Let the price be $1 and the price of be $0.50. original income is $5. originally buys 3 units of and 4 units of and uses up all of her income. At these levels the marginal utility of for her is 4 and marginal utility of for her is 2. Is she at an optimal solution?

Let the price OF X be $1 and the price of Y be $0.50. original income is $5. originally buys 3 units of X and 4 units of Y and uses up all of her income. At these levels the marginal utility of X for her is 4 and marginal utility of Y for her is 2. Is she at an optimal solution?

YES

Explanation:

marginal utility is the utility obtained by the consumption of the last unit of a product.

in this case, by spending $1 in product X, the marginal utility = 4, and by spending $0.50 in product Y, the marginal utility = 2

each marginal util costs $0.25 for either product:

product X: $1 / 4 = $0.25 per util product Y: $0.50 / 2 = $0.25 per util

Since her marginal utility for both products is equal, we can assume she is at an optimal solution.