Problem 1 Clark gains utility from consumption c and leisure L and his preferences for consumption and leisure can be expressed as U (C, L) = 20L. He has 16 hours per day to allocate between leisure and work. His hourly wage is $12 after taxes. Clark also receives a daily check of $30 from the government no matter how much he works. (a) Graph Clark's budget constraint with leisure on the xaxis and consumption on the y-axis. (b) At what wage rate would Clark be indifferent between working his rst hour and being unem- ployed (his \"reservation wage\")? (c) Find Clark's optimal amount of consumption and leisure. Problem 2 Matt and Jack run an ice cream business. To produce the ice cream, they hire labor (E) at a wage of 11) dollars per worker. Their production function is given by Q=f(E)=8EETZ Assume that w = 8 and p = 4. (a) Dene the prot function (b) What is the prot maximization level of labor demanded? What is their prot at this level? (c) Now suppose a competing shop has opened nearby driving down the price for a pint of ice cream to P = 2. What is the new prot maximizing level of labor demand? What is the new prot? Problem 3 Assume that labor demand is dened as L D = 25 %, and labor supply is dened as L3 = 2w. (a) Find the optimal level of employment and wages. (b) Graph the demand and supply curves. (c) What is the producer surplus in this situation? What is the worker surplus? ) (d Assume the government implements a new minimum wage of $28. Find the new labor demand and supply. How many workers are displaced by this change