Question

Gina works at a diner. She has 100 hours each week to spend at labor/leisure, earns a wage of $15 per hour, and works in a fancy modern restaurant that doesn't involve tips from customers. She has no sources of non-labor income, but she does have to pay $200 per week in childcare for her precious baby Carlos (regardless of how many hours she actually utilizes the childcare). Her utility function is U 1. 0.001CL2 (3 points) Each week she has the option of signing up for 20, 30, or 40 hours of work Calculate Gina's utility at each of her labor supply options at the diner. Since childcare is a fixed cost of working in this model, the amount she spends on it should not count towards consumption that gives utility (for example, if she worked 0 hours, her consumption would be-$200). How much will she choose to work? On a simple diagram, sketch Gina's budget constraint and the indifference curves that correspond with each of her supply options a. b. (4 points) The government in Gina's town becomes woke and decides to provide free childcare for lower-income households, in an effort to increase labor supply and productivity in the town. Use utility calculations to determine how much Gina will now choose to work (again her choices are 20, 30, or 40 hours), and depict this situation in a new graph. As before, you should draw the budget constraint and the indifference curves for each choice (you do not need to show before and after here, just the situation in part b). Discuss how Gina's labor supply has responded to the policy, and explain whether this would be a common reaction in the market. Does this mean the policy will not work? c. 4 points) The city council is still woke, but they are quickly running out of money to fund their childcare program. They decide to adjust the program. Now, it will pay for childcare for up to 20 hours per week. If Gina wants to work more than 20 hours, she will need to pay $100 per week for additional care (as before, regardless of how many hours she actually needs it). How will Gina rank her three work hour options now? Explain the intuition behind her preferences. Draw the budget constraint that Gina now faces, and again draw the indifference curves that correspond to her choices