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:

The marginal revenue is

Step-by-step explanation:

From the question we are told that

    The inverse demand for a downstream firm is  

    The cost of the critical input produced by  upstream division is  

     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

Also  

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

       i.e

So

Generally the total revenue of  downstream firm is mathematically represented as

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

=>      

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

Generally marginal downstream first cost is mathematically evaluated as

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

=>        

Generally the marginal upstream cost is mathematically represented a

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

So

=>        

=>          

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

=>        

=>        

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)