Question

Suppose that the inverse demand for a downstream firm is P = 150 − Q. Its upstream division produces a critical input with costs of CU(Qd) = 5(Qd)2. The downstream firm's cost is Cd(Q) = 10Q. When there is no external market for the downstream firm's critical input, the marginal revenue for the downstream firm is:

Answer 1

Answer:

The marginal revenue is $MT_d = 116.66$

Step-by-step explanation:

From the question we are told that

    The inverse demand for a downstream firm is  $P = 150 -Q$

    The cost of the critical input produced by  upstream division is  $CU(Q_d) = 5(Q_d)^2$

     The cost of the critical input produced by downstream firm  is  Cd(Q) = 10Q

Generally

The marginal revenue of the downstream firm - The marginal cost  of the downstream firm =  Net marginal revenue of downstream

i.e

    $MR_d - MC_d = MT_d$

Also  

  The marginal revenue of the downstream firm - The marginal cost  of the downstream firm =  Marginal upstream cost  

       i.e

            $MR_d - MC_d = MC_u$

So

     $MR_d - MC_d = MC_u$

Generally the total revenue of  downstream firm is mathematically represented as

          $TR = P * Q$

Here Q stands for quantity produced by the downstream firm  and  TR is the total revenue

         $TR = [150 - Q] * Q$

=>      $TR = 150Q - Q^2$

Generally the marginal revenue of the downstream firm is mathematically evaluated as  

         $MR_d =\frac{d (TR)}{d Q} = 150 - 2Q$

Generally marginal downstream first cost is mathematically evaluated as

         $MC_d = \frac{d(Cd(Q)) }{dQ} = 10$

Generally the net marginal revenue of the downstream firm is mathematically represented as

            $150 - 2Q -10 = MT_d$

=>        $MT_d = 140 - 2Q$

Generally the marginal upstream cost is mathematically represented a

               $MC _u =\frac{d [CU(Q_d)]}{dQ_d} = 10(Q_d)$

Generally  $Q_d = Q$ this because $Q_d$ represents the quantity produced by the downstream firm and also  Q is associated with the cost of the downstream quantity  

So

            $MC _u =\frac{d [CU(Q)]}{dQ} = 10Q$

=>         $10(Q) = 140 -2Q$

=>          $Q = 11.67$

So the net marginal revenue of the downstream firm is mathematically represented as

=>        $MT_d = 140 - 2(11.67)$

=>        $MT_d = 116.66$