а- Given the pay-off table below showing the profit (present value Rs.), a firm might expect in a foreign country for three alternative factory investments (X, Y, and Z) under different levels of inflation. Economists have assigned probabilities of 0.2, 0.3, 0.4, and 0.1 to the possible inflation levels A, B, C and D, respectively. Find the preferred investment alternative using criteria of (a) Maximin, (b) Laplace, (c) Maximum probability, and (d) Expected monetary value. Finally, e) Use your "judgment" (Write your own point of view based on your judgment). States of nature: amount of inflation i need d and e A B Build factory X 10 30 50 120 Build factory Y 40 50 60 70 Build factory Z 10 40 80 10

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please answer d and e

a-
Given the pay-off table below showing the profit (present value Rs.), a firm
might expect in a foreign country for three alternative factory investments (X, Y,
and Z) under different levels of inflation. Economists have assigned
probabilities of 0.2, 0.3, 0.4, and 0.1 to the possible inflation levels A, B, C and
D, respectively. Find the preferred investment alternative using criteria of (a)
Maximin, (b) Laplace, (c) Maximum probability, and (d) Expected monetary
value. Finally, (e) Use your "judgment" (Write your own point of view based on
your judgment).
States of nature: amount of inflation
i need d and e
А
D
Build factory X
10
30
50
120
Build factory Y
40
50
60
70
Build factory Z
10
40
80
10
Transcribed Image Text:a- Given the pay-off table below showing the profit (present value Rs.), a firm might expect in a foreign country for three alternative factory investments (X, Y, and Z) under different levels of inflation. Economists have assigned probabilities of 0.2, 0.3, 0.4, and 0.1 to the possible inflation levels A, B, C and D, respectively. Find the preferred investment alternative using criteria of (a) Maximin, (b) Laplace, (c) Maximum probability, and (d) Expected monetary value. Finally, (e) Use your "judgment" (Write your own point of view based on your judgment). States of nature: amount of inflation i need d and e А D Build factory X 10 30 50 120 Build factory Y 40 50 60 70 Build factory Z 10 40 80 10
a)
The Maximin is the maximum of the minimum. The minimum of Build factory X, Y, Z among all
c)
For maximum probability we find the expected values by multiplying the probability of each
inflation level with respect to their profit for each Build factory and are calculated as shown
inflation levels A, B,C and D are 10,40,10 respectively and the maximum among them id 40,
which will be the 40 which is Build factory Y at inflation level A preferred investment
alternative according to Maximin strategy.
below
States of nature : amount of inflation
States of nature : amount of inflation
A
B
D
calculation
Expected
A
В
D
Maximin
Probability
0.2
0.3
0.4
0.1
Probability
0.2
0.3
0.4
0.1
Build Factory X
120
10
30
50
0.2*10+0.3*30+0.4*50+0.1*120
43
Build Factory X
10
30
50
120
10
Build Factory Y
40
50
60
70
0.2*40+0.3*50+0.4*60+0.1*70
54
Build Factory Y
Build Factory Z
40
50
60
70
40
Build Factory Z
10
40
80
10
0.2*10+0.3*40+0.4*80+0.1*10
47
10
40
80
10
10
b)
Laplace method assume equal weight, as there are three factory investments X, Y and Z we use
the weight to be .
With respect to probabilities the best strategy will be Build Factory Y as its expected value is
higher than others.
Laplace method minimize the maximum loss and we multiply each inflation level with their
respective weights and add them
For example for Build Factory X
Laplace = * (10 + 30 + 50 + 120) = * 210 = 70
Doing the calculation for all we get the following and the preferred investment alternative
according to Laplace strategy Build Factory Y
States of nature : amount of inflation
A
В
D
Laplace
Probability
Build Factory X
0.2
0.3
0.4
0.1
10
30
50
120
70
Build Factory Y
40
50
60
70
73.33
Build Factory Z
10
40
80
10
46.67
Transcribed Image Text:a) The Maximin is the maximum of the minimum. The minimum of Build factory X, Y, Z among all c) For maximum probability we find the expected values by multiplying the probability of each inflation level with respect to their profit for each Build factory and are calculated as shown inflation levels A, B,C and D are 10,40,10 respectively and the maximum among them id 40, which will be the 40 which is Build factory Y at inflation level A preferred investment alternative according to Maximin strategy. below States of nature : amount of inflation States of nature : amount of inflation A B D calculation Expected A В D Maximin Probability 0.2 0.3 0.4 0.1 Probability 0.2 0.3 0.4 0.1 Build Factory X 120 10 30 50 0.2*10+0.3*30+0.4*50+0.1*120 43 Build Factory X 10 30 50 120 10 Build Factory Y 40 50 60 70 0.2*40+0.3*50+0.4*60+0.1*70 54 Build Factory Y Build Factory Z 40 50 60 70 40 Build Factory Z 10 40 80 10 0.2*10+0.3*40+0.4*80+0.1*10 47 10 40 80 10 10 b) Laplace method assume equal weight, as there are three factory investments X, Y and Z we use the weight to be . With respect to probabilities the best strategy will be Build Factory Y as its expected value is higher than others. Laplace method minimize the maximum loss and we multiply each inflation level with their respective weights and add them For example for Build Factory X Laplace = * (10 + 30 + 50 + 120) = * 210 = 70 Doing the calculation for all we get the following and the preferred investment alternative according to Laplace strategy Build Factory Y States of nature : amount of inflation A В D Laplace Probability Build Factory X 0.2 0.3 0.4 0.1 10 30 50 120 70 Build Factory Y 40 50 60 70 73.33 Build Factory Z 10 40 80 10 46.67
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