Question 6 lonsicler the cost function in the case of two inputs, c(w1, 102, y). (a) Show that 30001: 192: y) = 3y where A is the Lagrange multiplier from the cost-minimization problem. [5 marks] A [Hint: You will need to use the rst order conditions from the cost-minimization problem along with the derivative of the firm's constraint at its optimal choice with respect to y.] (b) Hence, show that at the rm's Optimal input choices, the elasticity of scale, e(x) = @511 mix) . AC can be re-wntten as e = . [5 marks] [In doing this assume all of the rm's costs are variable (i.e., no xed set-up costs).] (0) What does this imply about the relationship between returns to scale in production and economies of scale in costs? [5 marks]