 marginal rate of substitution along an indifference curve for altering the consumption of one commodity, consumer has to change the consumption of the other commodity. This is done while maintaining the level of satisfaction of the consumer unchanged. As we know, indifference curve is a negatively sloped curve and the slope of indifference curve is always change in perpendicular over change in base as along y axis we are taking oranges and on along horizontal axis we are taking apples. So slope of an indifference curve is change in oranges because of change in apples and this is also equal to marginal utility that someone is getting from apples over marginal utility of oranges and marginal utility is change in utility because of change in consumption of apples while marginal utility of oranges is change in total utility because of change in the consumption of oranges. To explain the slope of indifference curve we will use this diagram and to explain the slope of the indifference curve we will show it on the screen. To explain slope of the indifference curve we are using the diagram where we are taking apples on horizontal axis and oranges on vertical axis. If our objective is to find out the slope of the indifference curve between point A to B to find out the slope of the indifference curve we will compute what is change in oranges along vertical axis because of change in apples when a consumer moves from point A to point B there is change in the quantity of apples that are being used by that particular consumer and similarly when consumer moves from point A to point B there is also a change in the quantity of oranges. For example at point A consumer is using 10 units of oranges and 1 unit of apple and at point B consumer is using 5 units of oranges and 2 units of apples. Between these 2 points change in the quantity of oranges is equal to 5 minus 10 so there is a decrease in the quantity of oranges by 5 units between these 2 points. Similarly when we look at the quantity of apples we can see the consumption of apples is increased by 1 unit. So slope of the indifference curve between point A to B is equal to minus 5 over 1 minus 5 indicates change in the quantity of oranges because of change in quantity of apples. Similarly if we compute the slope of indifference curve between point B to C between these 2 points there is a decrease in consumption of oranges by 3 units at point B consumer is using 5 oranges while at point C consumer is using 2 units of oranges. So there is a decrease in consumption of oranges by 3 units between these 2 points but when we look at the quantity of apples there is increase in the quantity of apples by 1 unit. So slope of the indifference curve between point B to C is equal to minus 3 and similarly if we compute the slope of the indifference curve between point C to D it is equal to minus 1. So slope of the indifference curve indicates 8 changes when we move along an indifference curve. In fact as we move down along an indifference curve slope of indifference curve increases if we do not ignore the negative sign. Another concept that is very important is the marginal rate of substitution. This marginal rate of substitution is the rate at which consumer is willing to substitute one commodity with another commodity while keeping his satisfaction unchanged. So marginal rate of substitution of apples for oranges is equal to negative of the slope of an indifference curve or marginal rate of substitution for apples for oranges is equal to minus of the marginal utility of apples over marginal utility of oranges. And this marginal rate of substitution of apples for oranges in fact indicates the units of oranges that a consumer is willing to forego to get an additional unit of apples. So to elaborate the concept of the marginal rate of substitution again we are using sacrine. As we computed the marginal slope of the indifference curve in the earlier diagram it indicates slope of the indifference curve between point A to B is equal to minus 5 minus 3 between point B to C and minus 1 between point C to D. But when we make discussion about the marginal rate of substitution, marginal rate of substitution is the rate at which consumer is willing to forego units of one commodity to get an additional unit of an other commodity. So marginal rate of substitution between point A to B is equal to 5. So consumer is willing to forego 5 units of oranges here to get an additional unit of apple. Between point B to C marginal rate of substitution is equal to 3. Consumer is willing to substitute 3 units of oranges to get an additional unit of apples. So by looking in this diagram we can see marginal rate of substitution decreases as we move down along an indifference curve. Between point A to B marginal rate of substitution is equal to 5. Between B to C it is equal to 3. And between C to D it is equal to 1. So when there is increase in the quantity of apples and decrease in the quantity of oranges the rate of substitution of oranges to get additional unit of apple decreases. So on the basis of all we can make a conclusion that marginal rate of substitution falls as we move down along an indifference curve as our orange consumption falls its marginal utility rises while the increase in the consumption of apples results in a fall in their marginal utility. So marginal rate of substitution falls as we increase the consumption of the commodity that lies on x axis and decrease the consumption of commodity on y axis. In our case we are taking apples on x axis. So there is increase in the consumption of apples when we move down along an indifference curve. And there is a decrease in consumption of oranges that we are taking along y axis. So in fact law of diminishing marginal rate of substitution operates along an indifference curve.