Hi, I've got a series of questions related to the subject ECON1048 Managerial and Business Economics (Previously known as Price Theory). The questions are related to derivatives.

Please help me and include all working for each question so I can properly understand the material and apply this to future tasks.

Please also include the relevant formulas for each question and what the variables in the formula are!

Attached are the data and questions I need help with. As mentioned it is related to derivatives using the Cournot competition model.

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 2 46'8 _ 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 0;. 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 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) In the island nation of utarka, cardboard boxes are manulactured by four lirms: Andrew's Industries, Brett's Boxes, lCarla's Cardboard, and Delia's Durables. Cardboard boxes are purchased by numerous local manufacturers and food producers as an input into their respective production processes. In recent years, the customers of the cardboard box manufacturers have begun to com- plain that cardboard box prices are considerably higher in Autarka than in other countries. They accuse the Four manufacturers of colluding to set high prices; exploiting the [act that it is not economical to import cardboard boxes from another country. In response, the manufacturers clalm that the market price for cardboard boxes rellects the competitive reallty ol' manulacturing in a small country. They argue that local prices must be higher as they are unable to take advantage ol the scale economies available in larger markets