Dynamic Macroeconomic Modeling with Matlab

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3 A Short Introduction to Matlab Functions can be saved in m files in the same way as scripts. They have to be introduced according to function output = functionname(x1, x2) where functionname is the name of the function, output is the function output, and x1, x2, etc. are the input arguments. For example, the following function named test would yield the square of the input argument x if executed function output = test(x) output=x*x; >> test(3) ans = 9 Exercises 1. sin, cos, exp, sqrt, pi, inf, NaN, i Calculate √ 2, √ −2, 2. size, eye, zeros, rand, randn, det, inv cos(π) + 2 · e 0 sin(π) + 1 , sin(1010 · π), 1 −1 , 0 0 , Create two 3×3 matrices A and B with random entries equally distributed on the interval [0; 10] and check, if holds. (A + I)(A − I) = A 2 − I (A + B) t = A t + B t (AB) t = B t A t det(AB) = det(A) · det(B) A −1 −1 = A 3. Define the parameters α = 0.3, β = 0.4, δ = 0.05, and A = 10 and calculate for k = 1, 1.1, 1.2,...,3. Ak α+β − δk 0 0
3 A Short Introduction to Matlab 4. plot, plot3, subplot, axis, hold on, pause, close, xlabel, ylabel, title, grid, print -deps Plot the sinus and cosinus functions on the interval [0, 2π] in the same figure. Plot sinus in a solid blue line and cosinus in a dotted red line. Plot the helix (sin(t),cos(t)) on the interval [0, 10π] in 3 dimensions. Summarize the commands in an m file. Save the figure as an eps file on the hard disc. (Hint: Add the commands pause and close at last.) 5. Define the function f : t → sin(e t ) in an m file and print it on the interval [−6, 3]. 6. Check the commands clc, clear all, format, global, who, whos, which 7. for, ODE45 Solve the differential equation ˙x = −0.2x with x(0) = 1 numerically on the interval [0, 10] employing the explicit Euler method. Compare the numerical solution with the correct solution graphically. 8. fsolve Solve for x in the non-linear equation x 2 = 10 · log(x) numerically. Note that there are two solutions in (0, ∞).
Page 1 and 2: Dynamic Macroeconomic Modeling with
Page 3 and 4: 1 Introduction 1 Introduction The a
Page 5 and 6: 2 An Outline of the Theory x(t) 1 0
Page 7 and 8: 2 An Outline of the Theory South-Ea
Page 9 and 10: 2 An Outline of the Theory whereby
Page 11 and 12: 2 An Outline of the Theory c 0.68 0
Page 13 and 14: 2 An Outline of the Theory Figure 5
Page 15: 3 A Short Introduction to Matlab 3
Page 19 and 20: 4 Numerical Simulation of Macroecon
Page 37 and 38: References References Ascher, U. M.
Page 39: References Solow, R. M. (1956): “

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