question_answer

A consumer consumes only two goods X and Y both priced at Rs. 3 per unit. If the consumer chooses a combination of these two goods with Marginal Rate of Substitution equal ?to 3, is the consumer in equilibrium? Give reasons. What will a rational consumer do in this situation? Explain.

Or

A consumer consumes only two goods X and Y whose prices are Rs. 4 and Rs. 5 per unit respectively. If the consumer chooses a combination of the two goods with marginal utility of X equal to 5 and that of Y equal to 4, is the consumer in equilibrium? Give reason. What will a rational consumer do in this situation? Use utility analysis.

Answer:

At the point of consumer equilibrium the following equality should be met:

\[MRS=\frac{{{P}_{x}}}{{{P}_{y}}}\]

According to the question,

MRS = 3

\[\frac{{{P}_{x}}}{{{P}_{y}}}=\frac{3}{3}=1\]

So, MRS is greater than the price ratio. Thus, to reach the equilibrium point a rational consumer would decrease the consumption of good y.

Or

According to the utility approach, a consumer reaches equilibrium where the following equality is met.

\[\frac{M{{U}_{x}}}{{{P}_{x}}}\,\times \,\frac{M{{U}_{y}}}{{{P}_{y}}}\]

According to the given question,

\[\begin{align}   & \frac{M{{U}_{x}}}{{{P}_{x}}}\,\,=\frac{5}{4} \\  & \frac{M{{U}_{y}}}{{{P}_{y}}}=\frac{4}{5} \\ \end{align}\]

So, \[\frac{M{{U}_{x}}}{{{P}_{x}}}\,\] is greater than\[\frac{M{{U}_{y}}}{{{P}_{y}}}\]. Thus, to reach the equilibrium, a rational consumer would increase the consumption of good x and decrease that of good y.