Frankenstein Monster Model

Setting

Two upstream firms, two downstream firms, all firms set prices.

For downstream firms:

$q_i=10-p_i+p_j$

To make 1 unit downstream, you need 1 unit upstream input. Here is an graphically example:

Note: we make the setting that the downstream firms make differentiated products, while the upstream firms make identical products.

All firms set the prices simultaneously, and we could get:

Pre-merger

Since the products are identical, $U_1$ and $U_2$ would behave like Perfect Competition, which is $P=MC$, so that ${\pi }_{U1}={\pi }_{U2}=0$. (We assume there is no fixed cost)

For simplicity, we let $D_i$ buys from $U_i$

Post-merger

We now let $U_1$ and $D_1$ merge. When they claim to merge, $U_1$ would commit that it would not supply $D_2$

So it is easy to understand that $U_2$ now becomes a monopolist, (see Monopoly), it is able to set its own price now.

Consumers

Consumers are harmed by firms. Due to increase in $P$. So that the consumer surplus is significantly decreased.