A marketing executive must decide whether or not to use a new label on a product

Question

A marketing executive must decide whether or not to use a new label on a product. The firm will gain $800,000 if he adopts the new label and it turns out to be superior than the old label. The firm will lose $500,000 if the executive adopts the new label and it proves to be not superior than the old one. The firm will neither gain nor lose money if the executive sticks with the old label. The executive feels there is a 50-50 chance that the new label is superior to the old one and a 50-50 chance it is not. If he decides to take the action with the higher expected gain to the firm: should he decide to use the new label ornot?

Explanation / Answer

Probability of new label is superior = 0.5

Probability of new label not superior = 0.5

Gain by firm if new label is superior = $800,000

Loss by firm if new label is not superior = $ 500,000

Expected gain if new label is superior : Probability of new label is superior x Gain by firm if new label is superio = 0.5 x 800,000 = 400,000

Expected loss if new label is not superior : Probability of new label not superior x Loss by firm if new is not superior = 0.5 x 500,000 = 250,000

As Expected gain if new label is superior > Expected loss if new is not superior

The firm should use the new label.

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