This is because you are using a static page on homepage and there are no posts on your websites only pages. The theme by default doesn’t show Author on Pages. Author is only displayed on posts.
All themes are built this way because for eg. if you choose to enable author for single pages then all pages on your site will have author, even the about page, terms and conditions page which is not a good idea.
If you still want to display author on single pages, then do the following:
Open content-page.php,
Now paste the following code after line 21 ()
<div class="clear"></div>
<div class="author-info">
<div class="author-avatar">
<?php echo get_avatar( get_the_author_meta( 'user_email' ), apply_filters( 'themonic_author_bio_avatar_size', 68 ) ); ?>
</div><!-- .author-avatar -->
<div class="author-description">
<?php printf( __( 'Author: %s', 'themonic' ), get_the_author() ); ?>
</div><!-- .author-info -->