The starting file is as the picture below showing excel. A fictional company, Bashro, produces a toy called a Formertrans. Bashro identifies six consumer groups which have different willingness to pay for the Formertrans: Price willing to pay in USD (or marginal value of Formertrans) Formertrans Consumer 1 Consumer 2 Consumer 3 Consumer 4 Consumer 5 Consumer 6 1 $ 2 270,00 $ 6 450,00 $ 3 000,00 $ 4 400,00 $ 2 150,00 $ 2 940,00 2 $ 1 101,00 $ 2 957,00 $ 2 019,00 |$ 2 385,00 $ 1 193,00 $ 3 075,00 3 $ 813,00 $ 1 516,00 $ 1 226,00 $ 1 898,00 $ 577,00 $ 1770,00 4 $ 465,00 $ 1 047,00 $ 708,00 $ 1 001,00 $ 301,00 $ 598,00 5 $ 266,00 $. 525,00 $ 483,00 $.491,00 $ 198,00 $ 613,00 The variable costs per unit is 420 USD The number of consumers differs between groups: Number of consumers per consumer group Consumer 1 Consumer 2 Consumer 3 Consumer 4 Consumer 5 Consumer 6 Market size 22.000 7.500 48.000 12.500 63.000 42.000 Bashro objective is to maximize profits. a) Determine whether this is a linear or a non-linear problem. Explain why. b) Bashro charges a single price for all consumer groups. Find the optimal price, production quantity for each group and the corresponding profits. c) Bashro wants to know how much profit is lost by charging a single price. Assume that the company can implement perfect price discrimination (first degree) by charging each consumer group a different price. Find: (1) The optimal price for each group; (ii) Production quantity per group; and (iii) The associated profit. Price sensitivity Formertrans NM Price willing to pay (or marginal value of formertrans) Consumer group 1 Consumer group 2 Consumer group 3 Consumer group 4 Consumer group 5 Consumer group 6 $ 2 270.00 $ 6 450.00 $ 3 000.00 $ 4 400.00 $ 2 150.00 $ 2 940.00 $ 1 101.00 $ 2957.00 $ 2019.00 $ 2 385.00 $ 1 193.00 $ 3075.00 $ 813.00 $ 1516.00 $ 1 226.00 $ 1 898.00 $ 577.00 $ 1 770.00 $ 465.00 $ 1047.00 $ 708.00 $ 1001.00 $ 301.00 $ 598.00 $ 266.00 $ 525.00 $ 483.00 $ 491.00 $ 198.00 $ 613.00 3 4 5 Unit cost and unit price $ 420.00 Unit cost Unit price Market size Consumer group 1 22000 Consumer group 2 7500 Consumer group 3 48000 Consumer group 4 12500 Consumer group 5 63000 Consumer group 6 42000 Number of consumers The starting file is as the picture below showing excel. A fictional company, Bashro, produces a toy called a Formertrans. Bashro identifies six consumer groups which have different willingness to pay for the Formertrans: Price willing to pay in USD (or marginal value of Formertrans) Formertrans Consumer 1 Consumer 2 Consumer 3 Consumer 4 Consumer 5 Consumer 6 1 $ 2 270,00 $ 6 450,00 $ 3 000,00 $ 4 400,00 $ 2 150,00 $ 2 940,00 2 $ 1 101,00 $ 2 957,00 $ 2 019,00 |$ 2 385,00 $ 1 193,00 $ 3 075,00 3 $ 813,00 $ 1 516,00 $ 1 226,00 $ 1 898,00 $ 577,00 $ 1770,00 4 $ 465,00 $ 1 047,00 $ 708,00 $ 1 001,00 $ 301,00 $ 598,00 5 $ 266,00 $. 525,00 $ 483,00 $.491,00 $ 198,00 $ 613,00 The variable costs per unit is 420 USD The number of consumers differs between groups: Number of consumers per consumer group Consumer 1 Consumer 2 Consumer 3 Consumer 4 Consumer 5 Consumer 6 Market size 22.000 7.500 48.000 12.500 63.000 42.000 Bashro objective is to maximize profits. a) Determine whether this is a linear or a non-linear problem. Explain why. b) Bashro charges a single price for all consumer groups. Find the optimal price, production quantity for each group and the corresponding profits. c) Bashro wants to know how much profit is lost by charging a single price. Assume that the company can implement perfect price discrimination (first degree) by charging each consumer group a different price. Find: (1) The optimal price for each group; (ii) Production quantity per group; and (iii) The associated profit. Price sensitivity Formertrans NM Price willing to pay (or marginal value of formertrans) Consumer group 1 Consumer group 2 Consumer group 3 Consumer group 4 Consumer group 5 Consumer group 6 $ 2 270.00 $ 6 450.00 $ 3 000.00 $ 4 400.00 $ 2 150.00 $ 2 940.00 $ 1 101.00 $ 2957.00 $ 2019.00 $ 2 385.00 $ 1 193.00 $ 3075.00 $ 813.00 $ 1516.00 $ 1 226.00 $ 1 898.00 $ 577.00 $ 1 770.00 $ 465.00 $ 1047.00 $ 708.00 $ 1001.00 $ 301.00 $ 598.00 $ 266.00 $ 525.00 $ 483.00 $ 491.00 $ 198.00 $ 613.00 3 4 5 Unit cost and unit price $ 420.00 Unit cost Unit price Market size Consumer group 1 22000 Consumer group 2 7500 Consumer group 3 48000 Consumer group 4 12500 Consumer group 5 63000 Consumer group 6 42000 Number of consumers
