Question

A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm’s capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Suppose after a certain amount of discussion, the contractor is able to subjectively assess the probabilities of low and high demand: P (low) = .3 and P (high) = .7.

	NEXT YEAR'S DEMAND
Alternative	Low			High
Do nothing	$	50	*	$	60
Expand		20			80
Subcontract		40			70

* Profit in $ thousands.

a-1. Determine the expected profit of each alternative. (Enter your answers in thousands. Omit the "$" sign in your response.)

	Expected Profit
Do Nothing	$  thousands
Expand	$  thousands
Subcontract	$  thousands

a-2. Which alternative is best?

• Do nothing

• Expand

• Subcontract

c. Compute the expected value of perfect information. (Enter your answers in thousands. Omit the "$" sign in your response.)

EVPI           $  thousands

Answer 1

a-1) We are given the probability of low and high demand here as:
P(low) = 0.3, and P(High) = 0.7

The expected profit for each alternative here is computed as:
E(Do nothing) = 0.3*50 + 0.7*60 = 15 + 42 = $57 thousands
E(Expand) = 0.3*20 + 0.7*80 = $62 thousands
E(Subcontract) = 0.3*40 + 0.7*70 = 12 + 49 = $61 thousands

a-2) Based on the above expected profits for each alternative, we can clearly see here that the expected profit for Expand decision is $62 thousands. Therefore Expand is the best alternative here.

c) Expected value with perfect information here is computed as:
= 0.3*Best expected value for Low demand + 0.7*Best expected value for High demand

= 0.3*50 + 0.7*80

= 15 + 56

= $71 thousands

Therefore the expected value of perfect information is computed here as:
= Expected value with perfect information - Expected value without perfect information

= 71 - 62

= $9  

Therefore $9 thousands is the required value here.