Added new role with custom capability. But cannot access the page

Question

Created a new role (price_admin) with the following code and added capabilities. The menu item appeared, but clicking it shows "you are not authorized to access this page".

function ui_new_role() {  
    add_role('price_admin',
            'Price Calculator Admin',
            array(
                'read' => true,
                'edit_posts' => true,
                'delete_posts' => true,
                'publish_posts' => true,
                'upload_files' => true,
            )
        );
        $roles = array('price_admin','editor','administrator');
        foreach($roles as $the_role) { 
             $role = get_role($the_role);
                 $role->add_cap( 'read' );
                 $role->add_cap( 'read_price');
                 $role->add_cap( 'edit_price' );
                 $role->add_cap( 'edit_prices' );
                 $role->add_cap( 'edit_others_prices' );
                 $role->add_cap( 'edit_published_prices' );
                 $role->add_cap( 'publish_prices' );
        }
}
add_action('admin_init', 'ui_new_role');

My register_post_type code is:

             register_post_type(
                    'price',
                    array(
                        'labels' => array('name' => 'Treatment Questions'),
                        'capability_type'     => array('price','prices'),
                        'map_meta_cap'        => true,
                        'public' => true,
                        'show_ui' => true,
                        'show_in_menu' => 'my-menu',
                        'menu_position' => 15,
                        'supports' => array('title'),
                        'taxonomies' => array('location'),
                        'has_archive' => true,
                    )
                );

Edit: I use add_menu_page;

add_menu_page('My Page Title', 'Price Calculator', 'manage_options', 'my-menu', 'show_price', 'dashicons-calculator', '13');

This is how it looks like for my new user; (Cannot access both subpages.)

Answer 1

Apart from what I said in the comments — adding new roles should not be done on every (admin) init (here's why), your code is actually good, but your post type is set to show under the custom admin menu named "Price Calculator" (see the 'show_in_menu' => 'my-menu' in your post type arguments), so you'd want to either add the manage_options capability to specific users like the one in question, or lower the capability required to access that menu, e.g.

// I changed the 3rd parameter from manage_options to edit_prices.
add_menu_page('My Page Title', 'Price Calculator', 'edit_prices', 'my-menu', 'show_price', 'dashicons-calculator', '13');