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Suppose that the inverse demand for a downstream firm is P = -82 − 2Q. Its upstream division produces a critical input with costs of CU(Qd) = 3(Qd)2. The downstream firm's cost is Cd(Q) = 2Q. When there is no external market for the downstream firm's critical input, the downstream firm should produce:

Answer :

danialamin

Answer:

Q=8 Units

Step-by-step explanation:

FIrst from the Critical cost if we take first derivative we get marginal upcost i-e

[tex]CU(Qd) = 3(Qd)^2[/tex]

taking first derivative we get

[tex]MC_U = 3 \cdot2 Q[/tex]

[tex]MC_U = 6[/tex]

similarly taking derivative of downstream we get

[tex]MC_d = 2Q[/tex]

[tex]MC_d = 2[/tex]

[tex]MR= 2+6Q[/tex]

[tex]P = 82-2Q[/tex]

[tex]Revenue = P*Q = 82Q-2Q^2[/tex]

So [tex]Revenue = P*Q = 82Q-2Q^2[/tex]

[tex]82-4Q = 2+6Q[/tex]

[tex]10Q=82-2[/tex]

[tex]Q=\frac{80}{10}[/tex]

[tex]Q=8~Units\\[/tex]

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