Practice Questions on capital, comparative advantage, scale, and substitution

A fishing business uses boats and fishermen. A new boat costs $130,000 to purchase. The interest rate is 15 percent per year. At the end of one year, you can sell a used boat for $117,000. If buying and re-selling the boat costs the same as leasing, how much should it cost to lease the boat?

What should the leasing cost be if the interest rate is 20 percent per year?

"I built my deck myself. I'm more efficient at it than a contractor." Comment.

You and your roommate prepare meals together. It takes you one hour to cook and one hour to clean up after a meal. It takes your roommate 20 minutes to cook and 30 minutes to clean up after a meal. Are you better off taking turns, where you cook and clean one night and your roommate cooks and cleans the next night, or should one of you always cook and one of you always clean? What economic concept does this illustrate?

For each situation below, state whether it illustrates increasing returns to scale, decreasing returns to scale, or constant returns to scale.

To get two cups of cooked rice, start with two cups of water and one cup of uncooked rice. To get four cups of cooked rice, start with 3-1/2 cups of water and 2 cups of rice.

The school can add four students to the economics class without requiring another teacher.

The school cannot increase enrollment by 20 percent without increasing faculty and staff by at least 25 percent.

You are using a recipe for chocolate chip cookies. The recipe says that if you want to triple the number of cookies, you just triple all of the ingredients.

A school can use blackboards and chalk as well as whiteboards and markers. Will the elasticity of substitution between blackboards and chalk be higher or lower than the elasticity of subtitution between blackboards and whiteboards? Explain how a drop in the price of blackboards might affect the use of chalk, whiteboards, and markers.

Variable Input Levels

So far, profit maximization for Cool and Slick has actually been simple. We assumed that there would be exactly 2000 hours of Cool's technical input and 2000 hours of Slick's sales input. All we had to do is allocate them between two goods. We do this based on how much of each good can be produced and sold with different combinations of their input, and based on the relative prices of those two goods.

The problem becomes more complicated if we allow for variable hours. Perhaps one of them will work less than 2000 hours and take a pay cut, or work more and take a pay increase. Or we could allow them to hire additional technical and sales staff.

Suppose that we focus on the consulting business. Suppose that the cost of a salesperson works out to $20 an hour, and the cost of a technical person works out to $40 an hour. Each sales person can land 3 consulting contracts per 200 hours of work. The productivity of technical workers is as follows:

Hours of Technical Consulting | Contracts Completed | Sales Effort Required (hours) | Technical Cost ($40 an hour) | Sales Cost ($20 an hour) | Revenue ($8000 per contract) |
---|---|---|---|---|---|

1800 | 18 | 1200 | $72,000 | $24,000 | $144,000 |

2100 | 21 | 1400 | $84,000 | $28,000 | $168,000 |

2500 | 24 | 1600 | $100,000 | $32,000 | $192,000 |

3100 | 27 | 1800 | $124,000 | $36,000 | $216,000 |

4200 | 30 | 2000 | $168,000 | $40,000 | $240,000 |

5500 | 33 | 2200 | $220,000 | $44,000 | $264,000 |

Total cost is the sum of technical cost and sales cost. Total revenue minus total cost is profit. What level of output leads to the maximum profit?

The reason that profits start to decline after output increases beyond a certain amount is old friend, the law of diminishing returns. If you compare the first two columns, you will see that it starts to require more and more technical staff to complete three additional contracts. There are diminishing returns to adding technical staff.

Incidentally, there is a famous essay by Frederick Brooks on productivity in computer programming, which illustrates the law of diminishing returns. The essay is called "the mythical man-month." Brooks pointed out that a project manager will say that a project requires 2 people for 4 months, or 4 man-months. However, if you try to get the job done in one month with 8 people, it does not work. To an economist, this indicates that there are diminishing returns. As you add a person to a project for a month, you get less than one man-month's worth of results.