Question

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 1

Answer:

Q=8 Units

Step-by-step explanation:

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

$CU(Qd) = 3(Qd)^2$

taking first derivative we get

$MC_U = 3 \cdot2 Q$

$MC_U = 6$

similarly taking derivative of downstream we get

$MC_d = 2Q$

$MC_d = 2$

$MR= 2+6Q$

$P = 82-2Q$

$Revenue = P*Q = 82Q-2Q^2$

So $Revenue = P*Q = 82Q-2Q^2$

$82-4Q = 2+6Q$

$10Q=82-2$

$Q=\frac{80}{10}$

$Q=8~Units$