valid values of h, i.e. there is a maximum value that h can achieve.)(c) (4 points) Solve for Korben's optimal number of hours spent working as a rideshare driver (L).Give us a numeric answer and show the solution graphically. To help with grading, draw free time on the x-axis and consumption on the y-axis. On you graph, also show the number of hours worked. (Hint: make sure to use the chain rule when calculating marginal utility.)(d) (3 points) A new occupational licensing law is passed, which requires rideshare drivers to acquire a certification in order to work. Korben does not have a certification, and has no other job prospects. Korben's neighbor, Ruby, does have a certification and can lend Korben their car to use and split the proceeds from transporting passengers. What is Korben's outside option if he doesn't work with Ruby? What will be his level of utility at that point?(e) (3 points) Suppose Ruby can make a take-it-or-leave-it offer to Korben, a payment for a specified number of hours transporting passengers. Ruby will keep any remaining revenue. Assume that Ruby only cares about their own payoff. Draw a graph showing the feasible set of offers that Ruby could make. To help with grading, draw free time on the x-axis and consumption on the y-axis.(f) (4 points) Korben was able to finally get a certificate to be a rideshare driver, and is back to driving his own flying car. However, there is now a 30% tax on labor earnings. Find Korben's new level of hours working as a rideshare driver. What is his elasticity of labor supply with respect to wages?

'. (20 points total) Korben is a rideshare driver in New York City in the year 2263. He uses his own ying car. Every hour, he can transport 4 passengers, with an average fare of $10 per passenger. After getting a full night of sleep, he only has 16 hours in the day to either spend transporting passenger or using his free time to collect rare stones. He uses the money he earns to purchase consumption goods, such as food from the vendor Thai Fly By. Since he is a former member of the special forces unit in the Federated Army, he also receives a pension of $25 per day. (a) (3 points) What is Korben's daily budget set over free time (h) and consumption (6)? Present the budget set both as an equation and as a graph. To help with grading, draw free time on the xaxis and consumption on the y-axis. (b) (3 points) Korben's preferences over free time (h) and consumption (c) are represented by the following utility function: mm) = c 2 (16 :02 Draw some of his indifference curves over free time and consumption. To help with grading, draw free time on the xaxis and consumption on the yaxis. (Hint: only draw the curves over