A student has a monthly budget of $1,750 to spend on tutoring sessions (x) and all other things (y). The student's preferences are summarized by the utility function U(x,y) = y + 250ln(x). The price of y is $1. The average price of a tutoring session is $50.

1. In a diagram, draw the student's budget constraint. 2. Find the student's optimal bundle (you can use the Lagrangian method, the substitution method, or directly write the tangency condition and the budget constraint). 3. In your graph, add an indifference curve to illustrate the optimal bundle.

The student's parents are concerned that he/she is not receiving enough tutoring and asked what they should do about it. They are considering giving the student i. an extra $300 per month that the student can only spend on tutoring (x only). ii. $25 for each session of tutoring effectively reducing the cost of tutoring to P'x = $25 per session.

4. In two separate diagrams, show how each plan affects the student's budget constraint. 5. Find the student's optimal bundle under each plan. 6. To each diagram from part 3) add an indifference curve to illustrate the student's optimal bundle under that plan. 7. Which plan is the most effective at increasing the amount of tutoring the student receives? 8. Which plan raises the student's utility the most?