How many units of a commodity should a consumer buy to get its maximum utility ? Example with my help of a numerical example.

Explanation

(i) When purchasing a unit of a commodity a consumer compares its price with the expanted utility from the utility obtained is the benefit, and the price payable is the cost , the consumer compares benefit and the cost. He will by the unit of commodity only if the benefit is is greater than or at latest equal to the cost.
(ii) Equilibrium conditions for single commodity consumer Equilibrium .
(a) Necessary Condition
Marginal utility of Money = price `" "...(1)`
Or `(" Marginal Utility of a Product in Util " [MU_x])/("Marginal Utility of One Rupe "[MU_R]) " = Price of X "....(2)`
In particular, the condition (1) saya that the marginal utility of a product in terms of Money should be equal to its price.
Sometimes this is loosely stated as Marginal Utility is equal to price, i.e. ., MU = price .
`"*"` If MU `gt` price
`implies` As a rational consumer he will Continue to purchase an additional unit on a commodity as long as MU = price .
`implies` MU `gt` Price impulse benefit is greater than cost and when ever benefit is greater than cost the consumer keeps on consuming additional unit of a commodity till MU = price .
`implies` It is so because according to the law of diminishing marginal utility MU falls more is purchased . As MU falls it is bound to become equal to the price at some point of purchase.
`"*"` If MU `lt` Price
`implies` As a rational consumer he will have to reduce the consumption of a commodity as long as MU = price .
`implies MU lt` price implies when benefit is less than cost , never benefit is less than cost the dressing the additional unit of a commodity till MU = price.
`implies` It is so because according to the law of diminishing marginal utility, MU rises as less units are consumed. As MU rises , it is bound to become equal to the price at some point of purchase .
(b) Sufficient condition: Total gain falls as more is purchased after equilibrium . it means that consumer continues to purchase so long as total gain is increasing or at least constant.
(iii) It can be explained with the help of the following schedule :

(a) Suppose , the price of commodity X in the market is Rs3 per unit .It means he has to pay Rs3 per unit for all the units he buys. Suppose, the unility obtained from the first unit is 5 utils (=Rs 5) The consumer will buy this unit because the utility of this unit is greater than the price and this process continues till Marginal utility = price as shown in the above schedule at quantity 3 .
(b) Consumer will not buy the fourth unit utility of this unit is 2 unit because utility of this unit is 2 utils (= Rs 2) which is less than the price . It is not worth buying the fourth unit. The consumer will restrict his purchase to only 3 units.