With this, let’s again solve for the “Point of Position Indifference” for both A1 and A2. 

For A1, nothing changes including the CTRs. 

Thus X is still $2.60; i.e. A1 will continue to increase her bid for the number 1 position until she is paying $2.60; after that she would prefer the number 2 position. 

For A2, the CTRs have changed, doubled to be precise.  So let’s re-calculate this “Point of Position Indifference” which occurs when A2’s daily Expected Net Profits from the number 1 position = daily Expected Net Profits from the number 2 position. 

Daily Expected Net Profits daily from the number 1 position

Clicks per Day * Expected Net Profits per Click = 

Impressions per Day * Click Through Rate * (Expected Gross Profits per Click – Cost per Click) = 

100 * 0.20 * (0.04*$75 – Y) where Y is the click cost that A2 pays for the number 1 position (1c + A1’s bid) 

Daily Expected Net Profits daily from the number 2 position = 

Clicks per Day * Expected Net Profits per Click = 

Impressions per Day * Click Through Rate * (Expected Gross Profits per Click – Cost per Click) = 

100 * 0.12 * (0.04*$75 - $1.00) 

“Point of Position Indifference” occurs when we equate these: 

100 * 0.20 * (0.04*$75 – Y) = 100 * 0.12 * (0.04*$75 - $1.00) 

Solving for Y; Y = 1.80 (i.e. Y did not change either) 

So the surprising result is that “Point of Position Indifference” for A2 does not change even when A2’s ad copy is so much better that it is now getting twice as many clicks as A1 for any given position. 

Thus, even with a superior ad copy, A2 must, like before, concede the number 1 position to A1 who has the higher expected profits per click. 

The reason that this somewhat counter intuitive result is true is that the CTR from A2’s ad copy is uniformly better than A1 (twice as much in both position 1 and position 2).  So even though A2’s absolute daily profits can increase substantially as the CTR increases due to superior ad copy, the point of position indifference between position 2 and position 1 does not change since the ad’s 100% improvement in CTR applies equally to both position 2 and position 1.  (The result could be different if, for instance, the CTR on the number 1 position increases much more as a percentage than the CTR on the number 2 position).