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Question 1 Question 2 Question 3 Question 4 Theorem 22.2 (use this for question 3, 4) Question 5 Question 6 ( Optimal Control: Maximum Principle) Question 7 Optimal Control: Maximum Principle

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Question 1
Question 2
Question 3
Question 4
Theorem 22.2 (use this for question 3, 4)
Question 5
Question 6 ( Optimal Control: Maximum Principle)
Question 7
Optimal Control: Maximum Principle
question-1-aadzqceb.docx
Answered 1 days After Mar 17, 2021

Solution

Rajeswari answered on Mar 18 2021
155 Votes
Question 1
Steady state would be achieved when
i.e. when
:
Solving we get
Hence steady states are achieved at 0 and 4.
Phase diagram with yt+1 on y axis and yt on x axis is shown below
We find the curve meets y=x line at 0 or 4
These are steady points.
Rate of change is y_t-1 <0 for y_t <1 and positive for y_t >1
Qno.2
To find difference equation for Y_t
Given that
Also
Would be the difference equation in terms of y.
For alpha>0 and even we havesymmetrical about y axis.
Y intercept would be I+alpha.
For alpha >0 and odd we have
We find that as Y-t increases Y_t+1 also increases indefinitely hence does not converge.
Question 3
Phase diagram is as follows:
We are given that
Differentiate with respect to y
Y dot ‘ =...
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