Farmer Ingrid has to decide whether or not to fertilize her field. The decision
ID: 1177880 • Letter: F
Question
Farmer Ingrid has to decide whether or not to fertilize her field. The decision is a difficult one, because her profit depends not only on her decision with respect to fertilizer, but also on whether it rains or not. Her profit 'w' in each of the four possible cases as it follows.
Do Not Fertilize Fertilize
Rain w = $64 w = $216
No Rain w = $8 w = $0
Suppose that the probability of rain is 1/20. Will Ingrid fertilize her field if her utility function is U(w) = w^1/3?
If it is U(w) = w?
If it is U(w) = w^3?
Explanation / Answer
U(w) = w^1/3
E(fertilize) = (1/20*64)^1/3 + (19/20*0)^1/3 = $1.47
E(not fertilize) = (1/20*64)^1/3 + (19/20*8)^1/3 = $3.44
NOT FERTILIZE
U(w) = w
E(fertilize) = 1/20*216 + 19/20*0 = $10.8
E(not fertilize) = 1/20*64 + 19/20*8 = $10.8
INDIFFERENT
E(fertilize) = (1/20*216)^3 + (19/20*0)^3 = $1259.71
E(not fertilize) = (1/20*64)^3 + (19/20*8)^3 = $471.75
FERTILIZE
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