Please help!

1. Consider a Robinson Crusoe economy. Jim's Tea is a prot-maximizing producer of cups of tea (3;). It uses a single input, hours of labor (l), according to the production function y = 6W. Let the price of tea be 1 per cup, and call the price of labor w. a) Set up and solve Jim's Tea's prot maximization problem to nd its labor demand and prot as a function of w. As a consumer, Jim, the sole customer of Jim's Tea, owns Jim's Tea and so receives its prots. He also supplies labor to the rm and earns 10 per hour supplied. He chooses how much coifee to buy and how much labor to supply in order to maximize his utility function U=ygl2. b) Set up and solve Jim the consumer's utility maximization problem to nd his optimal consumption bundle as a function of w. c) Using your answers to a) and b), nd a competitive equilibrium in this economy. (:1) Say that we didn't know anything about the producer or the consumer in this model, but saw the competitive equilibrium. What information would we learn about the producer and consumer by looking at the equilibrium prices? 9) Without necessarily calculating anything, would we be able to nd a competitive equi- librium in this economy if Jim's Tea's production function had been 3; = $2? Why or why not