A consumer consumes only two goods $X$ and $Y$ . Her money income is $R s . 24$ and the prices of Goods $X$ and $Y$ are $R s . 4$ and $R s . 2$ respectively. Answer the following questions:
(i) Can the consumer afford a bundle $4 X$ and $5 Y$ ? Explain
(ii) What will be the $M R S_{X Y}$ when the consumer is in equilibrium? Explain.

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Solution

(i) No, the consumer cannot afford a bundle of $4 X$ and $5 Y$ .
Given, money income $= R s . 24; P_{X} = R s . 4$ and $P_{Y} = R s . 2$ , if he purchases $4 X$ and $5 Y$ , then
$4 \times 4 + 5 \times 2 = 26 > 24$
Therefore, he is not able to buy a bundle of $4 X$ and $5 Y$ .
(ii) When the consumer is in equilibrium : $M R S_{X Y} = \frac{P_{X}}{P_{Y}}$
The price ratio indicates that for every additional unit of $G o o d - X$ , the consumer has to sacrifice $2$ units of $G o o d - Y$ . So that price ratio is $2 : 1$ . Accordingly, in a state of equilibrium, the marginal rate of substitution between $G o o d - X$ and $G o o d - Y$ must be equal to $2 : 1$ .

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