Task 1: Transport pricing Description: An export-importing shipping company operates a general cargo carrier service between Melbourne and other Asian ports. It hauls two major types of freight: manufactured items (submarket 1) and semi-manufactured raw materials (submarket 2). The demand function for manufactured items is given by: The inverse demand function for raw materials is given by: Finally, the total cost function for the shipping company is given by: Required: Task 1.1: Provide algebraic expressions for (i) the average revenue function of each submarket. (ii) the total revenue function of submarket 1. (iii) the marginal revenue function of each submarket. (iv) the overall revenue function from both markets. (v) the overall profit function from both submarkets. (7.5 marks, with each worth 1.5 marks) Task 1.2: Graph (i) the marginal cost curve for each submarket. (ii) the marginal revenue curve for each submarket. (iii) the marginal profit curve for each submarket. (4.5 marks, with each worth 1.5 marks) Task 1.3: Suppose the freight company may apply discriminatory charges in both submarkets. Figure out (i) the amount of freight carried for each submarket. (ii) the optimal prices that maximises aggregate profit across both submarkets. (iii) the overall profit.(3 marks, with each worth 1 mark) Task 1.4: Suppose the freight company must charge a uniform price (i.e., the same price) in both submarkets. Figure out (i) the profit maximising price. (ii) the amount of freight carried for each submarket. (iii) the overall profit. (1.5 marks, with each worth 0.5 marks) Task 1.5: Suppose the freighting company is forced by the government to price efficiently in each submarket. Figure out (i). the amount of freight carried in each submarket. (ii). the optimal price in each submarket. (iii). the overall profit. (1.5 marks, with each worth 0.5 marks) Task 2: Cost-benefit analysis Description: The government is considering the construction of a bridge to replace a vehicular ferry service. The bridge will cost $1.1 million, but the government will save $50,000 per annum, the cost of providing ferry service. Also, motorists will benefit through not having to wait and through a faster crossing. Because of this, traffic volumes are expected to increase over their initial levels. Given this, the governments advisers have estimated the flow of costs and benefits (in $ 000) as follows. Cost/BenefitYear 0 1 2 3 4 5 6 7 .. . 20 Construction Cost 550 550 0 Operating Cost Saved 0 0 50 50 50 50 50 50 .. . 50 Time Savings 0 0 30 40 60 80 110 110 .. . 110 Required: Task 2.1: Draw a table with annual net cash inflows and outflows. (3 marks) Task 2.2: If the discount rate is 10%, what is the net present value? Is the project worthwhile? (3 marks) Task 2.3: Suppose that the estimated life of the bridge is extended by 10 years. What impact does this have on the result? (Assume discount rate is 10%, operating cost savings continue at $50,000 and time savings continue at $110,000 per annum). (3 marks) Task 2.4: Suppose now the discount rate is 5% (the bridge life is 20 years). What impact does this have on the result? (Assume bridge life is unchanged, operating cost savings continue at $50,000 and time savings continue at $110,000 per annum). (3 marks)