§1. I begin with few properties of Indifference curve (IC). one is higher the indifference curve higher utility of any particular consumer it gives. Second, it follows diminishing marginal rate of substitution when compared two goods in single IC. Let us assume two goods X and Y are being assessed for maximizing utility by Consumer Ram parsad. IC under consideration increased in such a fashion it is increased by 10 units of utility as it goes away from the origin or every increasing budget lines of Ram parsad can achieve such ICs. IC1 is supposed to give 10 units of utility and hence IC2 and so on 20 units of utilities and 30 and so on. (this blog will work even if such increase in utility is on diminishing rate in way to give {10,10+9,29+8,...})
§2. I think Budget constraint is only relevant when making decision about actual exchange for payment. for deciding individual's utility on the given quantity of goods, it is irrelevant to judge with ability to pay rather it should be on the basis of willingness to pay. willingness to pay also work for budget constraint decision. however, utility that any consumer wants to derive based on past experience or just on the basis of imagination is totally consumer's choice irrespective of budget constraints. Eg. How many hours Ram parsad wants to watch movie is independent whether or not he has ability to pay for Netflix. Ram parsad will decide whether or not to watch movie on Netflix, though depends upon his ability to pay.
Hence, budget constraint helps to determine how much can be consumed. i.e. in which IC one consumer will land. but numbers of ICs are independent of budget constraint.
§3. Suppose initially Ram parsad by tangency of Budget constraint and IC1 derive 10 units of utility by having 10 units of good X and 20 units of good Y. In IC1, if ram parsad wants to increase consumption of X then he will sacrifice consumption of good Y but in diminishing rate, i.e. if 15 units of X to be consumed by sacrificing 5 more units of Y then increasing further 5 units of X's consumption he will sacrifice less than 5 units of Y.
it shows that for gaining 10 units of utility for different units of X (when quantity of X to be increased) should be exchanged in diminishing rate of exchange with that of Y's consumption.
§4. No suppose, due to increase in income and by fulfilling all conditions, budget constraints of Ram parsad shift parallels to original budget constraint have ability to reach IC2 where he can get 20 units of utility. In this condition if Ram parsad decides to keep consumption of X constant to 15 units (which he derive by sacrificing 5 units of Y to be in {X,Y}={15,15} situation from original {10,20} situation), he will be getting more than 15 units of good Y too. Simply, higher utility can be achieved even if quantity of X made constant or increasing with simultaneous increase in consumption of Y.
§5. in section 3 we have seen that to make utility constant one good is sacrificed for another at decreasing rate. however, in section 5, it is possible that utility of higher level can be achieved by increasing one good or taking constant with increasing use of another good too.
§6. then marginal decision to get tangency of budget constraint with IC to get utility maximizing quantities of goods is rather a budget uses maximizing criteria rather than to maximize Pleasure of human over pain (original idea of Utility).
§7. As higher ICs gives higher utility and by increasing budget constraints men achieve or try to reach near satisfaction of his/her being. Maximizing utility by proving tangency on given budget constraint is mere intellectual pleasure and not the actual pleasure of the consumer.
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