Question

Derive the MR function for the demand function q = 400 - 0.1p

Answer 1

To find the marginal revenue (MR) function, we first need to determine the total revenue (TR) function.

The total revenue (TR) is equal to the price (p) multiplied by the quantity demanded (q):
TR = p * q

Using the demand function q = 400 - 0.1p, we can substitute q into the total revenue equation:
TR = p * (400 - 0.1p)

Expanding the equation gives:
TR = 400p - 0.1p²

To find the marginal revenue (MR), we take the derivative of the total revenue function with respect to quantity (q):

MR = d(TR) / d(q)

Differentiating the total revenue function with respect to q, we get:
MR = d(400p - 0.1p²) / d(q)

Consider p as a constant, since we're looking for the relationship between MR and q, not MR and p. Taking the derivative with respect to q gives us:
MR = 400 - 0.2p

So, the marginal revenue (MR) function for the demand function q = 400 - 0.1p is:
MR = 400 - 0.2p