How does monopoly output and price compare to perfect competition?

Both firms maximize profit the same way: produce where marginal revenue equals marginal cost. The difference is what marginal revenue looks like. A perfectly competitive firm is a price taker facing a flat demand curve, so an extra unit sells at the same market price and marginal revenue equals price. That collapses the competitive rule to price equals marginal cost, which is also where the market supply curve crosses market demand.

A monopoly faces the whole market's downward sloping demand curve instead of a flat one, so selling one more unit forces the price down on every unit already sold. Marginal revenue falls faster than demand and sits below price at every quantity. The monopolist still sets marginal revenue equal to marginal cost to find its quantity, but then reads the price off the demand curve above that point, not off marginal cost. That gap between demand and marginal revenue is the entire reason the two market structures land in different places.

Put numbers on it with demand P = 100 minus Q and a constant marginal cost of 20 for every firm. A competitive market sets price equal to marginal cost: 100 minus Q equals 20, so Q equals 80 and P equals 20. Marginal revenue for that same demand curve is MR = 100 minus 2Q, since total revenue is (100 minus Q) times Q. Setting MR equal to marginal cost gives 100 minus 2Q equals 20, so Q equals 40, and price off the demand curve at Q = 40 is 100 minus 40 = 60. The monopoly produces 40 units at 60 dollars; the competitive market would have produced 80 units at 20 dollars.

The 40 units between the two quantities, from Q = 40 to Q = 80, are worth more to buyers than they cost to make, since demand sits above marginal cost across that whole range, but the monopolist will not produce them because doing so would push marginal revenue below 20. That lost surplus is deadweight loss, and it can be measured directly. You can work the calculator with your own numbers, but by hand it is half the base times the height: base is the 40-unit quantity gap (80 minus 40) and height is the 40-dollar price wedge (60 minus 20), so DWL equals one half times 40 times 40, or 800 dollars.

This is why a monopoly is called allocatively inefficient: price sits above marginal cost, so the last unit sold is worth more to the buyer than it costs society to produce, and units beyond it that would still be worth producing simply are not. A competitive market drives price down to marginal cost and produces every unit worth making, leaving no such triangle. Graph both outcomes on one set of axes and see the full comparison in the perfect competition vs monopoly explainer, or build the monopoly graph yourself in the sandbox.