Imagine that there are two monopolies: upstream and downstream. The upstream monopoly produces units of wood, x, that it sells for $k each to the downstream monopoly. Its cost of making wood is C(x) = 20x. The downstream monopolist uses the wood to make tables, y, which it sells for $p each. The demand for tables is p = 80 - y. Wood is the only input used by the downstream monopoly. It needs 2 units of wood for each table, so y = x/2 for production. [Hint: think about how this will affect the cost of a table.]
- Find the following: k, p, y and x.
- Find the profits of each firm.
- Show that if the firms merged, the profits made by the merged firm would be greater that the sum of the profits when they do not merge.
- How much would the merger benefit table-consumers? Calculate the change in consumers' surplus due to the merger.