A manufacturer of a product has a marginal revenue function given by =200 + 70q - 3
)The demand function for the product is given by
A) p = - 6.
B) p = 70 - 6q.
C) p = 200q + 35 -
D) p = 200 + 35q -
E) p = 200q + 35 -

Question

A manufacturer of a product has a marginal revenue function given by  =200 + 70q - 3 
)The demand function for the product is given by
A) p = - 6. 
B) p = 70 - 6q. 
C) p = 200q + 35 - 
D) p = 200 + 35q - 
E) p = 200q + 35 -

Quizplus · Accepted Answer

Marginal revenue (MR) is given by the derivative of the total revenue function (TR). 
Here, MR = 70 - 6q
Demand (D) is given by the inverse of the total revenue function (TR). 
Therefore, D = (TR)^(-1) -> p = TR/q
From the given marginal revenue function, we can obtain the total revenue function as follows:
MR = d(TR)/dq = 70 - 6q
Integrating both sides with respect to q, we get:
TR = 70q - 3q^2 + C
Using the demand equation p = TR/q, and given that at quantity 0, the price is 20, we can find the constant C as follows:
20 = TR(0)/0 -> C = 20
Therefore, the total revenue function is: TR = 70q - 3q^2 + 20
Substituting this in the demand equation, we get:
p = (70q - 3q^2 + 20)/q
Simplifying, we get:
p = 200/3 - (100/q) + 35q
This matches the form p = 200 + 35q - 10q^(-1), which is option D.

A Manufacturer of a Product Has a Marginal Revenue Function