Suppose the consumer/worker values two things: a consumption good C and leisure L. Suppose that there are 24 hours in a day and the consumer/worker has a utility function U (C, L) = ln C + L The price of consumption is P and the wage rate is w: You donít need any more prices. Note that this is a conceptually difficult question with easy math. The difficulty in the problem is in setting it up correctly, conceptualizing it correctly and interpreting it correctly.
1. Write down the formula for the consumer/workerís income (5 points)
2. Set up the utility maximization problem by writing the Lagrangian (5 points)
3. Solve for the Marshallian Demand for L* (i:e: solve for L*) (5 points)
4. Take the derivative of L* with respect to w: Is the result surprising (it should be!)? How is this problem different from the standard utility maximization problem (hint: there is an extra effect of w here - explain what it is and how it works). (5 points)
5. Extra Credit: Suppose now the utility function changes to U (C, L) = 25 ln C + L Solve again for the Marshallian Demand for L: Compare your results with part 3 and explain intuitively.