Question

A consumer has the utility function U(x, y) = min{4x,y). That is, the consumer's utility is the lesser of 4x or 6y. If the prices of the goods are Px = $8 and Pax = $6 and the consumer's income is $360, what is the consumer's optimal consumption bundle?

Answer 1

The consumer's optimal consumption bundle, given their utility function and budget, is 11.25 units of good x and 45 units of good y to maximize total utility within their budget constraint.

Step-by-step explanation:

To determine the consumer's optimal consumption bundle, we must first set up the budget constraint based on the consumer's income and the prices of goods x and y. The consumer's budget constraint is represented by the equation: 8x + 6y = 360, where $8 is the price of good x (Px), $6 is the price of good y (Py), and $360 is the consumer's income.

The utility function U(x, y) = min{4x, y} indicates that the consumer achieves the maximum utility when 4x and y are equal because utility is defined by the lesser value. To maximize utility, we therefore set 4x = y.

Substituting 4x for y in the budget constraint equation gives us 8x + 6(4x) = 360, which simplifies to 32x = 360. Solving for x gives us x = 360 / 32 = 11.25. Substituting x back into the equality 4x = y, we find that y = 4(11.25) = 45.

Therefore, the optimal consumption bundle for the consumer is 11.25 units of good x and 45 units of good y.