How are the price and the output determined under monopoly in short run? Is monopoly price is always higher than competitive price? Give reasons.

Under monopoly there is a single seller of a product with no close substitutes who is a price maker, and in the short run this firm determines its price and output at the point where marginal cost equals marginal revenue, producing whatever profit or loss cost conditions allow.

The determination of price and output:

1. Downward-sloping demand: since the monopolist is the whole industry, it faces a downward-sloping demand (AR) curve and must lower price to sell more, so MR lies below AR.
2. Goal: the monopolist aims to maximise profit, where profit π = TR − TC.
3. Equilibrium condition (necessary): it produces the output at which MC = MR.
4. Equilibrium condition (sufficient): MC must cut MR from below (the slope of MC exceeds the slope of MR) for the point to be a profit maximum.
5. Output determination: the equilibrium output is fixed at the quantity where the MC and MR curves intersect at point E.
6. Price determination: the price is then read off the demand (AR) curve above that output, so the monopoly price is higher than MR at equilibrium.
7. Supernormal profit: if AR > AC at that output, the monopolist earns excess (supernormal) profit, equal to the gap between AR and AC times output.
8. Normal profit: if AR = AC, the monopolist earns only normal profit.
9. Loss (minimised): if AR < AC but price still covers average variable cost, the firm produces at a minimum loss rather than shutting down; if price falls below AVC it shuts down.
10. Persistence: because barriers to entry keep rivals out, a profitable monopolist is not competed away even in the short run.

Is the monopoly price always higher than the competitive price?

11. General tendency — usually higher: a monopolist restricts output and charges a higher price than a competitive industry would, because it produces where MC = MR (and MR < price), whereas a competitive firm produces where MC = price.
12. Reason — output restriction: by producing less and setting price above marginal cost, the monopolist keeps price above the competitive level, which is why monopoly is associated with output restriction and welfare loss.
13. Not always higher — economies of scale: where a single large firm enjoys large economies of scale (a natural monopoly), its costs may be so much lower than many small firms' costs that it can charge a price at or below the competitive price.
14. Not always higher — cost and demand conditions: if the monopolist's cost curves are much lower, or demand is such that a low-price high-volume strategy pays, the monopoly price need not exceed the competitive price.
15. Conclusion: so the monopoly price is generally higher than the competitive price because of output restriction, but it is not necessarily always higher — with strong economies of scale or much lower costs it can be equal to or even below the competitive price.

Thus, a short-run monopoly fixes output where MC = MR and price on the demand curve above it, earning profit, normal profit or a minimised loss; its price is usually higher than the competitive price because of output restriction, but not invariably so.