What connection do you realize between the convexity of indifferent curve and the marginal rate of substitution?
The negative slope of the indifference curve implies that the marginal rate of substitution is always positive. Indifference curves are typically represented to be convex. Convex preferences imply that the indifference curves cannot be concave to the origin, i.e. they will either be straight lines or bulge toward the origin of the indifference curve. If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the other good are required to keep satisfaction unchanged.