5. EITHER What is the firm's cost function and what does it tell us? (10% mark] A firm has a production function = L K . where L and K denote labour and capital services respectively. Let w and r denote the prices of these factors. (a) Increasing all inputs by some scale parameters (> 1), show that this production function is homogeneous and exhibits increasing returns to scale. [15% mark] (b) The firm wants to minimise its costs subject to producing an output of at least Qo (>0). Set out this problem and sketch it in a suitable diagram. [15% mark) (c) Set up the Lagrangian for the cost-minimisation problem and find the necessary conditions. Hence, find the compensated demands for L and K. and show that the firm's cost function is equal to: C = 2 (w r)11 Q . where Cis cost. [40% mark) (d) Find expressions for the firm's long-run average cost and long-run marginal cost curves. Sketch these in a separate diagram, and interpret. [20% mark) (Note: Some useful properties of power functions: x x= x a+b and 1/x'=x”). [ tum over)