Question

5. Assume that there is a market with 10 upstream intermediate-good producers and 10 downstream final-good producers. Four of these firms are vertically integrated leaving 6 independent upstream firms and 6 independent downstream firms. Each upstream firm has a constant marginal cost equal to 0. The only cost to the independent downstream firms is the price of the intermediate good. The inverse demand in the final-good market is P = 100 – Q_F. One unit of the intermediate good is needed to make one unit of the final good.

               a. Determine the equilibrium prices in the downstream market and the independent upstream market. Show your work.

               b. Determine what happens to the equilibrium prices in the downstream market and the independent upstream market if one more independent upstream firm merges with one of the remaining independent downstream firms. Show your work.

Answer 1

a)

The inverse demand function is given, i.e. P = 100 - QF.

From this equation, we can determine the total revenue and marginal revenue equations.

TR (PxQ) = 100QF - (QF)²

MR () = 100 - 2 QF

Now, note that for each intermediate good, there is one final good. The quantity in both the markets is the same. Let's start with this problem by assuming that the quantity for both the markets is 40 units.

It follows:

P = 100 - 40 = $60

MR = 100 - 2(40) = $20

Equilibrium exists where MR = MC. Thus, here, MR = MC = 20. Note that the question says the only cost to the downstream market is the price of the intermediate good. From this, we can safely assume price of intermediate good to be $20. This price applies only for the independent firms, since the vertically independent firms would be free of prices.

From this discussion, it follows:

Equilibrium price in the downstream market = $60

Equilibrium price in the independent upstream market = $20

b)

If one more upstream firm integrates with a downstream firm, the integrated firm's cost would decrease significantly, allowing it to sell at a lower price. This could result in decrease in prices in the final good industry.

In the independent upstream market, however, the total supply has reduced as there are only 5 firms now. This could result in increase in prices of this market.