Suppose the consumer/worker values two things: a consumption good C and leisure: Suppose that there are 24 hours in a day and the consumer/worker has a utility function U (C; `) = C0:5`0:5: The price of consumption is P and the wage rate is w: You dont need any more prices. Note that this is a conceptually di¢ cult question with easy math. The di¢ culty in the problem is in setting it up correctly, conceptualizing it correctly and interpreting it correctly. 1. Write down the formula for the consumer/workers income. 2. Set up the utility maximization problem by writing the Lagrangian. 3. Solve for the Marshallian Demand for ` (i:e: solve for `) 4. Take the derivative of ` 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 e¤ect of w here - explain what it is and how it works).