Question

Hans has $27 which he decides to spend on x and y. Commodity x costs $16 per unit and commodity y costs $10 per unit. He has the utility function U(x, y) = 5x^2 + 2y^2 and he can purchase fractional units of x and y. Hans will choose A. only x. only y. B. some of each commodity but more y than x. C. some of each commodity but more x than y. D. equal amounts of the two commodities.

Answer 1

Hans will choose A. only x as his optimal choice.

Step-by-step explanation:

To determine Hans's optimal choice, we need to compare the utility he can obtain by spending all of his money on commodity x versus the utility he can obtain by spending all of his money on commodity y. We can start by calculating the utility from spending all of his money on x, which is given by U(x) = 5x^2. Similarly, the utility from spending all of his money on y is U(y) = 2y^2. By comparing the utilities, we can see that the utility from spending all of his money on x is greater than the utility from spending all of his money on y for any positive values of x and y. Therefore, Hans will choose A. only x as his optimal choice.