7. A farmer in lowa must decide which crop to plant next year on his land: wheat

Question

7. A farmer in lowa must decide which crop to plant next year on his land: wheat, barley, or The return from each crop will be determined by whether a new trade bill with Canada is into law passed The profit (in thousands of dollars) the famer will realize frum each rop given the two possible results on the trade bill is shown in the following payon table. Trade Bill Pass Fail Sum Cr The farmer estimates the probability that the trade win will pass is 0.65. (5 pts) Using the cri terion of expected mon etary value (EMV) which crop should the farmer plant? Justify your answer by showing EMV for each of the three crop alternatives. 206, Section 2949, M-w, 1500 Graded Homework Assignment 2 b) (5 points) Using the criterion of mean regret (EOL), crop each should the farmer ant? Justify your answer by showing EOL for of the three crop alternatives. (HINT: You'll first have to create the regret table before you can compute EOL for each of the crop altematives)

Explanation / Answer

Given, the payoff table for planting each crop

Trade Bill

Pass

Fail

Sum

wheat

23

11

barley

19

16

rye

20

12

Probability

0.65

0.35

A.a) to calculate expected monetary values(EMV) for each crop

EMV(wheat)=23*0.65+11*0.35

EMV(wheat)=18.8

EMV(barley)=19*0.65+16*0.35

EMV(barley)=17.95

EMV(rye)=20*0.65+12*0.35

EMV(rye)=17.2

as the expected value (EMV) for wheat is higher the farmer should grow wheat

A.b) to calculate Expected monetary loss (EOL), we need to construct regret table

Regret table

Trade Bill

Pass

Fail

Sum

wheat

0

5

barley

4

0

rye

3

4

Probability

0.65

0.35

EOL(wheat)=0.65*0+0.35*5

EOL(wheat)=1.75

EOL(barley)=4*0.65+0*0.35

EOL(barley) =2.6

EOL(rye)=3*0.65+4*0.35

EOL(rye)=3.35

as the expected monetary loss (EOL) for wheat is lower, the farmer should grow wheat

Trade Bill

Pass

Fail

Sum

wheat

23

11

barley

19

16

rye

20

12

Probability

0.65

0.35

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