<p>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. </p>

<p><a href="https://i.sstatic.net/Oxc52.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Oxc52.png" alt="enter image description here"></a></p>

<p>My lecture note says the optimal pricing strategy is a form of P(q)=β(1-q) where
<a href="https://i.sstatic.net/YsRgJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YsRgJ.png" alt="enter image description here"></a></p>

<p>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?</p>

<p>Thanks a lot in advance :)</p>

CC BY-SA 4.0
2020-06-11T03:51:33.743Z
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:https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions
EconJohn
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2020-06-11T12:50:31.670Z
@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 :)
modern
<dynamic-programming><dynamic-optimization>
Coase conjecture and Stokey model
modern
# Coase conjecture and Stokey model

(Asked by: username_0 on 2020-06-10)

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](https://i.sstatic.net/Oxc52.png)](https://i.sstatic.net/Oxc52.png)

My lecture note says the optimal pricing strategy is a form of P(q)=β(1-q) where
[![enter image description here](https://i.sstatic.net/YsRgJ.png)](https://i.sstatic.net/YsRgJ.png)

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 :)

**Tags:** dynamic-programming, dynamic-optimization
> **Comments:**
> **username_1**: 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:https://economics.meta.stackexchange.com/questions/1465/economics-se-policy-on-homework-questions  
> **username_0**: @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 :)  

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