2.1 Your task Collusion is a criminal offence in Autarka. As such. the Treasurer has instructed you to conduct a preliminary investigation into collusion in the cardboard box market. Your investigation should determine, 0 whether collusion or competition better explains the price in the cardboard box mar- ket. 0 whether a more extensive criminal investigation is warranted and. 0 what. if any. impact collusion is having on the industries that rely on cardboard boxes as an input. (Note: A criminal investigation and prosecution would likely cost the government $20.000.0DD. 2.2 Industry structure In Autarka. cardboard boxes are sold in bundles of 100. At present. the market price for a bundle of boxes is $32. The technology for manufacturing cardboard boxes is readily available and common to all manufacturers. The cost of plant and machinery for a firm in the box manufacturing business is $8.500.000 per year. The labour. material. and energy cost of producing a bundle of 100 boxes is $23. A market study indicates that demand for cardboard boxes is given by the function. Q P = 45'8 _ 1.000.000' where P represents the price of a bundle of 100 boxes. and Q is the total number of bundles of boxes sold each year. 3.1 Required steps When completing the industry analysis you should assume that firms are engaged in Cournot Competition. Step 1: Using the information provided in the scenario. derive a total cost function for a typical cardboard box manufacturer. Use GA to denote the quantity produced by the typical firm. (4 marks) Step 2: Derive a profit function for the typical firm. Use X to denote the combined production of the remaining three firms in the market. (6 marks) Step 3: Find the profit of the typical firm if all firm's in the market sell at the current market price of $32. (8 marks) Step 4: Find the consumer surplus if all firm's in the market sell at the current market price of $32. (6 marks) Step 5: Derive the typical firm's best-response function. (8 marks) Step 6: Find the equilibrium quantity and profit for the typical firm. (11 marks) Step T: Find the equilibrium price and consumer surplus. (7 marks)