Ask HN: Prospect wants to work but won't increase budget – What are my options?

So, we run a small two people agency that offers services relating to wireframes, IA, UX and copywriting. This prospect approaches us to redo their existing website. He says he wants satire-based copywriting along with wireframes and UX support too. Also, his in-house team is not good enough at design and he wants us to direct them as well on design front. He asked us to do a sample so that he knows we understood what he wants. Turns out he liked our concept work and we met again. He had budget constraints so we asked him to what we could eliminate to meet his number. He is adamant you do all the work at $YYYY. Now, we followed him up and he gave us two reasons for not being able to convince his team - 1. our high prices 2. we don't have sufficient experience in the IT field.

We had sent him our samples of UX and copy relating to IT which clearly stated our expertise. He came up with the experience point now not back then.

When we emailed him that we are assuming we are not going ahead and not to use our sample for commercial purposes, he replied please send me a revised quote because your price is high and a portfolio if you have any that showcases your expertise.

He said for now he is going to do work in-house. But, if we send revised prices and portfolio, he could look to hire us.

What are our options in terms of convincing the client because its a project we would really like to work on but we don't want to reduce our prices because we have full confidence in our capabilities and other clients are paying us similar rates and even higher than this.

How do we convince him to give us the project?