Question 4 A firm's short-run Total Cost (TC) function is: TC = 0.5q²q + 3000 The firm is a monopolist and the inverse demand function for its product is: P = -0.5q + 105 a) Find the most profitable level of output, and the profits at that output. (3 marks) b) When maximizing profit, does the firm produce at minimum average cost? (6 marks) c) Sketch the graphs of the inverse demand function, Marginal Revenue (MR) and Marginal Cost (MC) function with the same axes, showing the equilibrium price, MR and MC at that output. (4 marks) d) Sketch the graphs of Total Cost (TC) and Total Revenue (TR) with the same axes showing the equilibrium output and profits. (4 marks) e) Sketch the graph of the Profit function, showing the equilibrium output and profits. (3 marks)