|n Autarka. cardboard boxes are sold in bundles of 100. At present. the market price for a bundle of boxes is $30. 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 $7.000.000 per year. The labour. material. and energy cost of producing a bundle of 100 boxes is $20. A market study indicates that demand for cardboard boxes is given by the function. 0 P 2 40 _ 500.000' where P represents the price of a bundle of 100 boxes. and O is the total number of bundles of boxes sold each year. 3 Industry analysis For your Industry Analysis you must complete each of the steps detailed below. When completing the steps you must: 0 Type all equations using the 'Insert Equation' function (or equivalent). 0 Show all of your working. 0 Include sufficient written description for the reader to follow your process. 0 Use appropriate notation and economic terminology. Your audience for the industry analysis is other expert economists who may be required to review your work. There is no page limit for the Industry Analysis. 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 On 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 $30. (8 marks) Step 4: Find the consumer surplus if all firm's in the market sell at the current market price of $30. (6 marks) Step 5: Derive the typical firm's bestresponse function. (8 marks) Step 6: Find the equilibrium quantity and profit for the typical firm. (11 marks) Step 7: Find the equilibrium price and consumer surplus. (7 marks)