1. Chapter 4 Limiting factor analysis Limiting factor analysis Graphical linear programming Using simultaneous equations

2. Syllabus learning outcomes Identify limiting factors in a scarce resource situation and select an appropriate technique. Determine the optimal production plan where an organisation is restricted by a single limiting factor, including within the context of “make” or “buy” decisions. Formulate and solve a multiple scarce resource problem both graphically and using simultaneous equations as appropriate.

3. Syllabus learning outcomes Explain and calculate shadow prices (dual prices) and discuss their implications on decision-making and performance management. Calculate slack and explain the implications of the existence of slack for decision-making and performance management.

4. Chapter overview We have looked at limiting factor analysis in connection with throughput accounting in Chapter 2d and you will have encountered it in your earlier studies. When there is more than one resource constraint, the technique of linear programming can be used. A multiple scarce resource problem can be solved using a graphical method and simultaneous equations. We also look at the meaning and calculation of shadow prices and slack.

5. Summary Shadow prices Single limiting factors Limiting factor analysis Slack / Surplus Multiple limiting factors Linear programming Graphical Simultaneous equations

6. Tackling the exam Questions will require you to establish how many constraints there are and identify an appropriate technique to use You are likely to be required to calculate the return per unit of limiting factor and the optimum product mix Graphical linear programming is a popular exam topic – questions could require you to sketch a graph Calculation of slack and shadow prices followed by discussion is also likely

7. Limiting factor analysis 1 Is there just one constraint? Determine optimum production using contribution / limiting factor Determine optimum production using linear programming Yes No

8. Limiting factor analysis 2 Key terms Slack – maximum availability of a resource has not been used Surplus – more output has been made than the minimum requirement Key terms Slack – maximum availability of a resource has not been used Surplus – more output has been made than the minimum requirement

9. Limiting factor analysis 3 Slack Occurs when maximum availability of a resource is not used The resource is not binding at the optimal solution Slack is associated with ≤ constraints Surplus Occurs when more than a minimum requirement is used Surplus is associated with ≥ constraints eg a minimum production requirement

10. Limiting factor analysis 4 Shadow price It is the increase in contribution created by the availability of an extra unit of a limited resource at its original cost. It is the maximum premium an organisation should be willing to pay for an extra unit of a resource. It provides a measure of the sensitivity of the result. It is only valid for a small range before the constraint becomes non-binding or different resources become critical.

11. Limiting factor analysis 5 Example A company makes two products, standards and deluxe. Relevant data are as follows. StandardDeluxeAvailability per month Contribution per unit$15$20 Labour hours per unit 5 104,000 Kg of material per unit 10 54,250

12. Limiting factor analysis 6 Define variables Let x = number of standards produced each month Let y = number of deluxes produced each month Establish constraints Labour 5x + 10y ≤ 4,000 Material 10x + 5y ≤ 4,250 Non-negativity x ≥ 0, y ≥ 0 Construct objective function Contribution (C) = 15x + 20y

13. Limiting factor analysis 7 There are two methods you need to know about when finding the solution to a linear programming problem: Graphical method Using equations

14. Graphical linear programming 1 Formulate the model (a)Define variables (b)Formulate objective function (c)Formulate constraints Solve the Problem (d)Plot constraints on a graph (e)Identify feasible space (f)Plot slope of objective function and slide to optimal point (g)Calculate value of objective function

15. Graphical linear programming 2 Graph the constraints: Labour 5x + 10y = 4,000 If x = 0, y = 400 If y = 0, x = 800 Material 10x + 5y = 4,250 If x = 0, y = 850 If y = 0, x = 425

16. Graphical linear programming 3 Establish the feasible area/region This is the area where all inequalities are satisfied Area above x axis and y axis (x ≥ 0, y ≥ 0), below material constraint (≤) and below labour constraint (≤) Add an iso-contribution line Suppose C = $3,000 so that if C = 15x + 20y then if x = 0, y = 150 and if y = 0, x = 200 Then sliding your ruler across the page if necessary find the point furthest from the origin but still in the feasible area

17. Graphical linear programming 4

18. Question: Linear programming (a)Ferny Chewer Co manufactures tables and chairs. Details of each are: Tables Chairs Per unit: Selling price $100 $80 Variable costs $40 $30 Materials (kg) 20 6 Labour (hours) 1 2 Resources are in limited supply and the maximum available each month are: Materials 24,000 kg Labour 2,050 hours

19. Question: Linear programming cont’d Required (a)Formulate the linear programme to maximise contribution and solve graphically. (b)If one more hour of labour were to be become available, how much would Ferny Chewer Co be willing to pay for it (above the usual cost per hour)?

20. Answer: Linear programming cont’d Define variables Let t = number of tables produced per month Let c = number of chairs produced per month Maximise contribution 60t + 50c Subject to Materials 20t + 6c  24,000 Labour 1t + 2c  2,050 Non neg t, c,  0

21. Answer: Linear programming cont’d Materials 20t + 6c = 24,000 When t = 0c = 4,000 When c = 0 t = 1,200 Plot on a graph Labour 1t + 2c = 2,050 When t = 0c = 1,025 When c = 0 t = 2,050

22. Answer: Linear programming cont’d T C Materials Labour 1200 1025 2050 4000

23. Answer: Linear programming cont’d Determine optimal point. Objective functionZ = 60t + 50c Let Z = $30,000 When t = 0c = 600 When c = 0 t = 500

24. Answer: Linear programming cont’d T C Materials Labour 1200 1025 2050 4000 500 600

25. Answer: Linear programming cont’d Optimal point where materials and labour intersect: 20t + 6c=24,000(1) t + 2c=2,050(2) (2)  33t + 6c=6,150(3) (1) – (3)17t=17,850 t=1,050 Sub in (2) 1,050 + 2c=2,050 2c = 1,000 c = 500 Z = 60t + 50c = (60  1,050) + (50  500) = $88,000

26. Answer: Linear programming cont’d Premium payable per hour = Shadow price Shadow price = Lost contribution If one more hour of labour became available the labour constraint would become: t + 2c = 2,051

27. Answer: Linear programming cont’d The coordinates of the optimal point become: 20t + 6c=24,000(1) t + 2c=2,051(2) (2)  33t + 6c=6,153(3) (1) – (3)17t=17,847 t=1,049.8 Sub in (2) 1,049.8 + 2c=2,051 2c=1,001.2 c=500.6 Z= 60t + 50c = (60  1,049.8) + (50  500.6) = $88,018 This is an increase of $18 over the solution to (a) and is the shadow price of labour.

28. Using simultaneous equations 1 Instead of sliding out the iso-contribution line, simultaneous equations can be used to solve the problem.

29. Using simultaneous equations 2 Use simultaneous equations To find the x and y coordinates at the optimal solution, the intersection of the material and labour constraints (x = 300, y = 250) Using equations Graph constraints and establish feasible area Determine all possible intersection points of constraints and axes using simultaneous equations Calculate contribution at each intersection point to determine which is the optimal solution

30. Question: Optimal production Jam & Sponge has just changed its cake mix and is struggling to cope with increased demand for its cakes. Machine time available is 300 hours per week. Required (a)What is the optimal production plan? (b)What would happen if five extra machine hours were made available? (c)What is the shadow price of one machine hour? FairyButterflyPixie Information per batch:$$$ Sales price150120100 Variable cost1008070 Fixed cost20 Profit302010 Machine time per batch5hrs2hrs1hr Demand per week50

31. Answer: Optimal production (a) Production planFairyButterflyPixieTotal Batches50 Hours / batch521 Hours needed25010050400 Hours available300 Shortfall100 Sales price / batch150120100 Variable cost / batch1008070 Contribution/batch$50$40$30 Hours / batch521 Contribution/machine hour$10$20$30 Rank3rd2nd1st

32. Answer: Optimal production cont’d (b)With five extra hours you would make one more batch of Fairy cakes. (c)The extra contribution from one batch is $50 Contribution per hour = $10/ hour Shadow price of 1 hour is therefore $10. Production scheduleHrs /unit hrs available$ contribution 300/hour Produce maximum P 501(50)30 Produce maximum B 502(100)20 Produce F with (150/5) 305(150)10

33. Question: Production mix PH plc produces three different products and has adopted throughput accounting for its short-term decisions. The employees are guaranteed a weekly salary that is equivalent to their normal working hours paid at their normal hourly rate of $7 per hour. Costs and selling prices per batch are as follows: ProductAdam JamesLuke $/batch Selling price340 450270 Material K ($5/kg)15012090 Material L ($10/kg)709040 Material M ($15/kg)307545 Labour ($7/hour)212842 Factory costs absorbed208040

34. Question: Production mix cont’d PH plc is preparing its production plans and has estimated the maximum demand from its customers to be as follows: Batches Adam500 James400 Luke350 However, these demand maximums do not include a contract for the delivery of 50 batches of each product to an important customer. If this minimum contract is not satisfied then PH plc will have to pay a substantial financial penalty for non-delivery. Material L is in short supply and the maximum amount available is 7,000 kg. Required Prepare calculations to determine the production mix that will maximise the profit of PH plc.

35. Answer: Production mix Step 1Calculate return per unit of scarce resource and rank ingredients. ProductAdamJamesLuke Return per batch ($)9016595 Kgs of mat L per batch794 Return per kg ($)12.8618.3323.75 Ranking321

36. Answer: Production mix cont’d Step 2Determine the optimum product mix. * 1,000 ÷ 7 = 142.86 Product Demand Batches Ingredient L required kgs Material L available kg? Batches produced 7,000 Contract – Adam50 (x7)35050 – James50 (x9)45050 – Luke50(x4)20050 (1,000) 6,000 Luke350 (x4)1,400 (1,400)350 4,600 James400 (x9)3,600 (3,600)400 1,000 Adam500 (x7)3,500 (1,000)142* 0

37. Question: Production plan KG makes two products, the Purse and the Handbag. Each purse earns $5 contribution and each handbag earns $6. Inputs are as follows: PurseHandbag Leather1.5 m 2 2m 2 Skilled labour45 min 30 min There are six skilled labourers each working a 35 hour week and delivery contracts limit the amount of leather available to 600m 2 each week. KG has a quota ruling whereby it has to produce at least as many handbags as it does purses. Leather costs $8 per m 2, wages are paid at $4.20 per hour. Required Determine the optimal production plan for KG and calculation the contribution that can be achieved.

38. Answer: Production plan a)Define variables let P = weekly number of purses to make and sell let H = weekly number of handbags to make and sell b)Formulate objective function maximise contribution, where 5P+ 6Hcontribution =

39. Answer: Production plan cont’d c)Formulate constraints (linear relationships) subject to: Leather:  600 + 2H 1.5P Labour:  210 + 0.5H0.75P Non-negativity:  0 P, H Quota:  0 P – H

40. Answer: Production plan cont’d d) Plot a graph Leather: 1.5P + 2H  600 When P =0H = 300 H = 0P = 400 Labour: 0.75P + 0.5H  210 When P = 0H = 420 H = 0P = 280

41. Answer: Production plan cont’d P H Leather Labour Quota 400 300 280 420

42. Answer: Production plan cont’d P H 400 300 280 420 e) Identify feasible space Quota Leather Labour An area of the graph

43. Answer: Production plan cont’d f) Plot the slope of the objective function Objective function Z = 5P + 6H Let Z = $1,500 When P = 0H = 250 When H = 0 P = 300

44. Answer: Production plan cont’d P H Leather Labour Quota 400 300 280 420 300 250 Optimal point

45. Answer: Production plan cont’d 1.5P + 2H = 6001 0.75P + 0.5H = 2102 Multiply 2 by 2 1.5P + 1H = 4203 1 subtract 3 H = 180 Substitute in 1 1.5P + (2 x 180) = 600 1.5P +360 = 600 1.5P = 240 P = 160 Optimal point where constraints for leather and labour intersect

46. Answer: Production plan cont’d g) Calculate value of objective function Objective function Z = $5P + $6H P = 160, H = 180 Z = ($5  160) + ($6  180) = $1,880 per week

47. Question: Simultaneous equations Required Solve the problem in Question: Production plan, using simultaneous equations.

48. Answer: Simultaneous equations Steps to determine the feasible region are exactly as before Quota Leather Labour P 400 300 280 420 H C B A

49. Answer: Simultaneous equations cont’d Determine optimal solution This will not be at 0. At A there are 168 handbags & 168 purses. At B there are 180 handbags & 160 purses. At C there are 300 handbags & 0 purses. Point B will generate the most contribution. Simultaneous equations will determine the exact values.

50. Answer: Simultaneous equations cont’d Optimal point Point B is where labour and leather intersect. 1.5P + 2H = 600 (1) 0.75P + 0.5H = 210 (2) 1.5P + 1H = 420 (3) (multiply (2) by 2) H = 180 (1) – (3) 1.5P + 360 = 600 Substitute H into (1) 1.5P = 420 P = 160

51. Answer: Simultaneous equations cont’d Optimal production 160 purses 180 handbags Contribution C = 5P + 6H = (5 × 160) + (6 × 180) = $1,880 per week

52. Question: Slack and surplus (a)Calculate the value of any slack and surplus that exists in Question: Production plan. (b)Determine the shadow price for materials and labour and explain the meaning of this for KG.

53. Answer: Slack and surplus (a)Optimal production plan is for 160 purses and 180 handbags. Leather required is therefore (160 × 1.5) +(180 × 2) = 600 m 2. Available leather is 600 m 2. Therefore there is no slack leather. Labour required is (160 × 0.75) +(180 × 0.5) = 210 hours Available hours are (6 × 35) 210. Therefore there is no slack labour. The quota ruled that at least as many handbags as purses had to be produced. 20 additional handbags were made therefore the surplus is 20 handbags.

54. Answer: Slack and surplus cont’d (b)If one more unit of leather were available: 1.5P + 2H = 601 (leather) 0.75P + 0.5H = 210 (labour) So:1.5P + 1H = 420 H = 181 1.5P + 362 = 601 1.5P = 239 P = 159.33 Optimal production:159.33 purses 181 handbags Contribution= 5P + 6H = (5  159.33) + (6  181) = $1,882.65 per week Original contribution= $ 1,880.00 Shadow price$2.65 $ Shadow price2.65 Usual price8.00 Maximum price10.65

55. Answer: Slack and surplus cont $2.65 is the maximum extra KG would be prepared to pay to obtain one further m 2 of leather. The maximum price it would pay is therefore $10.65 for 1 m 2 If one more unit of labour were available: 1.5P + 2H = 600(leather) 0.75P + 0.5H = 211 (labour) So:1.5P + 1H = 422 H = 178 1.5P + 356 = 600 1.5P = 244 P = 162.67

56. Answer: Slack and surplus cont Optimal production:178 handbags 162.67 purses Contribution = 5P + 6H = (5  162.67) + (6  178) = $1,881.35 per week Original contribution$ 1,880.00 Shadow price$1.35 $1.35 is the maximum extra KG would be prepared to pay to obtain one further hour of labour. The maximum price it would pay is therefore $5.55. $ Shadow price1.35 Usual price4.20 Maximum price5.55

57. Question: Specimen exam Highfly Co manufactures two products, X and Y, and any quantities produced can be sold for $60 per unit and $25 per unit respectively. Variable costs per unit of the two products are as follows: Product XProduct Y $$ Materials (at $5 per kg)155 Labour (at $6 per hour)243 Other variable costs65 Total4513

58. Question: Specimen exam cont’d Next month, only 4,200kg of material and 3,000 labour hours will be available. The company aims to maximise its profits each month. The company wants to use the linear programming model to establish an optimum production plan. The model considers ‘x’ to be number of units of product X and ‘y’ to be the number of units of product Y. Which of the following objective functions and constraint statements (relating to material and labour respectively) is correct?

59. Question: Specimen exam cont’d Objective functionMaterial constraintLabour constraint A60x + 25y3x + y ≤ 4,200 4x + 0.5y ≤ 3,000 B15x + 12y3x + y ≥ 4,200 4x + 0.5y ≥ 3,000 C15x + 12y3x + y ≤ 4,200 4x + 0.5y ≤ 3,000 D60x + 25y3x + y ≥ 4,200 4x + 0.5y ≥ 3,000

60. Answer: Specimen exam C15x + 12y 3x + y ≤ 4,200 4x + 0.5y ≤ 3,000 Contribution for X = $15 ($60 – $45) Contribution for Y = $12 ($25 – $13) Objective function is to maximise: 15x + 12y Constraints: Material = 3x + y  4,200 (as X uses 3 kg of material (15/5), Y uses 1 kg (5/5)) Labour = 4x + 0.5y  3,000 (as X uses 4 labour hrs (24/6), Y uses 0.5 hrs (3/6))

61. Question: Specimen exam A business makes two components which it uses to produce one of its products. Details are: Component AComponent B Per unit information $$ Buy in price1417 Material25 Labour46 Variable overheads67 General fixed overheads 43 Total absorption cost 1621

62. Question: Specimen exam cont’d The business wishes to maximise contribution and is considering whether to continue making the components internally or buy in from outside. Which components should the company buy in from outside in order to maximise its contribution? A A onlyCBoth A and B BB onlyDNeither A nor B

63. Answer: Specimen exam B B only For a make-or-buy decision, we compare the marginal cost (relevant cost) of in-house production with the cost of buying in the item. Profit is maximised by selecting the lower cost. Component A: Relevant cost = $(2 + 6 + 4) = $12. Buy in cost = $14. Therefore produce in-house. Component B: Relevant cost = $(5 + 6 + 7) = $18. Buy in cost = $17. Therefore buy in from an external supplier.

64. Summary 1Limiting factor analysis  Plans of the business are built around the limiting factor.  Slack occurs when not all of a resource has been used.  Surplus occurs when additional output has been made.  A shadow price is the additional contribution generated from one more unit of limiting factor.

65. Summary 2Graphical linear programming  Multiple limiting factor problems are solved via linear programming. First formulate the model. Then solve the problem using graphs.

66. Summary 3 Using simultaneous equations  If a graph does not have to be drawn, simultaneous equations can be used. Equations need to be prepared for each possible optimal point.

67. Chapter 5 Pricing decisions Pricing policy and the market Demand and price elasticity Profit maximisation Pricing strategies

68. Syllabus learning outcomes Explain the factors that influence the pricing of a product or service. Explain the price elasticity of demand. Derive and manipulate a straight line demand equation. Derive an equation for the total cost function (including volume-based discounts).

69. Syllabus learning outcomes Calculate the optimum selling price and quantity for an organisation, equating marginal cost and marginal revenue. Evaluate a decision to increase production and sales levels, considering incremental costs, incremental revenues and other factors. Determine prices and output levels for profit maximisation using the demand based approach to pricing (both tabular and algebraic methods).

70. Syllabus learning outcomes Explain different pricing strategies. ─ All forms of cost-plus, skimming, penetration, complementary product, product-line, volume discounting, discrimination, relevant cost Calculate a price from a given strategy using cost-plus and relevant costing.

71. Chapter overview In this chapter we will begin by looking at the factors which influence pricing policy. Perhaps the most important of these is the level of demand for an organisation's product and how that demand changes as the price of the product changes (its elasticity of demand). We will then turn our attention to the profit-maximising price/output level and a range of different price strategies.

72. Total cost function Y = a + bx Pricing decisions Summary Demand Price elasticityDemand function P = a – bQ Optimal pricing MR = MC Pricing strategies Cost plus ─ Full cost ─ Marginal cost ─ Relevant cost ─ Standard cost Market penetration Market skimming Premium pricing Price discrimination Product bundling Psychological pricing Product line pricing Complementary products Loss leaders Controlled pricing Volume discounting

73. Tackling the exam Longer pricing decisions are likely to be examined through a mix of calculations and discussion. Calculations involving cost-plus pricing and relevant costing link with topics covered in Chapter 6.

74. Pricing policy and the market 1 Demand Most important factor based on economic analysis of demand Market in which organisation operates: Perfect competition – many buyers and sellers, one product Monopoly – one seller who dominates many buyers Monopolistic competition – a large number of suppliers offer similar (not identical) products Oligopoly – relatively few competitive companies dominate the market

75. Pricing policy and the market 2 Price sensitivity Varies amongst purchasers. If cost can be passed on – not price sensitive. Price perception How customers react to prices. If product price increases, do people buy more before further rises? Compatibility with other products Eg operating systems on computers. User wants wide range of software available.

76. Pricing policy and the market 3 Competitors Prices may move in unison (eg petrol). Alternatively, price changes may start price war. Competition from substitute products Eg train prices increase, competition from coach or air travel Suppliers Organisation’s product price increases, suppliers may seek price rise in supplies

77. Pricing policy and the market 4 Inflation Price changes to reflect increase in price of supplies. Quality Customers tend to judge quality by price. Incomes When household incomes rising, price not so important. When falling, important. Ethics Exploit short-term shortages through higher prices?

78. Pricing policy and the market 5 Demand is the most important factor influencing the price of a product. Demand increases as prices are lowered.

79. Demand and price elasticity 1 Price elasticity of demand (η) A measure of the extent of change in market demand for a good, in response to a change in its price = change in quantity demanded as a % of demand ÷ change in price as a % of price

80. Demand and price elasticity 2 Response of demand to changes in price: PED = % change in Q % change in P PED = % change in Q % change in P If PED >1 = elastic demand If PED <1 = inelastic demand

81. Demand and price elasticity 3 P = a – bQ P = selling price Q = quantity demanded at that price a = price at which demand would be nil b = change in price/change in quantity a is calculated as: a = $(current price) +

82. Demand and price elasticity 4 Downward sloping relationship between price and quantity demanded If using equations need to assume straight line in exam questions P Q P = a + b Q Change in P Change in Q (ie gradient) always -ve Price when demand = 0 a b

83. Demand and price elasticity 5 %Δ Q (Δ means change) %Δ P PED >1 = elastic demand (Small change in price leads to large change in quantity demanded.) PED <1 = inelastic (Large changes in price do not lead to large changes in demand.)

84. Demand and price elasticity 6 Inelastic demand η < 1 Steep demand curve Demand falls by a smaller % than % rise in price Pricing decision: increase prices

85. Demand and price elasticity 7 Elastic demand η > 1 Shallow demand curve Demand falls by a larger % than % rise in price Pricing decision: decide whether change in cost will be less than change in revenue

86. Demand and price elasticity 8 Variables which influence demand The price of the good The price of other goods The size and distribution of household incomes Tastes and fashion Expectations Obsolescence

87. Demand and price elasticity 9 Demand and the individual firm Influenced by: Product life cycle Quality Marketing ─ Price ─ Product ─ Place ─ Promotion

88. Question: Demand function When the price of a product is $48 demand is 70,000 units each week. When the price is $78, only 40,000 units are demanded each week. Required What is the demand function?

89. Answer: Demand function b =Δprice/ΔQuantity = – $30/ + 30,000 = –0.001 a = $48 + ( $30) ∴ a = $118 P = 118 – 0.001Q

90. Question: Demand function 2 Required Assuming units demanded in Question: Demand function to be purely price dependent, what should the selling price be to ensure maximum demand of 54,500 units?

91. Answer: Demand function 2 P = 118 – (0.001  54,500) P = $63.50

92. Question: Ticket price A football club charges $12 per ticket for home games. Average attendance at these regular games is 16,000. When prices were increased by $1 per ticket, attendance fell by 2,500. Required Assuming attendance to be purely price dependent, what should be the ticket price to ensure a full house with capacity being 25,000?

93. Answer: Ticket price P = a – bQ b = b = $1 / 2,500 b = 0.0004

94. Answer: Ticket price cont’d P = a – bQ a = 12 + (16,000 / 2,500) a = 18.40

95. Answer: Ticket price cont’d To sell 25,000 tickets: P = 18.40 – (0.0004 × 25,000) P = 18.40 – 10 P = $8.40 per ticket

96. Profit maximisation 1 Determining the profit-maximising selling price/output level MR = additional revenue generated by increasing sales by 1 unit.

97. Profit maximisation 2 The total cost function To decide on profit maximising price and sales quantity, we need to consider costs as well as revenue. Cost behaviour can be modelled using equations and linear regression analysis. A volume-based discount is a discount given for buying in bulk. This reduces the variable cost per unit and therefore the slope of the cost function is less steep.

98. Profit maximisation 3 Method 1: using equations Profits are maximised where MC = MR Example MC = 320 − 0.2x MR = 1,920 − 16.2x ∴ Profits are maximised when: 320 – 0.2x = 1,920 − 16.2x ie when x = 100

99. Profit maximisation 4 You could also be provided with/asked to determine the demand curve in order to calculate the price at this profit-maximising output level. The marginal revenue equation MR = a – 2bQ Q is the quantity demanded a is the price at which demand = 0 b is change in price/change in quantity

100. Profit maximisation 5 Method 2: visual inspection of tabulated data Work out the demand curve and hence the price and total revenue (PQ) at various levels of demand. Calculate total cost and hence marginal cost at each level of demand. Calculate profit at each level of demand – determining the price and level of demand that maximises profit.

101. Profit maximisation 6 Gradient of the total revenue line is called the marginal revenue (MR). The marginal revenue line will be: MR = a – 2bQ Gradient of total cost line is called the Marginal cost (MC) Profits are maximised when the gradients are equal ie where Marginal revenue = Marginal cost

102. Question: Profit maximisation A firm charges $12 per unit for its product. At this price it sells 16,000 units. Research has shown that when prices were changed by $1 per unit sales changed by 2,500 units. The product has a constant variable cost per unit of $5. The demand function is given by P = a – bQ. The marginal revenue will be MR = a – 2bQ Required (a) Determine the demand function. (b) Determine the output level to maximise profit. (c) Determine the price to be charged to maximise profit.

103. Answer: Profit maximisation (a)P = a – bQ b = = 0.0004 12 = a – (0.0004  16,000) a = 18.4 P = 18.4 – 0.0004Q (b)MR = a – 2bQ MC = MR 5 = 18.4 – 0.0008Q Therefore, Q = 16,750 units

104. Answer: Profit maximisation cont’d (c) P= 18.4 – (0.0004  16,750) = $11.70 per unit

105. Question: Profit maximisation 2 Required Determine the output level and selling price that will maximise profit. OutputTotal CostMC Selling Price Total RevenueMRProfit (Units)$$$$$$ 10 5.00 20254.50 30454.00 40703.50 501003.00 601352.50

106. Answer: Profit maximisation 2 Output level of 30 units. Selling price of $4 per unit. OutputTotal costMC Selling price Total revenueMRProfit (Units)$$$$$$ 10 5.0050 40 2025154.50904065 3045204.001203075 4070253.501402070 50100303.001501050 60135352.50150015

107. Pricing strategies 1 Pricing strategies Penetration Complementary product Complementary product Bundling Discrimination Psychological Product line Loss leaders Controlled Volume discounts Volume discounts Premium Skimming Cost plus

108. Price strategies 2 In practice, cost is one of the most important influences on price. Full cost-plus pricing Determine the sales price by calculating the full cost of the product and adding a percentage mark-up for profit.

109. Price strategies 3 Example Variable cost of production = $4 per unit Fixed cost of production = $3 per unit Price is to be 40% higher than full cost Full cost per unit = $(4 + 3) = $7 Price = $7 × 140% / 100 = $9.80

110. Price strategies 4 Advantages of full cost-plus pricing Simple, cheap method Ensures company covers fixed costs Disadvantages of full cost-plus pricing Doesn’t recognise profit-maximising combination of price and demand Budgeted output needs to be established Suitable basis for overhead absorption needed

111. Price strategies 5 Marginal cost-plus pricing Determine the sales price by adding a profit margin onto either marginal cost of production or marginal cost of sale.

112. Price strategies 6 Example Direct materials = $15 Direct labour = $3 Variable overhead = $7 Marginal cost = $25 Price = $40 Profit = $40 – $(15 + 3 + 7) = $15 Profit margin = $15 / $25 × 100% = 60%

113. Price strategies 7 Advantages of marginal cost-plus pricing Simple and easy method Mark-up percentage can be varied Draws management attention to contribution Disadvantages of marginal cost-plus pricing Does not ensure that attention paid to demand conditions, competitors’ prices and profit maximisation Ignores fixed overheads – so must make sure sales price high enough to make profit

114. Pricing strategies 8 Cost plus strategies Cost plus:Ignores demand and competitors. Not profit maximising. Easily calculated. – Full / AbsorptionMay result in too high a price. – MarginalMay not be enough to cover fixed costs. – Relevant costAppropriate for one-offs or when have spare capacity. – Standard costStandards may be out of date. Encourages cost control.

115. Pricing strategies 9 New product pricing strategies Market penetrationLow price when product is first launched to obtain volume. Market skimmingHigh price when product is first launched. Try to recover development costs quickly.

116. Price strategies 10 Other pricing strategies Complementary product pricing – eg cheap electric toothbrush and expensive replacement toothbrush heads. One good sold relatively cheaply, stimulates demand for the other good it is used with. Relevant cost pricing – for special orders determine a minimum price using relevant cost approach Price discrimination - charging different prices for the same product for different groups of buyers. Discrimination may be by: Age, Location, Time.

117. Pricing strategies 11 Other strategies Product line pricingGroup of products interrelated. Prices reflect cost proportions or demand relationships. Assess profitability of product range rather than individual products within it. Loss leadersOne item sold at a loss, encourage sales of additional products in the range. Controlled pricingIf only one supplier they can set high prices. Volume discountingReduction in price for large purchases. Increase volumes without permanently reducing prices.

118. Pricing strategies 12 Other strategies Premium pricingImply product is different in some way, typically quality, enabling high price to be charged. Product bundlingA group of products sold together at a lower price than if bought individually. Psychological pricingSetting prices at $9.99 instead of $10.

119. Starbucks: Pricing in China It will come as no surprise that some Chinese believe Starbucks coffee is a bit too expensive. After all, we do pay a lot for a cup of water and milk. But are Starbucks’ prices bordering on criminal? Chinese state media seems to think so. In a series of attacks, the press has accused Starbucks of overcharging Chinese with “outrageous” prices compared to those paid by consumers in the US and elsewhere. The coffee-shop chain, however, is only the latest victim of an apparent campaign aimed at forcing down the prices of foreign goods in China. The government is investigating the price tags on foreign automobiles, while in August several foreign companies were fined for supposedly selling their milk powder at unfairly high prices. Nestle and Danone pledged to slash their prices amid the enquiry. http://business.time.com/2013/10/24/how-a-starbucks-latte-shows-china-doesnt-understand-capitalism/

120. Formula summary 1 Formula given in exam Demand function: P = a – bQ Where: P = selling price Q = quantity demanded at that price a = price at which demand would be nil b = The marginal revenue will be MR = a – 2bQ

121. Formula summary 2 Formula to learn Learn that a = $(Current price) + Price elasticity of demand (PED) = Profit is maximised where marginal revenue = marginal cost.

122. Question: Specimen exam A company has entered two different new markets. In market A, it is initially charging low prices so as to gain Rapid market share while demand is relatively elastic. In market B, it is initially charging high prices so as to earn maximum profits while demand is relatively inelastic. Which price strategy is the company using in each market? A Penetration pricing in market A and price skimming in market B BPrice discrimination in market A and penetration pricing in market B CPrice skimming in market A and penetration pricing in market B DPrice skimming in market A and price discrimination in market B

123. Answer: Specimen exam A Penetration pricing in market A and price skimming in market B Charging low prices initially to gain a large market share is market penetration pricing. Charging high prices in order to maximise unit profits is market skimming. Market penetration pricing is most effective when demand for the product is elastic (sensitive to price) and market skimming can maximise profitability when demand is inelastic (fairly insensitive to price).

124. Summary 1 Pricing policy and the market  Demand – most important factor based on economic analysis of price and demand  Market in which organisation operates: ─ Perfect competition – many buyers and sellers, one product ─ Monopoly – one seller who dominates many buyers ─ Monopolistic competition – a large number of suppliers offer similar (not identical) products ─ Oligopoly – relatively few competitive companies dominate the market

125. Summary 2Demand and price elasticity  PED measures the responsiveness of demand to a change in price. PED >1 = elastic demand. PED <1 = inelastic demand.  Price can be determined using the demand function: P = a – bQ

126. Summary 3 Profit maximisation  The output level to maximise profit is found when MR = MC  The output level to maximise revenue is where MR = 0  Prices at these output levels can then be determined from the demand function.

127. Summary 4Pricing strategies  There are several strategies that can be applied to a product.  These strategies may be changed depending upon the stage in the product life cycle.