One seller, downward MR, and a markup over marginal cost, with the profit rectangle shaded live.
Warming up the engine…
A single seller facing the whole market demand curve chooses output where marginal revenue equals marginal cost, then charges the highest price demand will bear for that quantity.
MR = MC ; P read off the demand curve above Q*
To sell one more unit a monopolist must cut the price on ALL units, so marginal revenue lies below demand. That gap makes the monopolist restrict output and price above marginal cost, transferring surplus from consumers and destroying some entirely: the deadweight-loss triangle.
Price comes from the DEMAND curve at Q*, never from the MR=MC intersection itself. Shade deadweight loss between demand and MC from Q_monopoly to Q_competitive.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at Q 38, P 60.
Equilibrium: Q* = 38.1, P* = 59.5
Current equations
One seller, so it faces the whole market demand, and to sell more it must cut the price on every unit, which is why marginal revenuemarginal revenueThe extra revenue from selling one more unit, below price for any firm that must cut price to sell more. (dashed) falls twice as fast as demand. The firm produces where MR = MC, then charges what demand will bear at that quantity. Price above marginal costmarginal costThe cost of producing one more unit. is the monopoly markup; the shaded box is profit.
Source: Varian, Intermediate Microeconomics, ch. 25-26