Both of these things have to do with what people want and how much of it they want. The law of diminishing marginal utility tells us that we will be willing to pay a lot for the first unit of something that we buy, but we will be willing to pay less and less for further units. Indifference curves are representations of the combinations of things that we will be satisfied with having.
In order to understand the law of diminishing marginal utility think about what would happen if you came upon a food truck when you are extremely hungry. Let’s say that burritos at this truck cost $2 each. You are so hungry when you get there, that you would be willing to pay $5 for the first burrito and maybe even for the second. You get a lot of utility (value) from those burritos because you are so hungry. But now you’ve eaten two burritos and you’re not that hungry anymore. A third burrito wouldn’t have so much utility for you. The utility you get from eating burritos drops as you eat more of them. This is the law of diminishing marginal utility.
Indifference curves are related to utility. Indifference curves show different possible combinations of goods that would all have the same utility for us. Let’s say you are at a barbecue and you can have as many hamburgers and/or hot dogs as you like. You may not really care which of these you have. So, you might be just as satisfied with 2 hot dogs and one hamburger as you are with 2 hamburgers and one hot dog. Your indifference curve would include those two combinations because they have the same utility for you.
Law of Diminishing Marginal Utility states that:
"The additional benefit which a person derives from a given increase of his stock of a thing diminishes with every increase in stock that he already has."
The above statement says that when a person consumes units of the same commodity consecutively, the Marginal Utility(additional satisfaction) that he gets from each successive unit decreases. In order to explain this concept lets consider the following example: A person is drinking glasses of water one after the other, the following table shows that even when his total utility increases upto a certain level marginal utility keeps on decreasing
Units in glasses of water Total Utility Marginal Utility(TU2-TU1
1 20(TU1) 20
2 38(TU2) 18
3 50 12
4 58 8
5 60 2
6 60 0
7 58 -2
8 50 8
This law only remains true under the following conditions units are suitable, commodity is taken consecutively, no change in consumer taste, consumer must be a normal person, the commodity must not be rare(antique coins, collectibles etc.) and also this law cannot be applied to wealth or gold.
"Indifference curve represents the satisfaction of a consumer from 2 commodities. It is drawn on the assumption that for all possible combinations of the 2 commodities on the curve, the total satisfaction or utility remains the same. Hence the consumer is indifferent between the various combinations lying on the curve."