In: Statistics and Probability
Recall that the company’s quarterly profits (excluding advertising costs) are $4 million when sales are high (State = 1) and $2 million when sales are low (State = 0). Therefore, in units of millions of dollars, the long run expected average cost (excluding advertising costs) is
To take advertising costs ($1 million) into account, we need to subtract 1 from each coefficient where advertising is done. This leads to the calculations shown below-
For the “never advertise” strategy, the long-run expected average profit is profit = 2(2/3) + 4(1/3) = $ 8/3 million.
For the “always advertise” strategy, the long-run expected average profit is profit = 2(1/3) + 4(2/3) -1 = $ 7/3 million.
For the marketing manager’s proposal, the long-run expected average profit is profit = (2-1)(1/2) + 4(1/2) = $ 5/2 million.
Therefore, when the objective is to maximize the long run expected average profit, the best strategy is “never advertise”