Why MR and AR sloping downward in monopoly?

Question

Why MR and AR sloping downward in monopoly?

Answer 1

Q = quantity, P = price, R = Total Revenue

MR = d R / dQ

The derivative of the revenue with respect to q.

Revenue = Q * P

by the chain rule

dR/dQ = P + Q*dP/dQ

in perfect competition dP/dQ the change in price caused by a change in your quantity is 0, dP/dQ = 0, because a firm can have no effect on the price level.

so dR/dQ = MR = P +Q*0 = P

AR = R / Q = P*Q/Q = P

In a monopoly

dP/dQ is not equal to zero. A firm can increase its price by reducing output or reduce its price by increasing output. So as Q is increased P will go down making MR decrease and AR decrease. The change in price with respect to quanitity output is the reason why these curves slow downward in a monopoly setting.

Let me know if you understood this answer if you didn't I can help explain it more it might depend on what is your experience in economic theory. You may have wanted a layman's explanation.