Leadership

1. Individual Problems 3-7

1. A business incurs the following costs:

Assume the firm produces 3 million units per month.

The total variable cost, per month, is

million.

The total fixed cost, per month, is

million.

The total cost is

million.

2. An end-of-aisle price promotion changes the price elasticity of a good from −2 to −3. Suppose the normal price is $34, which equates marginal revenue with marginal cost at the initial elasticity of –2.

What should the promotional price be when the elasticity changes to –3? (
Hint: In other words, what price will equate marginal revenue and marginal cost?)

3. A firm sells 1,000 units per week. Suppose the average variable cost is $20, and the average cost is $55.

In the short run, the break-even price is

. In the long run, the break-even price is

.

Suppose the firm charges a price of $5 per unit.

Use the following table to indicate whether the firm will shut down or continue to produce in the short run and the long run.

4. In early 2008, you purchased and remodeled a 120-room hotel to handle the increased number of conventions coming to town. By mid-2008, it became apparent that the recession would kill the demand for conventions. Now, you forecast that you will be able to sell only 10,000 room-nights, which cost $50 per room per night to service. You spent $30.00 million on the hotel in 2008, and your cost of capital is 10%. The current going price to sell the hotel is $25 million.

If the estimated demand is 10,000 room-nights, the break-even price is 

 per room, per night. (
Hint: Remember that the cost of capital is the opportunity cost, or true cost, of making an investment.)

5. Last year, a toy manufacturer introduced a new toy truck that was a huge success. The company invested $5.50 million in a plastic injection molding machine (which can be sold for $5 million immediately) and $300,000 in plastic injection molds specifically for the toy (not valuable to anyone else). The cost of labor and materials necessary to make each truck runs about $3. This year, a competitor has developed a similar toy, significantly reducing demand for the toy truck. Now, the original manufacturer is deciding whether it should continue production of the toy truck.

If the estimated demand is 100,000 trucks, the break-even price is 

 per truck.

A university spent $1.5 million to install solar panels atop a parking garage. These panels will have a capacity of 800 kilowatts (kW) and have a life expectancy of 20 years. Suppose that the discount rate is 20%, that electricity can be purchased at $0.10 per kilowatt-hour (kWh), and that the marginal cost of electricity production using the solar panels is zero.

Hint: It may be easier to think of the present value of operating the solar panels for 1 hour per year first.

Approximately how many hours 
per year will the solar panels need to operate to enable this project to break even?

3,850.40

5,775.60

2,310.24

3,080.32

6. If the solar panels can operate only for 3,465 hours a year at maximum, the project(would/would not)
    break even.

Continue to assume that the solar panels can operate only for 3,465 hours a year at maximum.

In order for the project to be worthwhile (i.e., at least break even), the university would need a grant of at least
    
$90,083.97 or $225,209.93 or $150,139.95 or $135,125.96

7. Suppose an initial investment of $50 will return $35/year for three years (assume the $35 is received each year at the end of the year).

At a discount rate of 20%, this investment

   

 Is/is not profitable.

8. George’s T-Shirt Shop produces 10,000 custom-printed T-shirts per month. George’s fixed costs are $30,000 per month. The marginal cost per T-shirt is a constant $2.

George’s break-even price is ___

per shirt.

Suppose George sells 50% more T-shirts per month.

At this quantity of shirts, George’s break-even price is____

per shirt.

9. A copy company wants to expand production. It currently has 20 workers who share eight copiers. Two months ago, the firm added two copiers, and output increased by 60,000 pages per day. One month ago, the firm added five workers, and productivity also increased by 25,000 pages per day. A copier costs about three times as much as a worker.

Assume these increases in productivity per worker and productivity per copier are good proxies for future increases in productivity when hiring additional workers or purchasing additional copiers.

Based on this information, the copy company should
Purchase another copier/Hire another worker
    in order to expand output.

10. You run a game-day shuttle service for parking services for the local ball club. Suppose you are compensated $16 per customer, per ride. In other words, your marginal revenue is $16. Your costs for different customer loads are summarized in the following table.

For each customer load, calculate both the marginal cost and the average cost. Then answer the question that follows.

Note: Round your answers to the nearest cent.

In order to maximize profits, you should carry
2,5, 7 or 6
    customers per load.