Suppose that Darth Vader gets utility from two hobbies: collecting lightsabers and practicing the force. The cost of collecting a lightsaber is 5 hours, and for practicing the force, it is 10 hours. His utility function is given by U = x 1/2y 1/2 , where x is for lightsabers, and y is force powers. Assuming there are only 24 hours in a day, solve the following:

1. Write down the budget constraint

2. Sketch the indifference curves (to the best of your abilities)

3. Solve for the optimal bundle of (x, y) that Vader will consume

4. Assume now that there are 36 hours in a day, solve for the optimal bundle under this new condition