Neoclassical Production and Costs

Question

Assume the following production function:  y = 2x₁^.5 + 3x₂^.5

a. Suppose x₂ = 16, derive the marginal product schedule for x₁­. In which direction is it moving?

b. What returns to scale does the production function show?

c. Consider p₁ = $4.00, p₂ = $2.00, and x₂ = 16; for the specified values of y find out average fixed costs, average total costs, average variable costs, and marginal costs:

                                           y        x₂            x₁            AFC        AVC        ATC        MC

                                          12       16

                                          13       16

                                          14       16

                                          15       16

                                          16       16

                                          17       16             

                                          18       16