Suppose that you are given a cost function c( w,r,x) = 2 w^1/2r^1/2x^3/2,where w is the wage rate for labor, r is the rental rate of capital and x is the output level.
(a) Find the contingent demand functions for labor and capital.
(b) Using your answers in (a), find the underlying production function.
(c) Does the production process that gives rise to this cost function have increasing, decreasing or constant returns to scale?
(d) Find the supply function for the firm.