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# The citizens of Ruritania are prodigious consumers of marmite. They can buy it from one of two sellers: Omni Corp (OCP) or the Umbrella Corporation.

The citizens of Ruritania are prodigious consumers of marmite. They can buy it from one of two

sellers: Omni Corp (OCP) or the Umbrella Corporation. The marmite sold by each is identical to

the other but for color of the packaging. OCP sells its marmite in a red package while Umbrella

sells its marmite in a green package. Competition between the two rms follows the Cournot

model. The inverse demand curve for marmite is p = 50 - q;

where q is the total amount of marmite produced by OCP and Umbrella.The production costs

consists of two components. The rst is processing, while the second comes from the price of the

main ingredient. OCP has a constant marginal cost of processing of $2 a unit while Umbrella has

a constant marginal processing cost of $4 a unit.

The main ingredient of marmite is Soylent green which is sold by a monopolist, Soylent Corp.

Soylent Corp enjoys a constant marginal cost of production for Soylent Green of $0 a unit. It

requires 1 unit of Soylent Green to produce 1 unit of either OCP's or Umbrella's marmite. Soylent

Corp charges OCP and Umbrella a wholesale price of w per unit of Soylent Green.

1. Let qO be the quantity of marmite produced by OCP and let qU be the quantity of marmite

produced by Umbrella. Write down an expression for OCP's prot as a function of qO; qU

and w.

2. Determine OCP's reaction function in terms of qU and w.

3. Determine Umbrella's reaction function in terms of qO and w.

4. Determine the equilibrium amounts of marmite produced by each rm as a function of w.

5. What value of w will maximize Soylent Corp.'s prot?

6. The CEO of Soylent Corp thinks her prots would be larger if there were no competition in

the Marmite market. She decides to stop selling to Umbrella, eectively making OCP the

monopoly supplier of marmite. What will Soylent Corp.'s maximum prot be under this

regime? In particular will Soylent Corp. be better o?