3. Suppose a bee keeper is located by an apple orchard. The bee keeper's cost function is CB(b) = 62, where b is the hundreds of bees it keeps. The apple orchard's cost function is CA(a, b) = a2 - b, where a is the number of pounds of apples it produces. Clearly, there is a positive production externality from the bee keeper to the apple orchard. Suppose the prices of apples and bees are 1 dollar for the respective chosen units. (a) Calculate the competitive equilibrium amounts produced by both firms. (b) Calculate the Pareto efficient levels of production. To do this, solve the joint profit maximize- tion problem. Compare the two allocations (competitive and Pareto efficient), emphasizing the difference in the level of the externality. (c) Suppose the bee keeper is subsidized with 1 dollar per unit of production. Calculate the new competitive solution. Is it Pareto efficient? Can you think of other solutions to this bad allocation of resources on the part of the market