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1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production function, and the total utility to be maximized is
where U is a given period utility function and β ? (0; 1) is a discount factor. Rephrase this as a standard (in finite horizon) control problem and write its Bellman equation.
2. Consider the discrete time control problem:
subject to x0 = x; xt+1 = g(t; xt; ut) for t = 0; : : : ; T - 1 (here f; g are C1, xt; ut ? R, x ? R given). Rewrite this as a Lagrangian optimization problem with 2T +2 variables (x0; : : : ; xT ; u0; : : : ; uT ) and T + 1 constraints. By applying the Lagrange condition to this problem, recover the maximum principle for the control problem (necessary conditions).
3. Consider the problem
subject to the initial and terminal conditions x0 = a; xT = b. One may think of it as a control problem by setting ut = xt+1-xt. Find the minimum and the optimal x *0 ; : : : ; x*T in two ways: directly (eg by Lagrangian method); and by writing the fundamental equation of dynamic programming for and computing Js(x) by backwards induction.
4. Consider the dynamic programming problem with \extended memory":
subject to xt+1 = g(t; xt; xt-1; ut) (x0; x-1 are given). Rephrase as a standard dynamic programming problem (with twice as many state variables).
what is 10+5..
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INTRODUCING COUNTING : From what you studied previous study, you know what it means to count. You would also agree that rote learning of number names does not always mean that the
Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.
Application of Linear Equations We are going to talk about applications to linear equations. Or, put in other terms, now we will start looking at story problems or word probl
Sin+cos
4 accounting majors, 2 economics majors and 3 marketing majors have an interview for5 different positions with a large company. Find the number of dfferent ways that 5 of these c
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Write the doubles fact you used to solve the problem. 7 + 8 = 15
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