Answer:
When the consumer is consuming two commodities (say X and Y) he can reach the equilibrium when ratio of MV of a commodity to its price \[\left( \frac{MUx}{px} \right)\] becomes equal to the ratio of MV of the other commodity to its price\[\left( \frac{MUy}{py} \right)\]. Symbolically it can be expressed as -
\[\]
This equation also implies that if the price of the commodity x is equal to the price of the commodity y (\[{{P}_{x}}={{P}_{y}}\]) the consumer will attain equilibrium when \[M{{U}_{x\,\,}}=\,\,M{{U}_{y}}\]
It also means that satisfaction is maximum when a rupee worth of MU is same in both the goods X and Y. Suppose a consumer has Rs. 20 with him to spend on two goods X and Y. Further suppose price of each unit of X is Rs. 5 and that of Y is Rs. 2. Now consumer may attain his equilibrium by utility approach in this way.
Utility schedule in case of two goods:
Unit of goods
Mux (Util)
Nux/Px (worth of No)
MUy (Util)
MUy/Py (worth of MU)
1
50
\[50\div 5=10\]
24
\[24\div 2=12\]
2
40
\[40\div 5=8\]
22
\[22\div 2=11\]
3
30
\[30\div 5=6\]
20
\[20\div 2=10\]
4
20
\[20\div 5=4\]
18
\[18\div 2=9\]
5
10
\[10\div 5=2\]
16
\[16\div 2=8\]
6
0
-
14
\[14\div 2=7\]
For obtaining maximum satisfaction from spending his given income of Rs. 20 the consumer will buy 2 units of X, by spending Rs. 10 and 5 units of Y by spending Rs. 10. This combination of goods brings him maximum satisfaction because a rupee worth of MU in case of good X is 8 \[\left( \frac{MU}{px}=\frac{40}{5} \right)\]and in case of good Y is also 8 \[\left( \frac{MU}{{{p}_{x}}}=\frac{16}{2} \right)i.e.\,\,\frac{M{{U}_{x}}}{{{P}_{x}}}\,\,=\frac{MUy}{{{P}_{y}}}\] since per rupee MU is same, there is no incentive for consumer to buy more of one good and less of the other good.
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