When is D=MR and S=MC, and when are they different? Is it only in the competitive price-taker situation when they are equivalent?
Supply is a truncated version of the marginal cost curve (above the shut-down condition) in a COMPETITIVE market. Demand equals marginal revenue when demand is perfectly elastic (i.e. horizontal). So the answer to your second question would be yes, unless for some bizarre reason market demand were randomly perfectly elastic.