Answer to Question #227734 in Microeconomics for Nahum

Question

Suppose that the price of good A and Good B are birr 3and birr 2 respectively suppose aconsumer is spending his entire income for buying 4 units of A and 6 unit of B,and the marignal utility of both 4th unit of A and 6th unit of B is 6, is the consumer at his optimal position?

Answer 1

At the optimal level of consumer's satisfaction, the following two conditions must be met:

a) Spending of the entire consumer income on goods consumption.

b) Equality of per birr marginal utility across all goods : Equation wise, if there are two goods : A and B with respective price : PA and PB , then it would be:

$\frac{MU_ A} {MU_ B}=\frac{ P_ A}{ P_ B}$

Here : MUA and MUB are marginal utility obtained from A and B. By marginal utility, we mean the amount of utility derived from the consumption of an additional unit of the good.

In the given case, the first condition (a) of optimal utility is satisfied as the entire income is being utilized on goods : A and B. Now, we will verify whether the condition (b) is also satisfied or not.

Computing $\frac{MU_A}{ P_A}:$

$\frac{MU_A}{ P_A}=\frac{6}{3}=2$

So, the per birr marginal utility of A is 2 utils.

$\frac{MU_B}{ P_B}=\frac{6}{2}=3$

Comparing the above both:

$\frac{MU_A}{ P_A}\ne\frac{MU_B}{ P_B}$

Since there is non-equality of per birr marginal utility for both goods : A and B, the condition (b) is not satisfied at this point. Hence, the consumer is not at optimal position at 4 units of A and 6 units of B.