Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium...

Question

Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium producers that act as price takers of the price Dysprocorp sets. Market inverse demand for dysprosium is P D (Q) = 400 – Q, with P measured in dollars per ton of dysprosium and Q measured in thousands of tons of dysprosium. The fringe marginal cost curve is MCF(qF) = XXXXXXXXXX5qF (with qF and MCF also in thousands of tons of dysprosium and dollars per ton of dysprosium, respectively). Dysprocorp’s marginal cost of production is constant at $52 per ton. Dysprocorp needs to plan its strategy for setting the price of dysprosium.

[In this problem, consider a static market equilibrium in one period only and assume that the user cost of dysprosium production for both Dysprocorp and firms in the competitive fringe is zero].

Determine the residual demand facing Dysprocorp after accounting for the quantity supplied by the competitive fringe.

Assume that Dysprocorp’s marginal revenue after accounting for the competitive fringe is MRr(Qr) = 160 – (2/3)Qr. How much dysprosium will Dysprocorp supply?

What is the resulting dysprosium price?

How much dysprosium is produced by the competitive fringe?

Komalavalli · Accepted Answer

2. Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium producers that act as price takers of the price Dysprocorp sets. Market inverse demand for dysprosium is P D (Q) = 400 – Q, with P measured in dollars per ton of dysprosium and Q measured in thousands of tons of dysprosium. The fringe marginal cost curve is MCF(qF) = 40 + 0.5qF (with qF and MCF also in thousands of tons of dysprosium and dollars per ton of dysprosium, respectively). Dysprocorp’s marginal cost of production is constant at $52 per ton. Dysprocorp needs to plan its strategy for setting the price of dysprosium. 
[In this problem, consider a static market equilibrium in one period only and assume that the user cost of dysprosium production for both Dysprocorp and firms in the competitive fringe is zero].
a. Determine the residual demand facing Dysprocorp after accounting for the quantity supplied by the competitive fringe. 
To find dominant firm demand curve we need fringe firm supply and price information lets us derive the required thing using the given information
Deriving supply curve of a fringe firm from MCF = 40+0.5qf
P = 40 +0.5qf
-0.5qf = 40-P
qf  = (40 –P)/-0.

Dysprocorp is a near-monopoly supplier of dysprosium. There is a competitive fringe of dysprosium producers that act as price takers of the price Dysprocorp sets. Market inverse demand for dysprosium...

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