Question

QUESTION 7 1. A farmer is deciding whether to take precautions to "weather-proof' his farm (in case mega typhoons hit it before harvest), "disease-proof" it in case diseases come out before harvest), do both to "full proof" it in case both typhoons & diseases hit it), or simply not take precautions and hope that no untoward event happens. The expected payoffs for each course of action under the four scenarios are presented below. Diseases Typhoons occur hit crops Weather Proofing Disease Proofing Full-proofing No precautions 100,000 65,000 90,000 75,000 50,000 90,000 80,000 60,000 Typhoons wl Diseases 45,000 60,000 70,000 20,000 No Typhoons & Diseases 110,000 100,000 90,000 120,000 What is the value of perfect information? Assume a probability of 0.3 for typhoons only to occur, 0.3 for diseases only to occur. 0.2 for both typhoons & diseases to occur an 0.2 for neither typhoons & diseases to occur. a. 95,000 b. 76,000 c. 83,000 d. 12,000 1 points Focus BLOOD

Answer 1

	Typhoons	deseases	tyhoons/deseases	no typhoons nodeseases
Weather prf	100,000	50,000	45,000	110,000
Deseases prf	65,000	90,000	60,000	100,000
Fullprf	90,000	80,000	70,000	90,000
Noprecautions	75,000	60,000	20,000	120,000
Probability	0.3	0.3	0.2	0.2

the expected value (Ev) for each diassion alternative is calculated as follous ① weather Proof © C100,000x0,3)+(50,000x0,3)+(45,000 X013 +110,000X012) = 30,000 + 15,000 +9,000 + 22,000 = 76,000 Desease Proof (65,000 X013)+(90,000*0,3)+(60,000 XO:34 +C100,000 8 002) -1950 + 27000 +12000 +20,000 = 60,950 3 (90,000 X013) +C80,000x003) +670,000x0134 +(90,0008012) 27000 + 24000 +14000 +18000 = 83000 6 No Precautions 5,000 X 0.3) HC60,000 X0r3)+20,000X03 +(120,0008012) 222580 +18000+4000 +24000 =68500 The Maximum Ev is given by the full proof deasion=83,000 io Expected value without perfect Information = [ 83000

- 30,000 + 27000 +140oot24ooo The expected value with perfect Information is calculated by best pay off given by states of natur le (100,000 XQ13) +(99000X0-3) + (70,000 X612)+(20,000X6.2) = 95.000 the expected value of Perfect Infor mation is EVOf PI = Evwithat PE - EV with Pr =95000 -83000 = 12000 (d) i 1 2000 w juhat 7