2. A version of the "IS-LM macroeconomic model leads to the system of equations: 1. 1 (r) = S(Y) 2.aY + L(r) = M where a is a parameter, and I,S, and L are given differentiable functions. Sup...
4. Consider the IS-LM model: Y =C+I+G C = co + C(Y - T) - Car T = to +tįY I = io ti Y - ir M = m;Y + mo - mar, where the endogenous variables of the system are Y and r. The simultaneous solution of the first four equations defines the set of values of Y and r that establishes equilibrium in the goods market. While the fifth equation defines the values of Y and r...
Consider the Mundel-Fleming small open economy model: Y=C(Y-T)+1(1) + G Y = F(K,L) (M/P) L(r+z® Y) Goods Money C = 50+0.8(Y- T) M 3000 I = 200-20r r*=5 NX = 200-508 P = 3 G=T= 150 L(Y, r) Y - 30r 1- find the IS* equation (hint : y as a function of e) 2- find the LM* equation (hint, also relates y and maybe e) 3-draw the IS-LM curve I y 4- find the equilibrium interest rate (trick question!)...
4. An economy can be described by the following equations: C = 5+.8(Y-T) I = 2-r G = 2 T = 2 L(r,Y) = 4 + 4y -.5r M = 2 P=1 Solve algebraically for an equation for the IS curve (with 'r' on the left-hand side). Do the same for the LM curve. Finally, solve for the equilibrium values of 'r' and 'Y' in the ISLM model:
Consider the model of a small DC motor, where the following parameter values are assumed: R-10 L-10mH,J-0.01kgm0.0.05 2. ra a. Write down the transfer function of the system b. Choose a sample time for the system c. Find the pulse transfer function (use MATLAB 'c2d' command) d. Find the range of K for stability for the closed-loop sampled-data system
Consider the model of a small DC motor, where the following parameter values are assumed: R-10 L-10mH,J-0.01kgm0.0.05 2. ra a. Write...
control system with observer
Consider the following system: -1-2-21 гг 1 0 1 L Where u is the system input and y is the measured output. 1. Find the transfer function of the system. 2. Design a state feedback controller with a full-state observer such that the step response of the closed loop system is second order dominant with an overshoot Mp settling time ts s 5 sec. Represent the observer-based control system in a compact state space form. 10%...
Consider the neoclassical closed economy model: Y=COY-T)+1(t) + G Y=F(K.L) M/P L(r+z* Y) CY-T) is describing consumptions as a function of disposable income, Kand L are fixed and do not change over time, G and T are chosen by government. And are exogenous and fixed. 1- Suppose K 150, L=500 Y-2.5 K"L- C 12+0.7(Y-T) 250 G 250, T I60-400r P 1 a 0.3 a) Calculate GDP value: I Derive the equations for marginal product of labor & marginal product of...
Differntial equations
Classwork 1. Find the inverse Laplace transform of the given functions. (k) Y(s) = (1) Y(s) = ? (m) Y(s) = 52 +58 +4 (n) y .)_ 1 (n) Y(s) = 53 +52 (0) H(-) = 32 + 25 + 4 1 ZS 4 (p) F(s) = * e-s (q) G(s) = (8 + 1)2 + 3 (r) H(s) = (s + 4)3
The state variable model of the two tanks process is given by the equations r1 10 01 r1o 2 0-1 lu Tank 1 Tank 2 Explain the differential equations for the tanks Draw the block diagram for the system model * .Modify the block diagram to realize the system model by first order transfer functions: 1+Ts Determine the controllability and observability of the system model Design a full-state feedback with the eigen values λ-λ2--2 of the closed loop system Design...
Problem1 A speaker is modeled with the system model given in the equations below. 2 m (x) + c(x) + kx = Kyi V(t) = L(i) + Ri + Kc(x) Given that the following constants, m- 2E-3 Kg, c 30 N.s/m, k 1.25E+5 N/m, K- Ke 2.5 Vls.m, L-0.02E-3 Henries (H) and R- 2 and the () indicate time derivatives, Find the maximum displacement, Xmax, when the speaker is given an input of V(t)-sin(2ft) when the frequency is varied between...
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...