Question
Why is an Indifference curve generally convex to the origin?
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Answer
- As, We know quantity of one commodity increases, its marginal rate of substitution falls because of law of diminishing marginal utility. Marginal rate of substitution is a slope of Indifference curve and whenever slope $(MRS)$ decreases it makes the curve convex to the point of origin.
- In the above diagram, units of y are measured on vertical axis and units of $x$ on horizontal axis. When the consumer moves from combination $A (1x + 25y)$ to $B (2x + 20y)$, he acquires one additional unit of $x$ and forgoes (sacrifice) $5$ units of $y$, if he wants to get the same level of satisfaction. The consumer has to reduce the consumption of $y$ when he increases the consumption of $x$. The number of units of good $y$ that the consumer is willing to sacrifice for an additional unit of good $x$, so as to maintain the same level of satisfaction is technically called the marginal rate of substitution of $x$ for $y$ and is denoted by $MRS_{xy}$.
- So, The $MRS_{xy}$ when the consumer move from combination $A$ to $B$ is $5 : 1$, further as the consumer move from combination $B$ to $C$, he acquires one more units of $x$, but the consumer forgoes a smaller number of $y$, i.e., $MRS$ at this stage is $4 : 1$. It may be observed now that $MRS$ diminishes as the consumer moves from combination $A$ to $B, B$ to $C, C$ to $D, D$ to $E$. The consumer forgoes less and less units of $y$ as he acquires additional unit of $x$.
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