Is $2K a reasonable price for a landing page and funnel analysis?

Depends on many, many things:

• How much work, exactly, are they doing for you? Just one page? A whole site? Are they doing the marketing copy, too, or just the aesthetic design?
• How good are they? Obviously, putting together a landing page is not something that can be done effectively without a deep understanding of your product and market.
• How much validation have you done? The further away you are from knowing 100% that your target customer likes your product, the less time and money you should be spending on stuff like this. Instead you should be whipping out crude prototypes and testing them quickly, or working on other means of validation and learning.
• How do you find your customers? Unless you have a bonafide way of getting customers to your landing page, you might want to consider alternatives. Not every business can be successful at driving customers to a landing page.
• What do the people in your market care about? If you're selling to programmers, for example, they tend not to care about aesthetics. In fact, they're often turned off by sleek designs. Making a text-only page is a good way to signal that "you're one of us." In that case, you wouldn't need a beautiful landing page. On the flip side, if you have an expensive product and/or a product in an industry where high trust is required, you want your page to look perfect and professional. The same might go if you're doing some sort of e-commerce play to a mass consumer audience, e.g. a Kickstarter.
• What's your runway? If you've got more time than money, spend your time (wisely) in order to save your precious money. If you have more money than time, spend your money (wisely) in order to conserve your precious time.

etc.

If you just want to do some market analysis with a landing page I would go with a hosted landing page provider like leadpages or unbounce (30-50€/month). 2K just for testing the water seems a little bit too much.

If you're asking it's that you do not know what you're doing. If you accept it will be a pain for them and for you.
Do it yourself, learn.

What's the value to you in dollars that an efficient funnel would bring? Thousands, tens of thousands, hundreds of thousands? $2k might not be that much with that perspective.

If its for testing, sytescope.com lets you do A/B testing in for your landing funnel pages. $30/m Canadian for base product, can even have custom domains for the funnels. Similar to leadpages.

Is it a landing page analysis and a funnel analysis or a landing page design and a funnel analysis?

Really depends:/
If you have content ready and mvp allows templated design etc it should be cheaper. But if your solution is complex and you invest into unique design... then mb fine.

Why not use some trmplate builder before paying money?