Microeconomics for Management

Kirsten Daniel Spring 2017

Microeconomics for Management

1

Solutions to Group Homework # 1

 

Problem # 1

Demand for a firm’s product is: P = 80 – 3Q. The firm’s cost equation is: C = 200 + 20Q.

 

a) Determine the firm’s optimal quantity and price.

 

b) Suppose that demand changes to P = 110 – 3Q. Determine the new optimal quantity

and price. Explain why the results differ from those in part a.

 

Answer:

a) Maximize profits by setting MR = MC. We can derive MR from the price equation as

MR = 80 – 6Q and MC = 20. Setting MR = MC implies Q* = 10. From the price

equation, it follows that P* = 80 – (3)(10) = 50.

 

b) With the new demand function, MR = 110- 6 Q. Setting MR = MC implies 110 – 6Q =

20, or Q* = 15. In turn, P* = 110 – (3)(15) = 65. Here, the increase in demand (in this

case a parallel outward shift in the demand curve) has induced the firm to increase both

its price and quantity.

 

 

Problem # 2

The college and graduate-school textbook market is one of the most profitable segments

for book publishers. A best-selling accounting text – published by Old School Inc (OS) –

has a demand curve: P = 150 – Q, where Q denotes yearly sales (in thousands) of books.

(The cost of producing, handling, and shipping each additional book is about $40, and the

publisher pays a $10 per book royalty to the author. Finally, the publisher’s overall

marketing and promotion spending (set annually) accounts for an average cost of about

$10 per book.

 

a) Determine OS’s profit-maximizing output and price for the accounting text.

 

b) A rival publisher has raised the price of its best-selling accounting text by $15. One

option is to exactly match this price hike and so exactly preserve your level of sales. Do

you endorse this price increase? (Explain briefly why or why not.)

 

c) To save significantly on fixed costs, Old School plans to contract out the actual

printing of its textbooks to outside vendors. When this happens, OS expects to pay a

somewhat higher printing cost per book (than in part a) from the outside vendor (who

marks up price above its cost to make a profit). How would outsourcing affect the output

and pricing decisions in part a?

 

https://www.coursehero.com/file/28045230/Solutions-to-Homework-1pdf/

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Kirsten Daniel Spring 2017

Microeconomics for Management

2

Answer:

a) The marginal cost per book is: MC = 40 + 10 = $50. (The marketing costs are fixed, so

the $10 figure mentioned is an average fixed cost per book.) Setting MR = MC, we find:

MR = 150 – 2Q = 50, implying Q* = 50 thousand books. In turn, P* = 150 – 50 = $100

per book.

 

b) When the rival publisher raises its price dramatically, the firm’s demand curve shifts

upward and to the right. The new intersection of MR and MC now occurs at a greater

output. Thus, it is incorrect to try to maintain sales via a full $15 price hike. For instance,

consider the case of a parallel upward shift, P = 165 – Q. Setting MR = MC, we find: MR

= 165 – 2Q = 50, implying Q* = 57.5 thousand books, and in turn, P* = 165 –57.5 =

$107.50 per book. Here, OS should increase its price by only $7.50 (not $15).

 

c) By using an outside printer, OS is saving on fixed costs but is incurring a higher

marginal cost (i.e. printing cost) per book. With a higher marginal cost, the intersection of

MR and MC occurs at a lower optimal quantity. OS should reduce its targeted sales

quantity of the text and raise the price it charges per book. Presumably, the fixed cost

saving outweighs the variable cost increase.

 

 

Problem # 3

Night Timers is a small company manufacturing glow-in-the-dark products. One of the

hottest items the engineering department has developed is adhesive tape that can be

applied to walls and floors. Night Timers’ chief engineer anticipates that the product will

be sold in ten-foot rolls. At present, the company’s maximum production capacity is

140,000 rolls per year. The engineer believes the cost function to be described by: C =

$50,000 + .25Q. (The high fixed costs represent development cost and tooling to prepare

coating equipment). Night Timers’ president seeks to establish a price that maximizes

profit (since she is the chief stockholder). She thinks that the firm should be able to sell at

least 125,000 rolls of tape per year.

 

a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the

firm is to break even? What if it can only sell 100,000?

 

b) The marketing manager forecasts demand for the tape to be: Q = 350,000 – 200,000P.

Find the firm’s profit-maximizing output and price.

 

c) If the demand forecast in part b is realized in the first year of production, should the

company consider expanding capacity? Explain.

 

https://www.coursehero.com/file/28045230/Solutions-to-Homework-1pdf/

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Kirsten Daniel Spring 2017

Microeconomics for Management

3

Answer:

a) Break even implies R = C or P*Q = 50,000 + .25Q at the level of output indicated. To

find the break-even price, set Q = 125,000 and solve for P. Doing so, we find: P = $.65

per unit. If Q = 100,000, the break-even price rises to: P = $.75 per unit.

 

b) After rearranging the demand equation, we have P = 1.75 – Q/200,000. Thus, MR =

1.75 – Q/100,000. From the cost function, we know that MC = .25. Set MR = MC to

maximize profit: 1.75 – Q/100,000 = .25. Therefore, Q = (1.5)(100,000) = 150,000 rolls.

However, maximum capacity is 140,000 rolls. Thus, an output of 140,000 is the best the

company can expect to do. The requisite price is: P = 1.75 – 140,000/200,000 = $1.05.

The firm’s projected profit is: (1.05 – .25)*(140,000) – 50,000 = $62,000.

 

c) The relevant question is whether the increased profit of expanding capacity exceeds

the increased cost of doing so. If it could produce and sell 150,000 rolls (by lowering

price to $1), the company’s profit would increase very slightly to: (1 – .25)*(150,000)

– 50,000 = $62,500. The extra $500 in profit is clearly not worth the cost of expansion.

 

 

Problem # 4

The University Eye Institute in upper New-York state is a state-of-the-art ophthalmology

center that specializes in a sophisticated laser surgery to correct myopia. Current annual

volume is 1000 operations. A major customer of the center is the United Health Insurance

system. United currently sends the University Eye Institute 200 patients per year or 20%

of the total.

 

United pays $2,500 per operation as does every payor. The United Health Insurance

Company is satisfied with the quality and service provided by the University Eye

Institute and has proposed that they send the Center an additional 100 patients

(operations) per year. United proposes that the fee be reduced to $2,000 for the additional

100 patients and for the prior 200 patients. Assume the fee paid by payors other than

United Health remains the same.

 

a) What is the marginal revenue per patient if the proposal is accepted?

 

b) What is the marginal cost per patient if the proposal is accepted?

Here are some cost data to help you answer part b. Volume 1000 per year 1100 per year

Average Total Cost $2,125 $2,100

 

c) Would you recommend that the proposal be accepted or not? Why?

 

https://www.coursehero.com/file/28045230/Solutions-to-Homework-1pdf/

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Kirsten Daniel Spring 2017

Microeconomics for Management

4

Answer:

a)



MR  800$2500 300$20001000$2500

100 $1000

 

 

b)

1850$ 100

2125$10002100$1100 

 



 

Q

TC MC

 

c) You would not because the MR of $1000 < MC of $1850.

https://www.coursehero.com/file/28045230/Solutions-to-Homework-1pdf/

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