Question

The demand function for a commodity is given as Q=100-p, where p is the price per unit and Q is the number of units. Find the marginal revenue when Q=20 units.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the marginal revenue, we need to find the derivative of the total revenue function with respect to quantity (Q).

Total revenue (R) is calculated by multiplying the price per unit (p) by the quantity (Q). So, R = p * Q.

Marginal revenue (MR) is the derivative of the total revenue function with respect to Q.

First, let's express p in terms of Q using the demand function:

Q = 100 - p
p = 100 - Q

Substituting this into the total revenue function, we get:

R = (100 - Q) * Q
R = 100Q - Q^2

Taking the derivative of R with respect to Q:

dR/dQ = 100 - 2Q

Now, we can find the marginal revenue when Q = 20:

MR = dR/dQ
MR = 100 - 2 * 20 (substituting Q = 20)
MR = 100 - 40
MR = 60

Therefore, the marginal revenue when Q = 20 units is 60.