3. (30) As may have been blatantly obvious to you all along, since Miranda is the only inhabitant of the island, all she's really doing is catching sh for herself and eating them. However, even a single agent ec0nomy such as this One has all of the features any economy would, such as supply and demand curves, and equilibrium prices and quantities. Miranda plays many roles in this ec0nomy, as all of the prot earned by Miranda the producer is transmitted to Miranda the shareholder, which represents additional income that Miranda the consumer can Spend on sh in addition to the labor income earned by Miranda the worker. (a) (10) Suppose Miranda earns both labor inc0me and prot, so that pg = mg + 7r(p). Rewrite her utility maximizatiOn problem and nd the new demand for sh qd(p) and leisure "r(p). (b) (10) Find the equilibrium price 19* and quantity (1* of sh. (c) (10) Find the equilibrium hours of labor 3* and labor r*