How can 【所】に【物】があります be converted to 【物】は【所】です?

Question

Consider the following,

1. 机の上に本があります。
2. 本は机の上です。

What I don't understand is the second sentence which is another form for the first one. It is caused by the fact that there is no preposition に in the second one.

If you don't understand what I meant, let consider the following sentences. The first two sentences are understandable because they have English equivalents. But it is not the case for the last one.

• This is a book. これは本です。
• This book is red.　この本は赤いです。
• This book is on the table.　この本は机の上です。I never read and hear この本は机の上にです。in which there is に inserted between 机の上 and です.

Can anybody here explain why?

Answer 1

You can say:

本はどこですか？ Where's the book? (＝本はどこにありますか？)
机の上です。 It's on the desk. (＝机の上にあります。)
本は机の上です。 The book is on the desk. (＝本は机の上にあります。)

and no one would think you're saying "The book is upper part of a desk".
Similar examples are:

お父さんは二階です。 Dad is upstairs.
太郎くんは学校です。 Taro is away at school.
姉は今、ロンドンです。 My sister is in London now.

You can even say:

僕はウナギです。(I'll have eel.)
私はオレンジジュース。(I'll have orange juice.)

at a cafe or restaurant, and no one would think you're saying you're an eel or orange juice.

*この本は机の上にです。

is incorrect.