Question 1.
Place your answers in the table provided at the end of the question
1. Use the following table to produce a risk efficient frontier below. Clearly label each axis. (7/20)
2. Identify the stocking rate that you would suggest to a risk averse farmer. (3/20)
3. Explain why you would recommend this stocking rate. (5/20)
4. Indicate the most appropriate stocking rate for a risk-neutral farmer. (5/20)
|
Stocking
rate
|
Gross
margin
|
Standard
deviation
|
|
|
1
|
22
|
2
|
|
|
2
|
32
|
7
|
|
|
3
|
43
|
12
|
|
|
4
|
52
|
18
|
|
|
5
|
63
|
24
|
|
|
6
|
67
|
30
|
|
|
7
|
68
|
37
|
|
|
8
|
69
|
42
|
|
|
9
|
67
|
50
|
|
Question 2.
Place your answers in the table provided at the end of the question
A producer has 380 ha of cropping land. He is faced with the problem of what summer crop to grow in this area. The two crops he feels are worth considering are sorghum and sunflowers. He considers two factors (events) are beyond his control. These factors are rainfall and commodity prices.
Rainfall Conditions
He assesses that the probability of good rainfall is 0.6 and the probability of bad rainfall is 0.4. If the rainfall is bad, he also has to consider a harvest/do not harvest decision. The cost of harvesting both crops irrespective of yield is $40/ha. The crops have no value to the producer if they are not harvested.
Sale Prices
The probabilities of good and bad prices for both crops are set out below:
|
|
probabilities
|
Price per tone
|
|
|
Sorghum sunflowers
|
sorghum sunflowers
|
|
Good price
|
0.7 0.6
|
$160 $380
|
|
Bad price
|
0.3 0.4
|
$110 $240
|
Costs of Cropping
The costs of cropping (includes cultivation, seed, fertiliser and sprays but excludes harvesting) are estimated as:
|
crop
|
Cost/ha
|
|
sorghum
|
$120
|
|
sunflowers
|
$140
|
Yields
The farmer estimates the following yield variation given rainfall conditions:
|
Rainfall conditions
|
Yield (tonnes/ha)
|
|
|
Sorghum sunflowers
|
|
Good
bad
|
2.8 1.9
2.1 0.8
|
Assume you are a consultant to the producer with the problem of choosing which crop to grow and that you know the producer is risk preferring. Use a decision tree diagram to choose whether Sorghum or Sunflower should be planted. Briefly explain your conclusion to the producer.