I have a seller say S and I have a buyer say B. Buyer’s willing to pay is equal to x which is private information. But Seller believe that it falls in the range [0,x1]. Seller’s belief distribution is F and cdf of F is f which is positive. Take it or leave it price offer is p which is offered by seller. Buyer accept it iff p is less then and equal to x. How can I write seller’s profit maximization.
How can I construct maximization problem. I cannot imagine it. But after construction I can solve it. Please give me a hint to construct it.
What I did is
$$\Pi_s=(1-F(x))q.r-pq$$ where r is income q is quantity.