Answer:
Indifference curve is a curve that depicts various combinations of two goods that provides a consumer with the same level of satisfaction. Properties of Indifference Curve (i) Indifference curves are downward sloping to the right: Downward slope of the indifference curve to the right implies that a consumer cannot simultaneously have more of both the goods. An increase in the quantity of one good is associated with the decrease in the quantity of the other good. This is in accordance with the assumption of monotonic preferences. (ii) Slope of IC: The Slope of an IC is given by the Marginal Rate of Substitution (MRS). Marginal rate of substitution refers to the rate at which consumer is willing to substitute one good for each additional unit of the other good. 
At point A Slope of Indifference curve (MRS) =\[\frac{\Delta Y}{\Delta X}\] That is, MRS shows the rate at which the consumer is willing to sacrifice good Y for an additional unit of good X. (iii) Shape of Indifference Curve: An indifference curve is convex to the origin. As we move down along the indifference curve to the right, the slope of 1C (MRS) decreases. This is because as the consumer consumes more and more of one good, the marginal utility of the good falls. On the other hand, the marginal utility of the good which is sacrificed rises. In other words, the consumer is willing to sacrifice less and less for each additional unit of the other good consumed. Thus, as we move down the 1C, MRS diminishes. This suggests the convex shape of indifference curve. At point A, \[MR{{S}_{xy}}=\frac{AD}{DB}\] At point B, \[MR{{S}_{xy}}=\frac{BE}{EC}\] \[\frac{BE}{EC}<\frac{AD}{DB}\] 
Therefore, MRS at B < MRS at A, so MRS has fallen.
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