Problems
(3). The Bramwell Corporation has estimated its demand function and total cost function to be as follows:
Q = 25 −0.05PTC = 700 + 200Q
Answer the following questions either by developing demand and cost schedules (Hint: Use quantities from 1 to 14) or by solving the equations.
o What will be the price and quantity if Bramwell wants to
Maximize profits?
Maximize revenue?
Maximize revenue but require the profit to be a minimum of $300?
o Now assume the cost function is TC = 780 + 200Q, while the demand function remains the same. What will the price and quantity be if Bramwell wants to
Maximize profits?
Maximize revenue?
Maximize revenue but require the profit to be a minimum of $300?
o Why are the answers the same in a(1) and b(1) but different in a(3) and b(3)?
(8). The Prestige Office Equipment Company produces and sells different types of office furniture. One of the important items it sells is a high-quality desk. During the past year, Prestige sold 5,000 of these at a price of $500 each. The contribution profit for this line of furniture last year was $700,000.
A consultant suggests that Prestige decrease the price of each desk by $30. In his opinion, another 500 desks could then be sold, and the total profit would be maintained. A trade publication that employs an economist has estimated price elasticity of office furniture (including desks) to be about −1.8.
Assume the variable unit cost per desk in the coming year will remain the same. Evaluate the consultant’s proposal. Be sure to include in your answer the price elasticity assumed by the consultant, as well as the published elasticity estimate.
(12). A firm makes two products, x and y. Inverse demand for each shows that pricing in one market depends on sales in the other according to the equations:
Px = 1000 −20x + 3y and Py = 500 −5y + x.
The firm faces joint fixed cost of $12,000 and constant marginal cost of production in each product segment, MCx = $200, and MCy = $100.
a. What bundle of products (x*, y*) should the firm produce?
b. What prices will the firm be able to charge for each product given production at (x*, y*)?
c. What profits result in this instance?
d. At (x*, y*), what are the values of ∂TRy∂x and ∂TRx∂y Provide a short (one- or two-sentence) explanation for each value. That is, explain to your less mathematically sophisticated boss the economic significance of each value.
Problems
1. Jay Wechsler agrees to purchase a car from a local dealer, the Con Car Co. The purchase price is $15,000. Jay has the cash to pay the entire amount and wants to do so. Con’s sales manager uses the following argument to convince him to finance the car: “All we require is a down payment of $3,000. Then you can borrow the $12,000 from our finance company at 12 percent. You will make monthly payments of $266.93 for 5 years (60 months), a total of $16,015.80. If you do that, you get to keep your $12,000. Now suppose you keep this money in a money market account that pays you 8 percent compounded quarterly. In 5 years, the $12,000 will grow to $17,831.40. That means that you will be better off by $1,815.60 than if you pay the $12,000 in cash.”
Assume all the numbers are correct. Does the offer sound too good to be true? Why? (This is an argument often used by automobile dealers. One of the authors encountered it when buying a car.)
2. Your firm has an opportunity to make an investment of $50,000. Its cost of capital is 12 percent. It expects after-tax cash flows (including the tax shield from depreciation) for the next 5 years to be as follows:
Year 1 $10,000
Year 2 20,000
Year 3 30,000
Year 4 20,000
Year 5 5,000
a. Calculate the NPV.
b. Calculate the IRR (to the nearest percent).
c. Would you accept this project?
3. You own a large collection of fine wines. You now decide that you must liquidate this valuable asset. However, you predict that the value of your collection will rise in the next few years. The following are your estimates:
Year Estimated Value
Today $70,000
1 88,000
2 104,000
3 119,000
4 132,000
5 142,000
6 150,000
If you assume your cost of capital to be 10 percent, when should you sell your collection to maximize your NPV?
11. Two mutually exclusive alternatives, projects C and D, have the following investments and cash flows:
Project C Project D
Investment at period t = 0 $40,000 $40,000
Cash inflow at t = 1 10,000 20,500
Cash inflow at t = 2 10,000 20,500
Cash inflow at t = 3 47,000 20,500
a. Calculate the NPV and IRR of each project. The company’s cost of capital is 12 percent.
b. Which of the two projects would you accept? Explain.
c. Sketch the two projects’ NPV profiles.