O$11(14$ points$)$: You must show your work for full credits.

$11.($ch$8$ & ch$9)$ Refer to discussion topic $9$: In $2006,$ three Coke employees sent a letter to Pepsi offering to sell them Coke's closely guarded secret recipe. The executives at Pepsi turned the letter over to Coca$-$Cola, which then turned it over to the FBI. The employees ended up serving up to $8$ years in prison for conspiracy. Consider the market structure currently faced by Coke and Pepsi. $($For more information, please refer to the article posted on the course website.$)$

a$.$ What barriers to entry exist in the soft drink industry other than Coke's secret formula?

b$.$ Suppose that the recipe for Coke is released, and dozens of new cola manufacturers enter the market. As a result, the market for soft drinks becomes perfectly competitive, and Pepsi faces the accompanying long$-$run cost curves. The graph below describes the long$-$run marginal cost $($LMC$),$ long$-$run average total cost $($LATC$),$ long$-$run average variable cost $($LAVC$)$ and marginal revenue $($MMD$)$ Price:

cost cost $($$$/$u$)$

Is it possible for Pepsi to operate in a perfectly competitive industry with a long$-$run competitive equilibrium at any point other than B$?$ Explain your answer.