3) A firm serves two distinct markets and knows that the effects of advertising

Question

3) A firm serves two distinct markets and knows that the effects of advertising on profits in the markets takes the following form: I, = 50 + 1 8A1-0.75A' II 50+ 20A - A where both profits and advertising expenditures are in millions of USS a) the firm has allocated advertising dollars equally between markets can they be maximizing their return per advertising dollar? (Explain your answer in terms of marginal benefits) b) If the total advertising budget is such that AA2 2, how should the firm allocate its advertising dollars?

Explanation / Answer

a) To maximize the profit, the level of advertising should be chosen such that the marginal profits are zero in both regions. This implies
d1/dA1 = 0 and d2/dA2 = 0
18 - 1.5A1 = 0 and 20 - 2A2 = 0
This gives the optimum advertising expenses to be
A1 = $12 M and A2 = $20 M
Now that firm has allocated A1 = A2, it is clearly not a profit maximizing strategy because according to what we get, A1 should be $12 M and A2 should be $8 M more than A1 to get the profit maximized
b) Now we have the limit where A1 + A2 = 2. From our results, we see that A1/A2 = 12/20 = 0.3 Hence we have a situation where A1 = 0.3A2. Use this to see that when A1 + A2 = 2, we must have
0.3A2 + A2 = 2
A2 = 2/1.3 = $1.54 M and A1 = $0.46 M
The allocation rule to be followed is A1/A2 = 0.3.

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