a) A firm's demand and total cost functions for a good are 4P+9-16=0 and TC =4+20 302 03 10 20 INST respectively. (i) What level of output, O, should the firm produce if it wants to maximize profit? (10 TIM marks) (ii) Show that at the point of maximum profit, MR = MC. (4 marks) OUT Sup Q d b) The demand function of a good is given by P =100e-0.10 M Show that demand is unit elastic when O = 10. (6 marks) Question 4 (20 marks) A firm's production function is given by 0 = 2K/21/2 Unit capital (K) and labour (L) costs are 4 and 3 currency units, respectively. a) Using the Lagrangean method, find the values of K and L which minimize total input costs if the firm is contracted to produce 160 units of output. (16 marks) b) Interpret the value of the Lagrange multiplier. (4 marks)