Miranda finds this entire exercise to be needlessly tedious. After all, it is rather ludicrous that she should be buying fish from herself from the wages she pays herself for her own labor and the profits she earns selling fish to herself. She figures that she can just ignore the entire market mechanism and prices entirely, and instead simplify her problem by just choosing some optimal number of hours to spend gathering fish that would yield the most satisfying balance of food and leisure time. (a) Write Miranda's utility function U(l) solely in terms of her hours of labor l and state the first order condition to her utility maximization problem. (b) Find the optimal hours of labor and how much fish q* and leisure r* this would provide Miranda.
Miranda finds this entire exercise to be needlessly tedious. After all, it is rather ludicrous that she should be buying fish from herself from the wages she pays herself for her own labor and the profits she earns selling fish to herself. She figures that she can just ignore the entire market mechanism and prices entirely, and instead simplify her problem by just choosing some optimal number of hours to spend gathering fish that would yield the most satisfying balance of food and leisure time.
(a) Write Miranda's utility function U(l) solely in terms of her hours of labor l and state the first order condition to her utility maximization problem.
(b) Find the optimal hours of labor and how much fish q* and leisure r* this would provide Miranda.
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