The durable goods monopolist can charge different prices by every periods. Critical type consumers are indifferent between buying today and buying tomorrow. So I construct a Bellman equation like below.

enter image description here

My lecture note says the optimal pricing strategy is a form of P(q)=β(1-q) where enter image description here

The thing is that I can't get that answer... There is a chance that I established the equation wrong, but if it's correct can you solve the above optimization problem and get the answer?

Thanks a lot in advance :)

  • $\begingroup$ Hi, Welcome to Economics SE! we have a policy regarding homework questions where users must demonstrate effort using text, markdown syntax and/or images space provided in the text of his question submission for the site. Using only images as proof of work is insufficient. for more details see:economics.meta.stackexchange.com/questions/1465/… $\endgroup$
    – EconJohn
    Jun 11 '20 at 3:51
  • $\begingroup$ @EconJohn Oh, Didn't know that policy! Actually I typed using another math input program and made a capture because had no idea how to insert math expressions, but I will give it a try. Thanks for the notice anyway :) $\endgroup$
    – modern
    Jun 11 '20 at 12:50

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