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This can be illustrated with the help of a simple example of two goods. Let X and Y be the goods a consumer wants to consume. Their prices are Px = $4 and Py = $2 respectively. The consumer’s allowance or budget is $10. He must spend the entire income so as to maximize his satisfaction from the two goods. His marginal utilities for the two goods and corresponding Mu/P ratios are shown in the table below:
|
Units
of good X
|
Mu
of
X
|
Mux/Px
(Px
= $4)
|
Units
of good Y
|
Mu
of
Y
|
Muy/Py
(Py
= $2)
|
|
1
|
48
|
12
|
1
|
18
|
9
|
|
2
|
36
|
9
|
2
|
16
|
8
|
|
3
|
24
|
6
|
3
|
12
|
6
|
|
4
|
12
|
3
|
4
|
6
|
3
|
(Equimarginal utility = 102, Total budget = $10)
In order to reach equilibrium and to maximize satisfaction the consumer has to equate Mu/P ratios for the two goods. This happens when he purchases and consumes two units of good X and one unit of good Y. This equilibrium combination has been highlighted in the table. The total expenditure of a consumer is $8 on good X for two units and $2 for one unit of Y. Therefore the total expenditure of $10 coincides exactly with the supposed allowance of the consumer. The total utility that the consumer derives from this combination is
48 + 36 = 84 of X units, and 18 of Y units
i.e. 102 units from the entire combination.
This is the highest level of satisfaction under the given price-income conditions. Any other combination cannot help the consumer to increase his utility further. For instance, if the consumer decides to purchase only one unit of X and decides to spend $4 on it he will attain utility of 48 units from it. The remaining $6 he can then spend on Y to purchase three units of it. From good Y the total utility he attains will be
18 + 16 + 12 = 46 units.
From such a combination the consumer’s total utility from the two goods will be:
48 + 46 = 94 units.
This is obviously lower than 102 units of utility from the equilibrium combination. It would be a similar case for any other combination.
(D) Variation in the price: The equimarginal or equiproportional rule helps to establish equilibrium for a consumer-maximizing utility. Such an equilibrium holds good only under the given market conditions. If the price of one of the goods alters the consumer will have to make a readjustment and change the combination. Let us assume that the price of good Y remains the same (Py = $2) as before, but the price of good X rises (from $4 to $6). The consumer will have to readjust the equilibrium.
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