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Optimal Advertorial Allocation and Contract Design of a Multichannel Networks Company on Video Sharing
Platforms

� �
�� � � � � � (����) �� � � � � � ��(���)� <0, we have decreases in
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=− <0 and =−
�� � � �� � � �
� � � � � � �� � �� � � � �
. Since � = >0 and � = <0, we have increases in and
��
�
�� � �� � �
decreasing in . Q.E.D.
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�
Proof of Proposition 2. We plug in and into and get
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( )
� �
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( , ) = (1 − ) � �
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�
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�

�
( (1 − ) )
� �
(1 − ) � �
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�

� �
( )( (1 − ) ) (1− ) (1 − )(1 − )
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� �

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( ) − ( (1 − ) ) (1− )
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� �
( (1 − ) ) − ( ) �1 − (1− )�
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�
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�
.
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� �
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We then have � � � = ��� (����) � <0, the Hessian matrix of being
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�
�� � � �
�
� � � �
��� (����) �� � �(����)(��(���)�)
�
� �
� � �
� �,
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�
�
�� � �(����)(��(���)�) ��� (��(���)�) �
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� �
� � �
and the determinant of the Hessian matrix being
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� �
�
�
�
( ) ( (1 − ) ) �
� �
� �
�� − �.
� �
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