John is buying some wood from Michael at a price of $50. He needs to build wareh
ID: 1196785 • Letter: J
Question
John is buying some wood from Michael at a price of $50. He needs to build warehouse to put them in. He has two options: (i) build a high quality warehouse at a cost of $100; or (ii) build a simple warehouse at a cost of $50. He will use the materials to build fancy wooden furniture which he will then sell. In the high quality warehouse the wood will definitely not be damaged and the furniture produced will be worth $500. In the simple warehouse some wood may be damaged and the expected sales will be only $300. John is concerned that Michael may not deliver the wood (with probability p) in which case John cannot produce any furniture.
a) If there is no rule that would hold Michael liable for any damages if he breaches the contract, which type of storage space should John build?
b) Suppose instead that Michael would be liable for perfect expectation damages if he fails to deliver the wood. What would these damages be and what type of storage space should John build? Is this efficient?
c) What remedy would produce an economically efficient outcome?
Explanation / Answer
a) Calculate the expected benefit of building high-quality warehouse.
Situation Probability Benefit
Wood not delivered p $350 (=500 – 100 – 50)
Wood delivered 1 – p –$150 (= – 100 – 50)
Expected benefit of Building HQ warehouse = 350p + (1 – p)(–150) = 500p – 150
Calculate the expected benefit of building low-quality warehouse.
Situation Probability Benefit
Wood not delivered p $200 (=300 – 50 – 50)
Wood delivered 1 – p –$100 (= – 50 – 50)
Expected benefit of Building LQ warehouse = 200p + (1 – p) (–100) = 300p – 100
If expected benefit of Building HQ warehouse is higher than the expected benefit of Building LQ warehouse, then
500p – 150 > 300p – 100
200p > 50
p > 0.25
If expected benefit of Building HQ warehouse is less than the expected benefit of Building LQ warehouse, then
500p – 150 < 300p – 100
200p < 50
p < 0.25
If expected benefit of Building HQ warehouse equals than the expected benefit of Building LQ warehouse, then
500p – 150 = 300p – 100
200p = 50
p = 0.25
Therefore, if the probability that Michael will not deliver the good is greater than 0.25, then John should build the HQ warehouse, if the probability that Michael will not deliver the good is less than 0.25, then John should build the LQ warehouse, and if the probability that Michael will not deliver the good equals 0.25, then investment in either of the two warehouses may be made.
b) If Michael is liable for all the expected damages in case he fails to deliver the good, then John will not have any risk. That is, if John builds a HQ warehouse and Michael fails to deliver wood, then John will get a full compensation of $500 from Michael. So John’s expected benefit from building a HQ warehouse is $350, regardless of whether Michael delivers the wood or not. Similarly, if John builds a LQ warehouse and Michael fails to deliver wood, then John will get a full compensation of $300 from Michael. So John’s expected benefit from building a LQ warehouse is $200, regardless of whether Michael delivers the wood or not. In this case, John expected benefit is greater if he builds a high quality warehouse. Therefore, John will build HQ warehouse only.
An economically efficient outcome should depend on the value of P. But since the value of p is not being taken into account for making the decision here, the decision is not economically optimal.
c) Michael should agree to compensate only when John has taken a socially efficient decision (that is the decision that minimizes the combined expected loss of John and Michael) based on the value of p.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.