You have $10,000 sitting in a savings account, 600 hours of leisure time this summer and an opportunity to work at a $30 hourly wage.
A: Next summer is the last summer before you start working for a living, and so you plan to take the whole summer off and relax. You need to decide how much to work this summer and how much to spend on consumption this summer and next summer. Any investments you make for the year will yield a 10% rate of return over the coming year.
(a) On a three dimensional graph with this summer’s leisure (ℓ), this summer’s consumption (c1) and next summer’s consumption (c2) on the axes, illustrate your endowment point as well as your budget constraint. Carefully label your graph and indicate where the endowment point is.
(b) How does your answer change if you suddenly realize you still need to pay $5,000 in tuition for next year, payable immediately?
(c) How does your answer change if instead the interest rate doubles to 20%?
(d) In (b) and (c), which slopes are different than in (a)?
B: Derive the mathematical expression for your budget constraint in 3.3A and explain how elements of this expression relate to the slopes and intercepts you graphed.