Question

Using the given information what will be the optimal production bundle? • Income = $10 • Utility function: xy • Px = Py = 1 a) 5,5 b) 6,4 c) 4,6 d) 8,2

Answer 1

The correct answer in this case, would be option a) given in the answer choices or 5,5.

Explanation:

• The utility function is given as U(x,y)=xy and the prices of each x and y are both $1.The income of the consumer, in this case, is $10.
• The marginal utility of good x or MU(x)=$\frac{dx}{dU} =y$ and the marginal utility of y or MU(y)=$\frac{dy}{dU} =x$.
• The utility maximizing bundle for any rational consumer of any two goods occurs at the consumption point where the ratio of marginal utilities of both goods is equal to their respective price ratio.
• Therefore, based on the utility maximizing condition of any rational consumer, we can state:-

       $\frac{MU(x)}{MU(y)} =\frac{P(x)}{P(y)}$

       $\frac{y}{x} =\frac{1}{1}$

       $y=x$

• Hence, based on the utility maximizing condition of any rational consumer, the utility maximizing consumption bundle indicates that the consumption quantity or level of both goods x and y are equal. Thus, the correct answer would (5,5) as given in the list of answer choices.