1. A publisher faces the following demand for the next novel of one of its popular authors:

Q

! = 400,000 − 2,000P

The author is paid $ 3 million to write the book and the marginal cost of publishing the book is a

constant at $25 per book.

!

FC

= $ 3,000, 000

!

MC

= $ 25

a) Derive the Marginal Revenue curve.

To derive the MR curve, we use the demand equation to derive the Revenue curve.

! = 400,000 − 2,000P

Q

2,000P

= 400,000 − Q

!

P

! =

400,000 − Q

2,000

! = 200 − 0.0005Q

P

! = PQ

R

R

! = (200 − 0.0005Q)Q

! = 200Q − 0.0005Q 2

R

!

MR

=

dR

dQ

!

MR

= 200(1) − 2(0.0005Q)

!

MR

= 200 − 0.001Q

b) Graph the marginal revenue, marginal cost, and demand curves. At what quantity do the

marginal revenue and marginal cost curves cross? What does this signify?

!

MR

= 200 − 0.001Q

!

MC

= 25

! = 200 − 0.0005Q

P

P

$200

MR

D

DWL

$25

MC

175,000 200,000

400,000

Q

In the graph, the red line represents the MR curve, the blue line presents the Demand curve, and

the green line represents the MC curve. The MR curve crosses the x-axis at Q = 400,000 while

the Demand curve crosses the x-axis at Q = 200,000. The triangle indicated by the DWL is equal

to the deadweight loss. The MR and MC curves cross at the point (175,000, $25) or when Q =

175,000 and P = $25. The point at which the MR and MC curves cross each other signify the

profit-maximizing point where the publisher should publish at the given quantity and price in

order to maximize their profit.

c) In your graph, shade the deadweight loss. Explain in words what this means.

P

$200

MR

D

MC

$25

175,000 200,000

400,000

Q

In the graph, the purple triangle represents the deadweight loss. The deadweight loss represents

the cost to society by market inefficiency. The deadweight loss signifies that the total surplus in

the economy is less than the total surplus if the market were to be competitive. This is due to the

fact that the monopolist produces less than the socially efficient level of output.

d) What quantity would a profit-maximizing publisher choose? What price would it charge?

Show how you derived these quantities.

The profit of the publisher will be maximized when MC = MR. Thus, we equate the two curves

and solve for Q to determine the quantity that would maximize the profit of the publisher.

!

MC

= MR

! = 200 − 0.001Q

25

!

0.001Q

= 200 − 25

Q

! =

175

0.001

Q

! = 175,000

From the calculation above, we see that profit is maximized when 175,000 books are produced.

Since the MC curve is constant at $25, the profit-maximizing price is equal to $25.

e) If the author were paid $2 million instead of $3 million to write the book, how would this

affect the publisher’s decision regarding the price to charge? Explain.

If the author were to be paid $2 million or any other amount other than the original price of $3

million, there would not affect the publisher’s decision regarding the price to charge. The amount

paid to the author is a fixed cost which will affect the total cost of producing books as well as the

profit, which would decrease; both the marginal revenue or marginal cost would not change. The

publisher would still be maximizing its profit by charging $25 per book regardless of the amount

they pay the author.

f) Suppose the publisher was not profit-maximizing but was concerned with maximizing

economic efficiency. What price would it charge for the book? How much profit would it make

at this price?

To maximize economic efficiency, the publisher should charge at a price equal to the marginal

cost, which is $25 per book. At this price, the publisher would earn negative profits which would

then be equal to the amount paid to the author, which is $3 million. To show this mathematically,

we derive the total cost curve and the profit curve.

TC

= (MC )Q + FC

!

!

TC

= 25Q + 3,000, 000

!

Prof

it, π = R − TC

! = 200Q − 0.0005Q 2 − (25Q + 3,000, 000)

π

! = − 0.0005Q 2 + 175Q − 3,000, 000

π

! (0) = − 0.005(0)2 + 175(0) − 3,000, 000

π

π

! (0) = − 3,000, 000

2. Based on market research, a monopolistic recording company obtains the following

information about the demand and production costs of its new CD.

!

Dem

a n d : P = 1000 − 2Q

!

Total

Re venu e : T R = 1000Q − 2Q 2

Margin

al Cost : MC = 100 +

!

1

Q

2

where Q indicates the number of copies sold and P is the price in cents.

a) Find the price and quantity that maximize the company’s profit.

To maximize the company’s profit, we equate the MR and MC curves and solve for Q. Then, we

substitute Q into either of the two curves to solve for P.

!

MR

=

dT R

dQ

!

MR

= 1000(1) − 2(2Q)

!

MR

= 1000 − 4Q

MC

= 100 +

!

1

Q

2

!

MR

= MC

1000

− 4Q = 100 +

!

1

Q

2

1

! Q + 4Q = 1000 − 100

2

9

! Q = 900

2

2

Q

! = 900

(9)

Q

! = 200

! = MR = 1000 − 4Q

P

P

! = 1000 − 4(200)

P

! = 1000 − 800

P

! = 200 ₵ = $ 2

Thus, the profit will be maximized when 200 copies of the CD are sold at a price equal to $2.

b) Find the price and quantity that would maximize social welfare.

To maximize the social welfare, we equate the demand curve and the MC curve and then solve

for Q. Using the Q, we then substitute it into either of the two curves to solve for P.

! = 1000 − 2Q

P

MC

= 100 +

!

1

Q

2

! = MC

P

1000

− 2Q = 100 +

!

1

Q

2

1

! Q + 2Q = 1000 − 100

2

5

! Q = 900

2

2

! = 900

Q

(5)

Q

! = 360

! = 1000 − 2(360)

P

! = 1000 − 720

P

P

! = 280₵ = $ 2.8

From the calculation above, we see that the social welfare is maximized when 360 units of the

CD are sold at the price of $2.8.

c) Calculate the deadweight loss from the monopoly.

To calculate the deadweight loss, we take the difference between the social welfare-maximizing

quantity and the profit-maximizing quantity.

Q

! social welfare − Qprofit = 360 − 200 = 160

Then, we take the difference between the demand when Q = 200 and the marginal cost when Q =

200.

! demand (200) − Qmarginal cost (200) = $6 − $ 2 = $ 4

Q

Finally, we calculate the deadweight loss by multiply the two quantities above and dividing the

product by two.

!

DW

L=

(160)($ 4)

= $ 320

2

Thus, the deadweight loss is equal to $320.

3. Bruce, Collen, and David are all getting together at Bruce’s house on Friday evening to play

their favorite game, Monopoly. They all love to eat sushi while they play. They all know from

previous experience that two orders of sushi are just the right amount to satisfy their hunger. If

they wind up with less than two orders, they all end up going hungry and don’t enjoy the

evening. More than two orders would be a waste, because they can’t manage to eat a third order

and the extra sushi just goes bad (although they receive no specific disutility from wasting food).

Their favorite restaurant, Chaya, packages its sushi in such large containers that each individual

person can feasibly purchase at most one order of sushi. Chaya offers takeout, but unfortunately

doesn’t deliver.

Suppose that each player enjoys $20 worth of utility from having enough sushi to eat on Friday

evening and 0 from not having enough to eat. The cost to each player of pick up an order of sushi

is $10. Unfortunately, the three have forgotten to communicate about who should be buying

sushi this Friday, and none of the players has a cell phone, so they must make independent

decisions of whether to buy (B) or not buy (NB) an order of sushi.

a) Write down this game in normal (table) form.

Options: B, NB

One buys

Two buy

All buy

(Bruce, Collen, David) (Bruce, Collen, David) (Bruce, Collen, David)

B, NB, NB

B, B, NB

No one buys

(Bruce, Collen,

David)

NB, B, NB

B, NB, B

NB, NB, B

NB, B, B

B, B, B

NB, NB, NB

b) Find all of the Nash equilibria in pure strategies.

From the table, we see that there are 8 pure strategies. We then transform the table such that the

number of orders is calculated with their corresponding total cost per strategy.

One buys

(Order, Cost)

Two buy

(Order, Cost)

1, $10

2, $20

1, $10

2, $20

1, $10

2, $20

All buy

(Order, Cost)

No one buys

(Order, Cost)

3, $30

0, $0

Then, we convert the table above into utility. When there is not equal to 2 orders, the utility is $0

while the utility is $20 when there are 2 orders.

One buys

(Utility)

Two buy

(Utility)

0

$20

0

$20

0

$20

All buy

(Utility)

No one buys

(Utility)

0

0

From the table above, we see that there are 3 pure strategies that will lead to Nash equilibria.

These are: (1) Bruce and Collen order, (2) Bruce and David order, and (3) Collen and David

order.

4. There are two distinct proposals, A and B, being debated in Washington. The Congress likes

proposal A, and the president likes proposal B. The proposals are not mutually exclusive; either

or both or neither may become law. Thus, there are four possible outcomes, and the rankings of

the two sides are as follows, where a larger number represents a more favored outcome.

Outcome

Congress President

A becomes law

4

1

B becomes law

1

4

Both A and B become law

3

3

Neither become law (status quo)

2

2

a) The moves in the game are as follows. First, the Congress decides whether to pass a bill and

whether it is to contain A or B or both. Then, the president decides whether to sign or veto the

bill Congress does not have enough votes to override a veto. Therefore, if the president vetoes

the bill, the status quo remains (i.e. neither A nor B become law). Draw the game tree, making

sure to label player’s nodes and branches and payoffs, and indicate the equilibrium derived using

backward induction.

President signs bill (5)

President vetoes bill (4)

Bill contains A

President signs bill (5)

Congress

Bill contains B

Bill contains A and B

President vetoes bill (4)

President signs bill (6)

President vetoes bill (4)

Bill contains neither A nor B

President signs bill (4)

From the game tree above, we see that the most favorable outcome

Presidentisvetoes

whenbill

the(4)

President signs

the bill that both contains A and B where the payoff is equal to 6.

b) Now suppose the rules of the game are changed in only one respect: the president is given the

extra power of a line-item veto. Thus, if the Congress passes a bill containing both A and B, the

president may choose not only to sign or veto the bill as a whole, but also to veto just one of the

two items. Show the new game tree and equilibrium.

President signs bill (5)

President vetoes bill (4)

Bill contains A

President signs bill (5)

Congress

Bill contains B

Bill contains A and B

President vetoes bill (4)

President signs bill (6)

President vetoes bill (4)

President signs A but vetoes B (5)

President signs B but vetoes A (5)

Bill contains neither A nor B

President signs bill (4)

President vetoes bill (4)

From the game tree above, we see that the most favorable outcome is still when the president

signs the bill containing A and B. Thus, equilibrium is maintained despite the new rule added.

…

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Next to these stages, there are four types of loyalty. The first type is no loyalty: this can be seen as the typical action supporter that is giving money to fundraiser friends/family. There is no connection between the action supporter and War Child, non-loyal customers add a small amount to the financial account of the organization. The second type is inertia loyalty: this type can be a potential Friend, the person is giving a donation because they always have done it. This person is not loyal to one charity because there is no deeper connection and is easy with switching from charity to charity. This person is reachable to get a deeper connection with to become a potential Friend. It is needed to give the potential Friend attention and please the person. The third type is latent loyalty: this type is based on situational influences such as time, social life, physical factors, reasons why to support charity and the mood of the person. Latent loyalty means that there are repeated purchases. The last type is premium loyalty: this is the greatest type an organization can get. This type indicates the loyal Friend who is proud to discover more and tell about War Child to everyone. (Griffin, 2010) Using the stages and types of loyalty, War Child will get a better understanding about their potential Friends. Increased loyalty can give benefits to more respects of the company. Increased loyalty will be cost saving because there will be reduced marketing costs, more positive word-of-mouth, satisfied loyal customers whereby the failure costs decrease. (Griffin, 2010) 1.2.4 Customer relationship management Kotler (2014, p. 9) stated in the book ‘’Principles of marketing’’ that customer relationship management (CRM) can be mentioned as delivering superior customer value and satisfaction by building and maintaining profitable customer relationships. (Kotler, 2014) Using a suitable approach for the action supporters will lead to charitable giving. To build and maintain profitable customer relationships, customer relationship management need to be implemented. It is very important to deliver customer value and make the action supporters satisfied. By doing this,>

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