question_answer

A consumer consumes only two goods X and Y, both priced at Rs. 2 per unit. If the consumer chooses a combination of the two goods with Marginal Rate of Substitution equal to 2, is the consumer in equilibrium? Why or why not?

What will a rational consumer do in this situation? Explain.

Or

A consumer consumes only two goods X and Y whose prices are Rs. 5 and Rs. 4 respectively. If the consumer chooses a combination of the two goods with marginal utility of X equal to 4 and that of Y equal to 5, is the consumer in equilibrium? Why or why not? 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 = 2

\[\frac{{{P}_{x}}}{{{P}_{y}}}=\frac{2}{2}=1\]

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.

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

According to the given question

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

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