AP4002 Problem Set 5

**Report on two companies and their related histories within the same line of business.Pick two competing companies, one of which is successful in their line of business and one who hasn�tbeen successful in recent years. Identify the role technology played in both companies. Your comparisonmust thoroughly examine the entire role that technology has played. This should address the followingpoints for both companies:�What part of the business do you consider to be the primary technology? (for example in a computercompany it may really be the software bundled with the computer that provides the competitive edge or inthe pizza business it may really be a novel method of delivery which is the distinguishing innovation thatestablishes a competitive edge).�What type of strategy did each company employ? Did they take an offensive role or defensive role?How did their strategy affect the outcome of their success? Was there an impact on the entire industry asa whole?�Report on whether each company performed internal innovation and if so, how was this accomplished?If they didn�t use internal innovation � describe their methodology. What was the management�s rolein fostering the incorporation of the innovation?Finally, you are expected to provide an analysis of both the strategies, recommendations and aconclusion.**

Question 1

For a firm operating with the following costs and revenues:p=20, VC=18q, FC=1000;

calculations are as follows:

(a) The contribution per unit

Contribution margin per unit = $20 – $18 = $2

Contribution margin ratio = (Contribution margin)/Sales

= $2/$20 = 0.1

(b) The quantity required before the firm breaks even

Let X = the number of units sold to break even

Sales revenue – Costs = Income

(Price × Quantity) – Variable costs – Fixed costs = Income

$20X – $2X – $1,000 = $0

$2X – $1,000 = 0

X = 500 units

AP4002 Problem Set 5 3

(c) What should be done by the firm considering that the maximum quantity they can sell is

just 400 units?

The company should determine its desired revenue necessary to earn pretax income of a certain

preset percentage of revenue. This helps to ensure that the costs are adjusted. For example, let X

= the number of units sold to generate desired revenue necessary to earn pretax income of 20%

of revenue at 400 units production level.

(d) Calculate profits for each of the following quantities:

(i) q=600

Profit = sales revenue – total costs (fixed costs + variable costs)

Profit = ($20 x 600) – ($1000 + $18×600)

Profit = ($12,000 – ($1000+$10,800)

Profit = $12,000-$11,800 = $200

(ii) q=700

Profit = sales revenue – total costs (fixed costs + variable costs)

Profit = ($20 x 700) – ($1000 + $18×700)

Profit = ($14,000 – ($1000+$12,600)

Profit = $14,000-$13,600 = $400

(iii) q=800

Profit = sales revenue – total costs (fixed costs + variable costs)

Profit = ($20 x 800) – ($1000 + $18×800)

Profit = ($16,000 – ($1000+$14,400)

Profit = $16,000-$15,400 = $600

AP4002 Problem Set 5 4

(e) Is it reasonable to assume that the firm can sell any quantity at the given price?

Yes. The company can sell any quantity at the given price mainly because an increase in the

produced quantity is directly proportional to the costs of production and then profits which

means the production can be effectively sustained.

Question 2

Calculate the optimum quantity and price, along with maximum possible profits for the firm

described below:

q d = 10000 – 25p

FC = 50000

VC = 200q

Marginal cost (MC) = 100 + 2Q

Total cost (TC) = FC + VC

TC = 50,000 + 200Q

To obtain optimum quantity and price MC is equated to TC to get:

100 + 2Q = 50,000 + 200Q

-198Q = 49,900

Q = 252 (the negative sign is ignored)

To get the optimal price quantity demanded is equated to TC, since the optimal quantity is

already known as follows:

q d = 10000 – 25p

TC = 50,000 + 200Q

10,000 – 25p = 50,000 + 200Q

Q = 252 units

10,000 – 25p = 50,000 + 200 x 252

AP4002 Problem Set 5 5

10,000 – 25p = 100,400

-25P = 100,400 – 10,000

-25P = 90,400

P = $3616 (ignore the negative sign)

Maximum profit for the company obtained from:

Maximum profit = Total revenue (TR) – TC

TR = Price (P) x Quantity (Q)

TR = $3616 x 252 = $911,232

TC = $100,400

Maximum profit = $911,232 – $100,400 = $810,832

Question 3

(a) Calculate equilibrium price and quantity for the following market model (price is in

pence here):

q d = 2500 – 0.5p

q s = -200 + 4p

At optimal price and quantity the demand is equal to supply

Thus, the two equations are substituted to get the price (p)

2500-0.5p =-200 + 4p

2500+200 = 0.5p+4p

2700 =4.5p

P = $600

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

AP4002 Problem Set 5 6

Optimal quantity demanded = 2500 – 0.5 x 600 = 2200 units

Optimal quantity supplied = -200 + 4 x 600 = 2200 units

(b) Now include a 10 pence tax per unit (remember to modify the supply equation for this).

Calculate the new equilibrium price and quantity and comment on the effect on price

charged – who absorbs the majority of the tax? Why?

Tax increases production costs and the supply equation Is modified as follows:

q s = -200 + 4p + 10

At equilibrium price and quantity the demand is equal to supply

Thus, the two equations are substituted to get the price (p)

2500-0.5p =-200 + 4p + 10

2500+200 -10 = 0.5p+4p

2690 =4.5p

P ~ $598

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

Optimal quantity demanded = 2500 – 0.5 x 598 = 2201 units

Optimal quantity supplied = -200 + 4 x 598 +10 = 2201 units

The tax decreases the price charged and the increased charge is absorbed by the manufacturer

because a decrease in the market price without effect of tax.

Question 4

(a) Calculate equilibrium price and quantity for the following market model (price is in

pence here):

q d = 2500-20p

q s = -200+4p

AP4002 Problem Set 5 7

At optimal price and quantity the demand is equal to supply

Thus, the two equations are substituted to get the price (p)

2500-20p = -200 + 4p

2500+200 = 20p+4p

2700 =24p

P = $112.5

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

Optimal quantity demanded = 2500 – 20 x 112.5 = 250 units

Optimal quantity supplied = -200 + 4 x 112.5 = 250 units

(b) Now include a 10 pence tax per unit (remember to modify the supply equation for this).

Calculate the new equilibrium price and quantity and comment on the effect on price

charged – who absorbs the majority of the tax? Why?

Tax increases production costs and the supply equation Is modified as follows:

q s = -200 + 4p + 10

At equilibrium price and quantity the demand is equal to supply

Thus, the two equations are substituted to get the price (p)

2500-20p =-200 + 4p + 10

2500+200 -10 = 20p+4p

2690 =24p

P ~ $112.5

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

Optimal quantity supplied = -200 + 4 x 112.5 +10 = 260 units

AP4002 Problem Set 5 8

The tax decreases the price charged and the increased charge is absorbed by the manufacturer

because a decrease in the market price without effect of tax.

Question 5

(a) Calculate equilibrium price and quantity for the following market model (price is in

pence here):

q d = 23000 – 50p

q s = -1000 + 10p

At optimal price and quantity the demand is equal to supply

Thus, the two equations are substituted to get the price (p)

23000-50p = -1000 + 10p

23000+1000 = 50p+10p

24000 =60p

Equilibrium price = $400

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

Optimal quantity demanded = 23000 – 50 x 400 = 3000 units

Optimal quantity supplied = -1000 + 10 x 400 = 3000 units

(b) Now calculate the new equilibrium assuming 40 pence per unit subsidy is applied.

Comment on your result.

Subsidy reduces production costs and the supply equation is modified as follows:

q s = -1000 + 10p – 40

At equilibrium price and quantity the demand is equal to supply

AP4002 Problem Set 5 9

Thus, the two equations are substituted to get the price (p)

23000-50p = -1000 + 10p – 40

23000+1000 +40 = 50p+10p

24040 =60p

P ~ $401 (rounded)

Substituting p for the demand quantity and supplied quantity we can get the optimal quantities:

Optimal quantity demanded = 23000 – 50 x 400 = 2960 units (rounded)

Optimal quantity supplied = -1000 + 10 x 401 – 40 = 2960 units

The tax decreases the price charged and the increased charge is absorbed by the manufacturer

because a decrease in the market price without effect of tax.

Question 6

Calculate the elasticity of demand (Pe d ) for:

Q d = 3000-10p at:

(i) p=100

Q d = 3000-10p

Q d = 3000-10 x 100

Q d = 3000-1000 = 2000

(ii) p=150

Q d = 3000-10p

Q d = 3000-10 x 150

AP4002 Problem Set 5 10

Q d = 3000-1500 = 1500

(iii) p=200

Q d = 3000-10p

Q d = 3000-10 x 200

Q d = 3000-2000 = 1000

Question 7

Calculate the elasticity of supply (Pe s ) for:

Q s = -1000+12p at:

(iv) p=100

Q s = -1000+12p

Q s = -1000+12 x 100

Q s = -1000+1200 = 200

(v) p=150

Q s = -1000+12p

Q s = -1000+12 x 150

Q s = -1000+1800 = 800

(vi) p=200

Q s = -1000+12p

Q s = -1000+12 x 200

AP4002 Problem Set 5 11

Q s = -1000+2400 = 1400

AP4002 Problem Set 5 12

References

Atkinson, A., Kaplan, R. S., Matsumura, E. M. & Young, S. M. (2011). Management

Accounting: Information for Decision Making and Strategy Execution, (6 th ed.). New

York, NY: Prentice-Hall.