INDIFFERENCE CURVE ANALYSIS

An indifference curve is a locus of point representing the combination of two commodities that provide an individual with a given level of satisfaction. Provided a consumer has more of one commodity he must give up some units of the other commodity to compensate and still maintain the same total satisfaction; therefore an indifference curve must slope downwards from left to right. 

 The law of diminishing -marginal-utility propounds that each additional unit of commodity B would provide successively less and less additional utility. This means successively less of product A has to be sacrificed to maintain the same utility. This can be seen by the gradient of the indifference curve.
The Marginal Rate of Substitution (MRS) gives the gradient of an indifference curve. This shows the amount of a commodity a consumer would be prepared to sacrifice for additional unit of another commodity and still maintain the same level of satisfaction. A consumer gets the same level of satisfaction along a given indifference curve. An increase in the quantity of commodity X is always accompanied by a similar decrease in the quantity of commodity Y and thus the marginal rate of substitution must be negative.