Derive the law of demand from the single commodity equilibrium condition Marginal utility = Price

Law of demand can be derived from the conept of consumer equilibrium in case of single commodity as follows.
we know that at equilibrium, 
MUX = Price 
Now, according to the law of dimishing marginal utility, the marginal utility derived from every additional unit of a good consumed tends to decline at the same price. Consequently, for each additional unit of the good, the consumer is willing to pay a lesser price. Thus, the consumer will increase his demand only when the price falls and vice-versa. 

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