Bus 640: Managerial Economics

Week 2 Assignment Applied Problems 2

Bus 640: Managerial Economics

Week 2 Assignment Applied Problems 2

Chapter 3 Applied Problems 2 & 4:

2. Appalachian Coal Mining believes that it can increase labor productivity and, there- fore, net revenue by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is

MC + 40P

where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is

MR = 1,000 – 10P

How much pollution reduction should Appalachian Coal Mining undertake?

MC = MR and solve for P.

Dual benefits are enjoyed with the installation of new equipment; reduced pollution and an increase in productivity. Nevertheless the cost exceeds the benefit. The alternative is to adjust the level of pollution in an optimal manner.

40P = 1000-10P

40P+10P=1000

50P=1000

P=20 units.

4. Twenty first Century Electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week.

Number of Security Guards | Number of radios stolen per week |

0 | 50 |

1 | 30 |

2 | 20 |

3 | 14 |

4 | 8 |

5 | 6 |

A. If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?

a) Marginal Benefit = Marginal Cost ~ MB = MC

MC = w = 200, however, the MB from the hiring second worker is:

MB (2) = (30-20) * 25 = 250

TB = (50-20) * - (200*2) = 750 – 400 = 350 ~ Two guards are needed.

B. If the cost of a stolen radio is $25, what is the most the firm would be willing to pay to hire the first security guard?

The firm has got to see the benefit of hiring the guard. Therefore, if the cost is equal to the...