Microeconomics,, 16th Canadian Edition

24. To prove that for a negatively sloped demand curve, marginal
    revenue is less than price, let. Then

For a negatively sloped demand curve, is negative, and
thus MR is less than price for positive values of Q.
25. The equation for a downward-sloping straight-line demand curve
with price on the vertical axis is

where a is the vertical intercept (when ) and –b is the slope

of the demand curve. Total revenue is price times quantity:

Marginal revenue is

Thus, the MR curve and the demand curve are both straight lines,

they have the same vertical intercept (a), and the (absolute value

of the) slope of the MR curve (2b) is twice that of the demand

curve (b).

p=p(Q)

TR=p⋅Q=p(Q)⋅Q

MR= ddTQR =Q⋅ddQp +p

dp/dQ

p=a−b⋅Q

Q= 0

TR=p⋅Q=a⋅Q−b⋅Q^2

MR= ddTQR =a− 2 ⋅b⋅Q