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The difference is this:
In perfect competition, the MR curve is the same as the demand curve and the MC is the same as the supply. So the point at which they meet is the equilibrium price.
In a monopoly, the firm still produces the QUANTITY where MR=MC, but in this case the MR curve is NOT the same as the demand curve. Instead, the demand curve is farther right than the MR curve.
So in both cases, the firms produce the QUANTITY where MR = MC. In perfect competition, that's the equilibrium price too. But in a monopoly you have to go up to the demand curve to find the price.
Is there a graph of this in your text? It should help you understand. Or look at the graph in the rochester.edu link. Qm is the equilibrium quantity but then you go straight up from there to the demand curve to get the price. The other link shows perfect competition.
In monopolistic competition the demand curve for the whole market and for the monopolistic firm is same. That is the demand curve for the firm is also downward sloping. In comparison in perfect competition the demand curve for the firm is a straight line.
Thus a monopolistic firm has to reduce its price to increase its sale. This means that at any time the marginal revenue is less than the price level essential for selling the increased sale. Thus marginal revenue for a monopolistic firm is always less than price. In contrast the marginal revenue for a firm is always same as the market equilibrium price which remains constant irrespective the quantity sold.
Both monopolistic firm and a firm in a perfectly competitive market maximize their profit by selling a quantity where marginal revenue equals marginal cost. But for this marginal revenue and marginal cost is lower than the market price. This point is reached for a quantity that is less than the quantity corresponding to lowest average cost. In perfect competition, the the quantity sold by each firm also corresponds to its lowest average cost.
Thus a monopoly firm increases its profit by producing and selling at a level which is lower than the quantity corresponding to most efficient production. In contrast, every firm in a competitive market produces and sells a quantity that enables it to produce most efficiently with lowest average cost.
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