Assume that a demand equation is given by pq=9000100p. Find the marginal revenue

Question

Assume that a demand equation is given by pq=9000100p. Find the marginal revenue for the given production levels (values of q). (Hint: Solve the demand equation for p and use R(q)=qp .

Assume that a demand equation is given by q : 9000-100p Find the marginal revenue for the en production eve s va eso Hint S vethe demand equation orpandus R p a. 3000 units The marginal revenue at 3000 units is Simplify your answer) b. 4500 units The marginal revenue at 4500 units isSimplify your answer.) c. 5000 units The marginal revenue at 5000 units is (Simplify your answer.)

Explanation / Answer

Here we are given that:

q = 9000 - 100p

Therefore, p in terms of q is written as:

p = (9000- q ) / 100 = 90 - 0.01 q

Therefore the revenue is given as:

R(q) = pq = 90q - 0.01 q2

The marginal revenue is computed by differentiating the revenue with respect to q. Therefore, we get:

MR = 90 - 0.02 q

a) The marginal revenue for q = 3000 is computed as:

MR = 90 - 0.02*3000 = 30

Therefore 30 is the required marginal revenue here.

b) The marginal revenue for q = 4500 is computed as:

MR = 90 - 0.02*4500 = 0

Therefore 0 is the required marginal revenue here.

c) The marginal revenue for q = 5000 is computed as:

MR = 90 - 0.02*5000 = -10

Therefore -10 is the required marginal revenue here.

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