a) Indifference curves are convex to the origin due to the diminishing marginal rate of substitution. As a consumer substitutes one commodity for the other, the marginal rate of substitution diminishes as one moves along the curve.
b) Indifference curves cannot intersect because different curves indicate different levels of consumer satisfaction. Therefore, if they intersect, the point of intersection will depict equality in satisfaction levels along the two curves while the satisfaction levels are different on other points along the two curves.
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