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Theory Of Consumer Behaviour

Question
CBSEENEC12013405

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.

Solution

At the point of consumer equilibrium, the following equality should be met:
MRS = Px/Py
MRS = 3 (given)
Px/Py= 3/3 = 1
Thus, MRS is greater than the price ratio.
In order to reach the equilibrium point, a rational consumer would increase the consumption of good X and decrease that of good Y.

Or
According to the utility approach, a consumer reaches an equilibrium where the following equality is met.
MUx/Px = MUY/Py
MUx/Px =5/4 (given)
MUY/Py = 4/5
So MUx/Px is greater than MUY/Py . Thus a rational consumer has to increase the consumption of good X and decrease that of good Y in order to reach equilibrium.