Pricing

1. The goal of the telephone company is to Max profit=price*quantity. There is a tradeoff between price and quantity.

i.

Profit | 　 | 　 | 　 | 　 | 　 | 　 |

Price per min | $1 | $2 | $3 | $4 | $5 | 　 |

Type1 | 5 | 8 | 9 | 8 | 5 | 　 |

Type2 | 4 | 6 | 6 | 4 | 0 | 　 |

Type3 | 3 | 4 | 3 | 0 | 0 | 　 |

Type4 | 2 | 2 | 0 | 0 | 0 | 　 |

Type5 | 1 | 0 | 0 | 0 | 0 | 　 |

　TPsum | 15 | 20 | 18 | 12 | 5 | 　 |

Linear Pricing Profit |

According to the total profit matrix $20 is the highest among (15, 20, 18, 12,5). The price of profit-maximizing linear pricing scheme should be $2/minute.

ii.

Profit | 　 | 　 | 　 | 　 | 　 |

min\price | 1 | 2 | 3 | 4 | 5 |

1st | 5 | 8 | 9 | 8 | 5 |

2nd | 4 | 6 | 6 | 4 | 0 |

3rd | 3 | 4 | 3 | 0 | 0 |

4th | 2 | 2 | 0 | 0 | 0 |

5th | 1 | 0 | 0 | 0 | 0 |

Customer# | 　 | 　 | 　 | 　 | 　 | 　 | 　 |

min\price | $1 | $2 | $3 | $4 | $5 | Price | Profit |

1st min | 5 | 4 | 3 | 2 | 1 | 3 | 9 |

2nd | 4 | 3 | 2 | 1 | 0 | 2 | 6 |

3rd | 3 | 2 | 1 | 0 | 0 | 2 | 4 |

4th | 2 | 1 | 0 | 0 | 0 | 1 | 2 |

5th | 1 | 0 | 0 | 0 | 0 | 1 | 1 |

Quantity-Discount Profit | 22 |

According to the total profit matrix, the price of profit-maximizing quantity-discount scheme should be $3 for the first minute, $2 for the second minute, $2 for the third minute,$1 for the fourth minute, $1 for the fifth minute.

The maximum profit for the first minute is $9 when priced at $3.

The maximum profit for the second minute is $6 when priced at $2 or $3, , therefore it should be $2.

.

The maximum profit for the third minute is $4 when priced at $2.

The maximum profit for the forth minute is $2 when priced at $1 or $2, therefore it should be $1.

The maximum profit for the fifth minute is $1 when priced at $1.

Since the cost is 0, we want to capture more customers so we choose the lower price.

iii. Because the quantity-discount scheme is more flexible and it is able to capture the highest customer surplus. Because of the decreasing...