Managerial Economics Persuasive

1. Complete the following table and answer the accompanying questions.

a. At what level of the control variable are net benefits maximized?

Net Benefit is also profit. The formula for this is MB = MC. As seen in the table completed above, after applying the formula then net benefit is maximized where Q = 106.

b. What is the relation between marginal benefit and marginal cost at this level of the control variable?

Where marginal benefit is equal to marginal cost (MB = MC), net benefit is maximized 2. Arcadia recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by Arcadia’s leadership in this area. The costs of recycling include all of the energy, labor, and space required to do the recycling. Suppose these benefits and costs are given by B(Q) = 100Q – 2Q2 and

C(Q) = 2Q
(Note that Marginal Benefit (MB) = 100 – 4Q, and Marginal Cost (MC) = 2.) a. What level of Q maximizes the total benefits of recycling?

To maximize total benefit of recycling, marginal benefit must be equal to zero (MB = 0). At Q = 25, total benefits of recycling is maximized.

Reason: MB = 0  100-4Q = 0  25 = Q

b. What level of Q minimizes the total costs of recycling?

Total cost of recycling is minimize where Q = 0 (zero).

c. What level of Q maximizes the net benefits of recycling?

To maximize net benefit of recycling, marginal benefit must be equal to marginal cost (MB = MC). At Q = 24.5, net benefits of recycling is maximized.

Reason: MB = MC  100-4Q = 2  24.5 = Q

d. What level of recycling is optimal? Why?

At Q = 24.5, level of recycling is optimal as this is the maximum net benefit of recycling considering the benefit and cost. 3. You are a strong advocate for a one-year investment project that would cost your firm $10,000 today, but generate virtually certain earnings of $15,000 at year-end. Those in your firm’s financial group concur that the investment is virtually risk-free, but nonetheless your boss is concerned about the firm’s cash flow problems. In fact, the problems are so severe that the firm’s bank currently charges it 20 percent on one-year loans. Convince your boss to undertake the project.

NPV = – Initial investment + expected earnings (1/ 1+ i)
= -10,000 + 15,000 (1/1.20)
= 2,499.99 or 2,450.00

Net present value of the investment is $2,499.99, which is more than zero. Thus, it is recommended to undertake the project.

Point 2: By also looking at the cost for the firm to invest in such project ($10,000 + 2000 interest to be paid to bank if initial investment is loaned) is still lower than the risk-free earning of $15,000. Risk free means a
very high probability of reaching the expected earning at maturity. Thus, it is recommended to undertake this one-year investment

4. You have just been hired as a consultant to help a firm to decide which of three options to take to maximize the value of the firm over the next three years. The following table shows year-end profits for each option. Interest rates are expected to be stable at 8 percent over the next three years.

a. Discuss the difference in the profits associated with each option. Provide an example of real-world options that might generate such profit streams.

Profit in option A is highest in year 1. Profits are highest in option B & C in later years. Both options A & B have a total profit of $240,000, while option C has a total profit of $245,000. Not looking at the Net present value of the profits to be earned, option C is the most attractive investment.

Some of the examples that generate such profit streams as option A are those plantations that can have its harvest and sell its produce in the market within a short period of time. Profit streams as option C, on the other hand, are those investment that requires huge investment like telecommunication services that requires installation of expensive infrastructures in its area of operation and will only receive a return in a longer term as its customer base grows overtime.

b. Which option has the greatest present value?

NPV = CF1 + CF2 + CF3
(1+i) (1+i) 2 (1+i) 3

Option A = 70,000 + 80,000 + 90,000
1+ .08 (1+.08) 2 (1+.08) 3
= 64,814.81 + 68,587.11 + 71,444.90
= 204,846.82

Option B = 50,000 + 90,000 + 100,000
1+ .08 (1+.08) 2 (1+.08) 3
= 46,296.30 + 77,160.49 + 79,383.22
= 204,840.01

Option C = 30,000 + 100,000 + 115,000
1+ .08 (1+.08) 2 (1+.08) 3
= 27,777.78 + 85,733.88 + 91,290.71
= 204,802.37

By calculating the present value of the three options, option A is the most attractive with $204,846.82.

5. Consider a market characterized by the following demand and supply conditions: Demand: PX = 50 -5QX Supply: PX = 32 + QX.
Graph the demand and the supply. Label the axis and the equilibrium. The equilibrium price and quantity are, respectively?

To find the equilibrium price and quantity, find the point where demand curve crosses the supply curve.

Demand = Supply  50 -5Qx = 32 + Qx  Q = 3
To find price, substitute 3 to Qx of demand or supply function  P = 50 – 5(3)  P = 35

The equilibrium price and quantity of demand function PX = 50 -5QX and supply function Supply: PX = 32 + QX are 3 units and $35 respectively.

6. The demand curve for product Y is given by: Qy = 1,000 – 20Py. a. Find the inverse demand curve.

Qy = 1,000 – 20Py  20Py = 1000 – Qy  Py = 50 – 0.05Qy.

To graph, if Py = 0, Qy = 1000;
If Qy = 0, Py = 50

The inverse demand curve is Py = 50 – 0.05Qy.

b. How much consumer surplus do consumers receive when Py = $20?

Qy = 1,000 – 20Py  Qy = 1,000 – 20 (20)  Qy = 600

Consumer Surplus = ½ (Py*Qy)
= ½ (50-20*600)
= 9,000

When Py = $20 and Qy = 600 units, the consumer surplus is equal to 9,000.

c. How much consumer surplus do consumers receive when Py = $10?

To find Qy, assign Py = $ 10 in function Qy = 1,000 – 20Py Qy = 1,000 – 20 (10)  Qy = 800

Consumer Surplus = ½ (Py*Qy)
= ½ (50-10*800)
= 16,000

When Py = $10 and Qy = 800 units, the consumer surplus is equal to 16,000.

d. In general, what happens to the level of consumer surplus as the price of a good falls?

Based on the calculation above where demand function is Qy = 1,000 – 20Py, when a price of the good falls, the consumer surplus increases.

7. You are an aide for the Senate Banking Committee Chairman. He comes to you with a bill that proposes setting limits on what ATM owners can charge non-account holders, over and above what banks charge their own customers. Currently, large banks charge non-customers an average fee of $1.35 per transaction in addition to the fees the customer’s own bank imposes. The
Senator asks you to look at a proposal that would place a $0.50 cap on the fees ATM owners can charge noncustomer for accessing their money. If this legislation is enacted, what would be the likely effects? A graphically analysis is preferred.

As seen on the graph above, when there is a cap of $0.50 on the fees charged by ATM owners to non-customers, there will be (a) producer surplus for ATM owners will be smaller, while consumer surplus for non-customers will be either bigger or smaller depending if area gained is higher or lower than area loss, (b) deadweight loss between the demand of a non-customer shortage and the supply of the ATM owners, (c) shortage on bank who will be willing to cater non-customers.

8. You are the manager in charge of global operation at BankGlobal—a large commercial bank that operates in a number of countries around the world. You must decide whether or not to launch a new advertising campaign in the U.S., market. Your accounting department has provided the accompanying statement, which summarizes the financial impact o the advertising campaign on U.S. operation. In addition, you recently received a call from a colleague in charge of foreign operations, and she indicated that her unit would lose $8 million if the U.S. advertising campaign were launched. Your goal is to maximize BankGlobal’s value. Should you launch the new campaign? Explain.

Financial Impact on US Operations

a. Find the change in revenue and cost:
Change of Revenue before and after advertising campaign:
$32,347,800 – $22,540,100 = $9,807,700

Change of Variable cost before and after advertising campaign: $12,581,900 – $8,457,100 = $4,124,100

Change of Direct and Indirect Fixed Cost before and after advertising campaign: None

b. Find the opportunity cost if advertised or not advertised.

Opportunity Cost if not advertised: None

Opportunity Cost if advertised: $8,000,000 lost in foreign operations

c. Find the net change if advertised:
Net change if advertised: $9,807,700 – ($4,124,100 + $8,000,000 ) = -2,317,100.00 This shows that Revenue to be earned is lesser than the Cost to be incurred, thereby net benefit is a loss.

Net change if not advertised: Zero (0)
DECISION: DO NOT LAUNCH CAMPAIGN!
PROBLEM SET #2
1. The demand curve for a product is given by Qxd = 2,000 – 5Px + 0.2Pz, Where, Pz = $500.

To simplify the equation, substitute Pz to the formula:
Using Qxd = 2,000 – 5Px + 0.2Pz, if Pz = $500 ,
Qxd = 2,000 – 5Px + 0.2(500) becomes Qxd = 2,100 – 5Px

a.1 What is the own price elasticity of demand when Px = $120?

Given the demand function Qxd = 2,100 – 5Px and price of Px = $120, find the quantity:

If Px = 120,
Qxd = 2,100 – 5Px
= 2,100 – 5(120)
= 1500

a. Is demand elastic or inelastic at this price?
To find the own price elasticity of demand, use the formula ε = (∆Q/∆P)*(P/Q) Elasticity (ε)x = (∆Q/∆P)*(P/Q)
= (-5) * (120/1500)
= -0.40  inelastic

At Px = $120 and Qx = 1500, the own price elasticity of demand is inelastic of -0.40.

Current Revenue = Px*Qx
= 120*1500
= $180,0000

a.3 What would happen to the firm’s revenue if it decided to charge a price below $120?
If Px (price below $120) = $100,

Qxd = 2,100 – 5Px
= 2,100 – 5(100)
= 1600

Elasticity (ε)x = (∆Q/∆P)*(P/Q)
= (-5) * (100/1600)
= -0.3125  more inelastic

New Revenue = Px*Qx
= 100*1600
= $160,0000

As the price goes down from $120 to $100, the own price elasticity of demand becomes more and more INELASTIC from -0.40 to 0.3125 respectively. Revenue goes down when price becomes more and more inelastic ($180,000>$160,000)

b.1 What is the own price elasticity of demand when Px = $250? Is demand elastic or inelastic at this price?

If Px = 250,
Qxd = 2,100 – 5Px
= 2,100 – 5(250)
= 850

Elasticity (ε) = (∆Q/∆P)*(P/Q)
= (-5) * (250/850)
= -1.47  elastic

Revenue = Px*Qx
= 250*850
= $212,500

At Px = $250 and Qx = 850, the own price elasticity of demand is elastic of 1.47.

b.2 What would happen to the firm’s revenue if it decided to charge a price above $250?

If Px = 270,
Qxd = 2,100 – 5Px
= 2,100 – 5(270)
= 750

Elasticity (ε) = (∆Q/∆P)*(P/Q)
= (-5) * (270/750)
= -1.80  becomes more elastic

New Revenue = Px*Qx
= 270*750
= $202,500

As the price goes up from $250 to $270, the own price elasticity of demand becomes more and more ELASTIC from -1.47 to -1.80 respectively. Revenue is also lowered when price becomes more and more elastic ($212,500>$202,500)

To find maximum revenue (MR = 0). With MR = 2100 – 10Px = 0, Px = 210 and Q = 1,050.

Revenue = Px*Qx
= 210*1050
= $220,500

Elasticity (ε) = (∆Q/∆P)*(P/Q)
= (-5) * (210/1050)
= -1 Unit-elastic

*Own price elasticity of demand = 1 when revenue is maximized.

2. As the manager of a local hotel chain, you have hired an econometrician to estimate the demand for one of your hotels (H). The estimation has resulted in the following demand function: QH = 2,000 – PH – 1.5PC – 2.25PSE + 0.8POH + .01M , where PH is the price of a room at your hotel,

PC is the price of concerts in your area,
PSE is the price of sporting events in your area,
POH is the average room price at other hotels in your area, M is the average income in the United States.

What would be the impact on your firm of
a. A $500 increase in income?

Having all other factors constant,
QH = + 0.01M
=0.01(500)
= 5  quantity demanded for the hotel will be increase by 5 units

b. A $10 reduction in the price charged by other hotels?

Having all other factors constant,
QH = + 0.8POH
= 0.8(-10)
= -8  quantity demanded for the hotel will be decrease by 8 units

c. A $7 increase in the price of tickets to local sporting events?

Having all other factors constant,
QH = – 2.25PSE
= – 2.25 (7)
= -15.75  quantity demanded for the hotel will be decrease by 15.75 units

d. A $5 increase in the price of concert tickets, accompanied by an $8 increase in income?

Having all other factors constant,
QH = – 1.5PC + .01M
= – 1.5 (5) + .01(8)
= – 7.5 + 0.08
= -7.42  quantity demanded for the hotel will be decrease by 7.42 units

3. Your firm’s research department has estimated the income elasticity of demand for Art Deco lawn furniture to be 1.5. You have just learned that due to an upturn in the economy, consumer incomes are expected to rise by 8 percent next year. How will this event affect your ordering decision for PVC pipe, which is the main component in your furniture? Formula for Income Elasticity(ε) is:

ε = (%∆Q)/(%∆I)
1.5 = (%∆Q)/(8%)
12% = %∆Q

With the income elasticity of 1.5 and expected increase of income by 8%, it is expected that the ordering quantity for the PVC pipe will also increase by 12%.

4. You are a manager at the DaimlerChrysler. Daimler-Chrysler has lost money on the Smart car since the first model rolled off the assembly line in 1998. By bringing its little car into the huge U.S. market, the firm hopes to reverse its fortunes. Former race car driver Roger Penske has signed on to develop a network of up to 50 Smart dealerships across the U.S. Penske says the car is not just smart, it is also safe. If your marketing department estimates that the annual demand for the Smart Car is Q = 200,000 – 8.0P, what price should you charge in order to maximize revenues from sales of the Smart Car?

To maximize revenue, marginal revenue must be equal to zero (MR = 0). To calculate marginal revenue, the demand function Q = 200,000 – 8.0P must be calculated with P and differentiated:

Revenue = (200,000 – 8.0P)*P
= 200,000P -8.0P2

Marginal Revenue = 200,000 – 16.0P

Maximize revenue: 200,000 – 16.0P = 0.
16P = 200,000
P = 12,500

At price = $12,500, revenue is maximized

Q = 200,000 – 8.0P  Q = 100,000 units

5. A stockholder named Sue must cast a vote for chair of the board. Sue prefers Mr. Lee to Ms. Doe, Ms. Doe to Mr. James, and Mr. James to Mr. Lee. a. Are Sue’s preferences consistent with our assumptions about consumer behavior? Explain.

No. Sue’s preference is not consistent with our assumption about consumer behavior. This violates the property of indifference curve TRANSITIVITY where rational person’s indifference curve cannot cross.

b. If all stockholders had the same preferences as Sue, who would win the appointment as chair of the board? Explain.

No one will win the appointment as chair of the board. Choosing any person among the three will violate Sue’s other statement of preference.

6. Airlines give away millions of tickets each year through their frequent flyer programs, with the typical airline awarding a free ticket for each 25,000 miles flown on the airline. The average airline ticket costs $500 and is for a 2,500-mile round trip. Given this information, evaluate the following statement: Airlines could have the same effect on demand by eliminating their frequent flyer programs and simply lowering the average ticket price by 10 percent.

Lowering the average ticket price by 10 percent has a better effect on demand than awarding the passenger with a free ticket at each 25,000 miles as the saving of $500 due to the discounted ticket price will actually make the consumer buy more tickets. As seen in diagram below, the original line point A to C will be shifted at 25,000 miles to point A, C, D and F when a passenger is awarded with a free ticket. However, if the average ticket price is lowered by 10 percent, there will be a shift of budget to point A to H, where the indifference curve will be moving to a flatter position having the tangent move from point E down to point G. This allows the passenger to buy more tickets with the extra savings earned from the 10% discounted price of the ticket.

I CHOSE TO ANSWER 7A INSTEAD OF 7B.

7A. In the accompanying figure, a consumer is initially in equilibrium at point C. The consumer’s income is $300, and the budget line through point C is given by $300 = $50X + $100Y. When the consumer is given a $50 gift certificate that is good only at store X, she moves to a new equilibrium at point D. a. Determine the prices of goods X and Y.

With the Income equation I = PxQx + PyQy, price of good X = $50 and price of good Y = $100

b. How many units of product X could be purchased at point A?

As seen in graph below, zero unit is purchased at point A

c. How many units of product X could be purchased at point E? To determine the price of goods X, assume that $300 will only be used to buy goods X:

I = PxQx + PyQy
$300 =$50Qx + $100(0)
$300 =$50Qx + 0
6 = Qx  units of product X that could be purchased at point E is 6 units.

d. How many units of product X could be purchased at point B?

As the shift of demand curve is due to $50 gift certificate that is good only at store X and that the price of goods X = $50, the quantity purchased at point B will be 1 unit.

e. How many units of product X could be purchased at point F?

New income will become $350 having income increased by $50. I = PxQx + PyQy
$350 =$50Qx + $100(0)
$350 =$50Qx + 0
7 = Qx  units of product X that could be purchased at point E is 7 units.

f. Based on this consumer’s preferences, rank bundles A, B, C, and D in order from most preferred to least preferred.

Order of preference is based on the idea that more satisfaction is received to indifference curve located in the north-east IC: Most preferred: point D
2nd preferred: point B
3rd preferred: point C
Least preffered: point A

g. Is product X a normal or an inferior good?
Based on the graph below, it cannot be determined as $50 increase in income is limited to buying goods X only.

8. In February 2004, the Federal Communications Commission (FCC) effectively deregulated the broadband industry in a close 3–2 vote that changed the rules of the 1996 Telecommunications Act. Among other things, the decision eliminates a rule that required the Baby Bells–BellSouth, Qwest Communication International, SBC Communications, and Verizon Communications–to provide rivals access and discounted rates to current broadband facilities and other networks they may build in the future. Providers of digital subscriber lines (DSL) that use the local phone loop are particularly affected. Some argue that the agreement will likely raise many DSL providers’ costs and reduce competition. Providers of high-speed Internet services utilizing cable, satellite or wireless technologies will not be directly affected, since such providers are not bound by the same facilities-sharing requirements as firms using the local phone networks. In light of the recent FCC ruling, suppose the News Corp., which controls the United States’ largest satellite-to-TV broadcaster, is contemplating launching a Spaceway satellite that could provide high-speed Internet service. Prior to launching the Spaceway satellite, suppose that News Corp. used least squares to estimate the regression line of demand for satellite Internet services. The best-fitting results indicate that demand is Qsat d = 168 -.9Psat + 1.05 PDSL + 1.10 Pcable (in thousands), where Psat is the price of satellite Internet service, PDSL is the price of DSL Internet service, and Pcable is the price of high-speed cable Internet service. Suppose that after the FCC’s ruling the price of DSL, PDSL, is $25 per month and the monthly price of high-speed cable Internet, Pcable, is $30. Furthermore, News Corp. has identified that its monthly revenues need to be at least $14 million to cover its monthly costs. If News Corp. set its monthly subscription price for satellite Internet service at $60, would its revenue be sufficiently high to cover its cost?

Given:
Qsat d = 168 -.9Psat + 1.05 PDSL + 1.10 Pcable (in thousands), where: PDSL = $25 and Pcable = $30

Qsat d = 168 -.9Psat + 1.05 (25) + 1.10 (30)
= 227.25 – 0.9 Psat
Revenue (in thousands)= Q * P
= 227.25P – (0.9 Psat)2

If Psat = $60, Revenuesat = 227.25*(60) – 0.9 (60) 2 = 10,395 (in thousands) The revenue of $10,395,000 will not be able to cover its monthly cost ($10,395 < $14,000) Is it possible for News Corp. to cover its cost given the current demand function? Justify your answer.

If MR = 227.25 – 1.80P, to maximize revenue, marginal revenue must be equal to zero (MR = 0). MR = 0  227.25 – 1.80P = 0  P = $126.25
To find Qsat, assign P = $126.25 to formula Qsat,=227.25 – 0.9 Psat  Q = 113.625 Revenue = P*Q  $126.25 * 113.625 = $14,345.156(in thousands) With price of $126.25 and Q = 113.625, the News Corp can earn revenue of $14,345,156.25 which is higher than $14 million. PROBLEM SET #3

1. The following table summarizes the short-run production function for your firm. Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is $20 per unit. Complete the following table, and then answer the accompanying questions.