Analytical 1. Consider Laila, a single mother in Tritonlandia. She has 2,000 hours per year, which she can allocate to either work or leisure. If she works, she makes an hourly wage of $12. She spends all of her income from working on food. The price of each unit of food is $6. In addition, Tritonlandia has a TANF program with a benefit guarantee of $6,000 and a benefit reduction rate of 1/3 (33.33...%), meaning that for each dollar earned, benefits are reduced by 1/3 of a dollar.

a) Draw Laila's budget constraint, with leisure (L) on the x-axis and food (F) on the y-axis. Be sure to label the axes, intercepts, kink points, and slopes.

b) What is Laila's effective wage if she participates in TANF? How does it compare to the hourly wage she earns at her job? Explain.

c) Suppose that Laila's utility function is given by U = L (1/5)* F (4/5). Solve for her optimal bundle if she doesn't participate in TANF. Solve for her optimal bundle if she does participate in TANF. Note #1: If it helps, you can round your answers to the nearest 1 --- fractions reduced to the lowest terms are OK, too. Note #2: The partial derivative of U with respect to L is (1/5)*L (-4/5)F (4/5), and the partial derivative of U with respect to F is (4/5)*L (1/5)F (-1/5)

d) Now suppose the government of Tritonlandia wants to reform the program to encourage work and lowers the benefit guarantee to $3000, keeping the BRR equal to 1/3. Draw the new budget constraint, as in part (a). Be sure to label all relevant points, as in part (a).

e) Consider a different mother - Jane -, who also has 2,000 hours and faces an hourly wage of $12. Jane participates in TANF when the BG is $6,000 and the BRR is 1/3. Consider what happens to the Jane's choice of leisure (L) when the BG is lowered to $3,000. What is the direction of the substitution effect on L? Provide an explanation (in words - no numbers necessary to answer this question).