2. (15) Now suppose that, rather than each farmer being free to choose his own level of output, there is a social planner that chooses how much of each crop to grow in order to maximize the total 1'tr'aulue of the output. (a) (5) Find an equation for the production possibilities frontier. {b) (5) Set up the value maximization problem. and nd the rst order conditions. (c) (5) Find the supply of corn qpc, pm) and wheat qpc, pm) chosen by the social planner. Is this the same output that the farmers would have chosen themselves