ σ2 ]‚ and X and Y are indepen2 2 dent‚ then X + Y is N [µ1 + µ2 ‚ σ1 + σ2 ]. n Corollary 1: 2 If Xi are independent N [µ‚ σ ] for i = 1 . . . n then Xi is i=1
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P r ob lem s in M alays ia Mala y si a is ca te g o riz e d a s thi rd w or ld countr y a nd ha s re c e ived r a pid growt h in s oc ioec onomi c a nd a dva n c e te c hnolog i e s. The g lob a li z a ti on make s the w or ld be c ome sma ll e r a nd a ll the infor mation could be obt a ined e a sil y b y c li c kin g o n the c omput e rs. W or ld wi thout a n y ba rr ier s a ll ows c ult ur e
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Integration Differential Equation Solution dy f x dx y f x dx C dy f y dx 1 dy f y dx 1 f y dy 1 f y dy d2 y f x dx 2 1 1 dx dy dx F x C y f x dx C F x C dx G x Cx D xC 2. Substitution Use the substitution v x y to find the general solution of the differential equation dy 2 x y . dx Step 1: Apply product rule/quotient rule/chain rule
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Calculus in 3D Geometry‚ Vectors‚ and Multivariate Calculus Zbigniew H. Nitecki Tufts University August 19‚ 2012 ii This work is subject to copyright. It may be copied for non-commercial purposes. Preface The present volume is a sequel to my earlier book‚ Calculus Deconstructed: A Second Course in First-Year Calculus‚ published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at Tufts‚ a two-semester
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level of output Components of Aggregate Demand Two-sector Model AD = C + I Consumption Function (C) • A functional statement of the relationship between disposable income (Y) and consumption expenditure (C) C = f(Yd) • Consumption is a positive linear function of income C = a + bYd Note: In a two-sector model Y = Yd. (Why?) a is a positive constant‚ (a>0) showing the level of consumption at zero level of income‚ also known as autonomous consumption b represents the slope of the consumption
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Consider the figure shown below y x A dA y x Product of Inertia of A wrt x and y axis: Product of Inertia of Element dA: 2 5/3/2011 Product of Inertia for an Area Consider the figure shown below y x A dA y x Unit: length4 – m4‚ mm4‚ ft4‚ in4 g NOTE: 1. Ixy can be positive‚ negative or zero. 2. The product of inertia of an area wrt any two orthogonal axes is zero when either of the axes is an axis of symmetry. Product of Inertia of A wrt x and y axis: Product of Inertia for an Area
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edu/~busch/courses/theorycomp/fall2008/ 1 The Pumping Lemma: • Given a infinite regular language L • there exists an integerm | w | m with length • for any string w L • we can write w x • with |x y| m • such that: Fall 2006 (critical length yz and | i xy z L Costas Busch - RPI y | 1 i 0‚ 1‚ 2‚ ... 2 Non-regular languages R L {vv : v *} Regular languages Fall 2006 Costas Busch - RPI 3 Theorem:The language R L {vv : v *} {a‚ b} is not regular Proof: Fall
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relationship between the Infant Mortality rate (Y)‚ the Literacy rate (X1)‚ the Population Density (X2)‚ the N. of Inhabitants Per Physician (X3)‚ and Income per Capita (X4). The data collected were summarized with the following statistics. Variable | | S | b | Y X1 X2 X3 X4 | 48.3681.0588.472062.2712000.00 | 23.6823.48141.852009.256000.00 | --------1.05.05.002-.003 | 1. Find the simple regression equation for the relationship between Y & X1‚ and explain its meaning as well as the meaning
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