Question

store must decide whether or not to stock a new item. The decision depends on the reaction of consumers to the item, and the payoff table (in dollars) is as follows. PROPORTION OF CONSUMERS PURCHASING 0.10 0.20 0.30 0.40 0.50 Stock 100 -10 I -2 I 12 22 I 40 DE SION Stock 50 - 4 6 12 16 16 Do not stock 0 0 10 (0.10) = 0.2, P(0.20) -0.3, P(0.30) - 0.3, P(0.40) = 0.1, and P(0.50) 0.1, what decision maxi- s expected payoff? If perfect information is available, find VPI for each of the five possible States of the world and compute EVPL.

Answer 1

ANSWER :

15.

A store must decide whether or not to stock a new item. The decision depends on the reaction of the customers to that item and the pay off table is as follows.

proportion of consumer purchasing

	0.10	0.20	0.30	0.40	0.50
stock 100	-10	-2	12	22	40
stock 50	-4	6	12	16	16
do not stock	0	0	0	0	0

Now,

P(0.10) = 0.2

P(0.20) = 0.3

P(0.30) = 0.3

P(0.40) = 0.1

P(0.50) = 0.1

So expected pay off for stock 100 would E(X) = value * probability

be,

(-10 * 0.2) = -2 for 0.10 proportion of consumer purchasing

(-2 * 0.3) = -0.6  for 0.20 proportion of consumer purchasing

(12 * 0.3) = 3.6 for 0.30 proportion of consumer purchasing

(22 * 0.1) = 2.2 for 0.40 proportion of consumer purchasing

(40 * 0.50) = 20 for 0.50 proportion of consumer purchasing.

Now for stock of 50 the same calculation goes like,

(-4 * 0.2) = -0.8

(6 * 0.3) = 1.8

(12 * 0.3) = 3.6

(16 * 0.1) = 1.6

(16* 0.1) = 1.6

Now for do not stock option , the calculation goes like,

0 for every  proportion of consumer purchasing.

So, from here we can safely say, the decision of having stock of 100 maximizes the expected payoff.

Suppose the sample information is available in the form of a random sample of consumers.

For a sample of size one,

the value of the sample information would be

For stock 100 ; 0.2, 0.3, 0.3, 0.1, 0.1

For stock 50 ; 0.2, 0.3,0.3, 0.1, 0.1

For do not stock ; 0.

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