Question

Suppose an individual's utility function for two goods X and Y is given by U(X,Y) = X¹/²Y¹/². Denote the price of good X by Px, price of good Y by Py, and the income of the consumer by I. Write down the budget constraint for the individual.

Answer 1

The budget constraint for an individual with the utility function U(X,Y) = X½Y½ is given by the equation Px*X + Py*Y = I, where Px and Py are the prices of goods X and Y, and I is the income.

Step-by-step explanation:

The student has asked to write down the budget constraint for an individual whose utility function is U(X,Y) = X½Y½. Given the prices of goods X and Y as Px and Py respectively, and the consumer's income as I, the budget constraint is represented mathematically by the equation:

Px*X + Py*Y = I

This equation explains that the total amount spent on goods X and Y must not exceed the individual's income, I. For example, if the price of good X (Px) is $2 per unit of X, the price of good Y (Py) is $0.50 per unit of Y, and the individual's income (I) is $100, then the budget constraint would be $2*X + $0.50*Y ≤ $100. This shows the various combinations of goods X and Y that the consumer can afford, given their income.