MGCR352 MARKETING MANAGEMENT 1

Transcription

1 MGCR352 MARKETING MANAGEMENT 1 QUANTITATIVE ANALYSIS NOTES 1. Market Share (a) Calculating Market Share (b) Estimating the Size of a Market (Step Down Analysis) 2. Types of Costs and Margins (a) Fixed and Variable Costs (b) Contribution and Profit Margins 3. Breakeven Analysis (a) In units and dollars (b) Using breakeven analysis strategically 4. Price Elasticity (a) For a single product (b) Cross price elasticity between two products. 5. Price Chains 1. Market Share (MS) Market share is the percent of the total market (expressed in units or dollars) that your brand or product controls. MS $ Your brand $ sales Total segment $ sales MS Your brand sales Total segment sales Not all brands in a segment are sold at the same price, therefore the answer to these two market share calculations may differ. Estimating Market Size - The Step Down Approach Suppose we want to know our market share of the price sensitive segment of liquid laundry detergent in Montreal. Suppose we know that our brand has $365,000 in sales and that the total Canadian market of all laundry detergent is $217,500,000. What information do we need to know to calculate our particular market share of just the liquid detergent segment just in Montreal? Mgcr352 quantitative analysis - 1 of 30

2 1. Size of the Quebec laundry detergent market in comparison to all of Canada 21% 2. Size of the Montreal laundry detergent market in comparison to all of Quebec 48% 3. Size of the Price Sensitive segment of consumers in Montreal 20% 4. Size of the Liquid (as opposed to Powder) Detergent sales in Montreal 45% Total Detergent Sales in Quebec: 0.21 $217,500,000 $,, Total Detergent Sales in Montreal: 0.48 $45,675,000 $,, Total Price Sensitive Detergent Segment Sales in Montreal: 0.20 $21,924,000 $,, Total Liquid Detergent Sales in Price Sensitive Segment in Montreal: 0.45 $4,384,800 $,, MS $ $ 365,000. % $1,973, Types of Costs and Margins 1. Fixed Costs (FC) do not fluctuate with changes in volume of production (i.e. advertising, public relations, fixed salaries, administration and overhead, rent, research and development ). 2. Variable Costs (VC) are directly associated with volume of production (i.e. labour, materials, transportation, promotion costs such as allowances, coupons, ). 3. Contribution Margin (CM) represents how much is left over after accounting for the variable costs to cover fixed expenses. Contribution Margin % tells you what % of each $ you earn goes towards covering fixed expenses. CM unit SP unit VC unit *SP stands for Selling Price CM unit as a % SP unit VC unit SP Unit 4. Profit Contribution (PC) represents how much is left over after accounting for all costs (fixed and variable). Note that: 100% = VC (% of Sales or Price) + CM (% of Sales or Price) In other words: Unit SP - Unit VC Per Unit Contribution (CM) - Per Unit Fixed Costs Per Unit Profit Margin (PC or PM) Mgcr352 quantitative analysis - 2 of 30

3 3. Breakeven (BE) Analysis BE Units Total FC SP unit VC unit BE $ Total FC SP unit VC unit SP unit Total FC BE $ VC unit 1 SP unit For example, consider a microbrewery that wants to enter the Quebec market. Total unit sales of micro beer in Quebec = 7,000,000 bottles per year. Per unit VC for this microbrewery is $0.85 per bottle. Strategy 1: Heavy advertising in order to try and sell at a higher per unit price. Advertising = $500,000 Price = $3.00 per bottle Strategy 2: Lower advertising, and therefore sell at a lower price per unit. Advertising = $200,000 Price = $2.25 per bottle Which strategy is best according to a breakeven analysis? Strategy 1: BE Units $500, ,558 units or 3.3% of the market $3.00 $0.85 Strategy 2: BE Units $, $. $., or % of the market The marketer would then determine how much of the market they can realistically capture and compare this to their breakeven analysis. Suppose it is determined that they can only capture 2% of the market. What price do they have to sell their beer for in order to make the $500,000 advertising strategy pay off? BE Units $500, ,000 $0.85 $. Mgcr352 quantitative analysis - 3 of 30

4 4. Price Elasticity (PE) Price Elasticity (PE) measures how responsive demand would be to a change in price. PE % change in Demand % change in SP Where % change New Old Old Going back to the microbrewery example, suppose:...at $2.25 per bottle, they ll sell 300,000 bottles....at $4.42 per bottle, they ll sell 140,000 bottles. % in Demand % in SP 300, , ,000 $2.25 $4.42 $4.42 PE %. % If absolute PE < 1, the product is said to be price inelastic. Here, a decrease in price yields a less than proportional increase in demand and an increase in price yields a less than proportional decrease in demand. Generally, lowering price a decrease in profits; raising price increase in profits. If absolute PE > 1, the product is said to be price elastic. Here, a decrease in price yields a greater than proportional increase in demand and an increase in price yields a greater than proportional decrease in demand. Generally, lowering price increase in profit; raising price decrease in profit. If absolute PE = 1, the product is said to be unit elastic. Here, an increase or decrease in price yields the same change in demand. 5. Cross Price Elasticity (CPE) Cross-Price Elasticity (CPE) examines the relationship between changing the price of one product and measuring the effect on the demand of a second product. With complementary products, raising the price of one will yield a decrease in demand in the other (e.g., hockey sticks and pucks; hamburgers and French fries, bread and cheese). Mgcr352 quantitative analysis - 4 of 30

5 With substitute products, raising the price in one product will lead to an increase in demand for the other (e.g., cassette and CD players, butter and margarine, tea and coffee). Suppose that butter is promoted and its price is dropped from $3.09 to $2.79. Moreover, suppose that this yields an increase in demand for bread from 4,000 loaves to 6,300 loaves. % in Butter Price % in Bread Demand $2.79 $3.09 $3.09 6,300 4,000 4,000.. CPE Price Chains 1 CM % on SP 2 Markup % on Cost SP unit VC unit SP unit SP unit VC unit VC unit : SP VC unit 100% CM % on SP % : SP VC unit Markup % on Cost VC unit Mgcr352 quantitative analysis - 5 of 30

6 Basic quantitative analysis in marketing Exercises Market Share (MS) 1. Last year Warner-Lambert sold 14 million superpacks of Trident. The average retail price per pack was $1.69. In 1996, the chewing gum market racked up $850 million in retail sales. (a) Calculate Warner-Lambert s share of the chewing gum market. (b) Warner-Lambert targets the frequent gum chewers with their superpack that contains 16 pieces of gum. Assuming frequent gum chewers make up 28% of the chewing gum market, calculate Trident s new market share. 2. Use the following information to answer questions a-e: Total coffee sales for 1996 = $800.5 million Maxwell House s 1996 coffee sales = $105 million Folgers 1996 coffee sales = $21 million (a) What is Maxwell s share of the market? (b) What is Folgers share of the market? Mgcr352 quantitative analysis - 6 of 30

7 Suppose there are two unique segments in the coffee market: percolated coffee drinkers and instant coffee drinkers. Percolated coffee drinkers make up 86.5% of the coffee market and instant coffee drinkers 13.5%. (c) Assuming Maxwell House targets percolated coffee drinkers, calculate the target market share. (d) Assume Folgers coffee is targeted at instant coffee drinkers, calculate the target market share. (e) Discuss the meaning of the figures you just calculated: who has stronger market share in terms of total market and segmented market? Contribution Margins (CM) 3. (a) What is the meaning of contribution margin? What is the difference between contribution margin expressed in terms of % sales vs. % selling price? Mgcr352 quantitative analysis - 7 of 30

8 (b) Can the terms contribution margin and profit margin be used interchangeably? Why or why not? (c) Fly-a-kite Canada carries a 35 item product line. Their newest addition was the Batman kite, which they sold at $26.75 (to distributors). Variable cost per kite is $8.09. Assuming they sold 110,500 kites in 1996, calculate contribution margin as a percentage of sales and selling price. (d) Refer to question c. Fly-a-kite hired 50 kite experts to build the Batman kites and paid them each a $40,000 salary for Since experts needed special tools to build these Batman kites, Fly-a-kite spent $70,000 on new machinery and equipment. Calculate the profit margin in dollars and as a percentage of sales. Mgcr352 quantitative analysis - 8 of 30

9 4. TrueWax Company sells their scented candles to wholesalers for $5.89 each. If variable costs amount to $2.83 per candle, what is the unit contribution margin in dollars and as a percentage of selling price? 5. Use the following information to calculate total contribution margin as dollars and as a percentage of total sales. Total candle sales for 1996 = $798,500 Total variable costs for 1996 = $383, Compare contribution margin as a percentage of selling price (Q4) and contribution margin as a percentage of total sales (Q5). Discuss the discrepancies or similarities. Mgcr352 quantitative analysis - 9 of 30

10 Breakeven (BE) Analysis 7. (a) Heinz sells their 400ml bottle of ketchup for $2.99 per bottle. Variable costs per unit is $1.85. Fixed production and distribution expenses amount to $10.6 million. Calculate break-even in units and required break-even dollar sales. (b) Assume the total Canadian market for ketchup is $375 million. Calculate Heinz s breakeven market share. 8. Jack s Key shop is going through a rough period in terms of business. For the past 2 years Jack s corner store has been experiencing a decrease in demand. For 1998, Jack would like to know how many keys he needs to sell to break-even. Use the following information to help Jack. Average selling price per key = $3.89 Cost per blank key = $1.75 Labour cost per key = 2% of selling price Rent and utilities = $4,500 Advertising = $2,500 Other miscellaneous expenses = $5,000 It is October 1 st, 1997 and Jack has sold 1,859 keys. What do you recommend Jack do? Mgcr352 quantitative analysis - 10 of 30

11 9. Use the following information from firm C to answer questions a-d. Average price for existing beer fridge = $480 Tentative price for new beer fridge with freezer = $595 Expenses incurred for new product: Raw material expenses = $ Labour expenses = $ Transport expenses = 4% of sales Variable promotional expenses = 6% of sales Rent for new plant = $96,000 Allocated overhead = $890,000 Advertising = $2,950,000 Other fixed expenses = $602,000 Competitive environment: General Electric dominates 30% of the market Kenmore owns 24% of the market Total refrigerator sales in Canada = $510,400,000 Segmentation: Beer fridge segment is 15% of refrigerator market 46% of beer fridge segment prefers beer fridges with freezers Other important information: The market for refrigerators is expected to remain stable in the next couple of years. (a) Calculate Firm C s break-even point for its new fridge with freezer in units and dollars. (b) Calculate Firm C s required break-even market share for its new fridge with freezer. Mgcr352 quantitative analysis - 11 of 30

12 (c) Is market share feasible? Why or why not? (d) Suppose that the average price of a beer fridge with freezer, in Firm C s target segment is $620, and also suppose that the largest market that Firm C can hope to achieve is 20% of segment sales. What is the lowest average price Firm C can charge for its beer fridge with freezer and still break-even? 10. General Motors plans to launch a new car January 1, This new vehicle will be powered by electric current. GM wants to minimize fixed costs, by choosing test markets rather than providing for the complete North American launch. Financial analysis shows required breakeven market share to 15% above projected. Given this information, how can GM reduce market share required to break-even? Mgcr352 quantitative analysis - 12 of 30

13 Price Chains 11. Solve the following price chains: (a) Manufacturer s Price $15.55 Manufacturer s VC $6.35 Manufacturer s $$ Margin Manufacturer s %% Margin Wholesaler s Price $22.21 Wholesaler s VC Wholesaler s $$ Margin Wholesaler s %% Margin Distributor s Price Distributor s COGS Distributor s $$ Margin Distributor s %% Margin 12% Retail Price Retail COGS Retail $$ Margin Retail %% Margin 25% Mgcr352 quantitative analysis - 13 of 30

14 (b) Manufacturer s Price $80.15 Manufacturer s VC $45.20 Manufacturer s $$ Margin Manufacturer s %% Margin Wholesaler s Price Wholesaler s VC Wholesaler s $$ Margin Wholesaler s %% Margin 12% Distributor s Price Distributor s COGS Distributor s $$ Margin Distributor s %% Margin 15% Retail Price Retail COGS Retail $$ Margin Retail %% Margin 20% Mgcr352 quantitative analysis - 14 of 30

15 (c) Manufacturer s Price Manufacturer s VC Manufacturer s $$ Margin $10.00 Manufacturer s %% Margin 50% Wholesaler s Price Wholesaler s VC Wholesaler s $$ Margin Wholesaler s %% Margin 9% Retail Price Retail COGS Retail $$ Margin Retail %% Margin 45% Mgcr352 quantitative analysis - 15 of 30

16 (d) Manufacturer s Price $ Manufacturer s VC $ Manufacturer s $$ Margin Manufacturer s %% Margin Wholesaler s Price Wholesaler s VC Wholesaler s $$ Margin Wholesaler s %% Margin Retail Price $ Retail COGS Retail $$ Margin Retail %% Margin 25% Mgcr352 quantitative analysis - 16 of 30

17 (e) Manufacturer s Price $85.00 Manufacturer s VC Manufacturer s $$ Margin $36.00 Manufacturer s %% Margin Wholesaler s Price $ Wholesaler s VC Wholesaler s $$ Margin Wholesaler s %% Margin Retail Price $ Retail COGS Retail $$ Margin Retail %% Margin Mgcr352 quantitative analysis - 17 of 30

18 12. Now try solving one that s inverted. If you can do this one, you re all set! Retail Price $ Retail COGS Retail $$ Margin Retail %% Margin Wholesaler s Price $ Wholesaler s COGS Wholesaler s $$ Margin Wholesaler s %% Margin Manufacturer s Price $ Manufacturer s VC Manufacturer s $$ Margin $ Manufacturer s %% Margin Price Elasticity (PE) 13. If the price elasticity of 1 liter of Gallo wine increases from $12.00 to $15.00, and demand for wine in Quebec decreased from 68,000,000 bottles of wine sold per year to 65,000,000 bottles per year. Calculate price elasticity of wine, and explain your results. Mgcr352 quantitative analysis - 18 of 30

19 14. Indicate if the following products are suitable for price promotion. Product Price Elasticity Libby s Beans 1.04 Picasso Painting 3.65 Clothing 4.75 Ancient Greek Vase 0.98 Cigarettes Multiple Choice: A. The price elasticity refers to a measure that shows the: (a) responsiveness of quantity demanded of a good to changes in its price. (b) variation in prices due to a change in demand. (c) size of price changes caused by a shift in demand. (d) degree of substitutability across commodities. B. If the price elasticity for product A is -2 and price increases by 2%, the quantity demanded: (a) decreases by 4% (b) increases by 1% (c) decreases by 2% (d) does not change (e) is indeterminable with the data provided C. If the percentage change in price is greater than the percentage change in quantity demanded, product B is: (a) elastic (b) inelastic (c) unit-elastic (d) none of the above Mgcr352 quantitative analysis - 19 of 30

20 D. If a 10% increase in the price of ski lift tickets causes a 5% decrease in demand, then ski tickets are: (a) elastic (b) inelastic (c) unit-elastic (d) none of the above 16. Just a couple more you ll thank me. Calculate price elasticity for the following: (a) Soft n Dry deodorant was featured in the drugstore circular. Regular price was $3.49 and the special promoted price was $2.29. Sales increased from 300 units per week, to 560 units per week. (b) The price of Eggo s increase by 30%. Demand fell from 15,000 units to 12,000 units. (c) Demand for CD players increased by 55% when price was reduced from $650 to $400. Cross Price Elasticity (CPE) 17. Just one little multiple choice question Which of the following pairs of goods is likely to have a cross-elasticity that is positive? (a) Hockey sticks and pucks (b) Cassettes and CD players (c) Hamburgers and French fries (d) Bread and cheese (e) Perfume and garden hoses Butter Bread Margarine Normal Price $3.09 $1.89 $1.99 Sale Price $2.79 $1.29 $1.19 Regular demand 800 4,000 1,000 Sale demand 1,200 7,000 1,600 Demand w/promo on butter N/A 6, Demand w/promo on bread 1,000 N/A 1,100 Demand w/promo on marg ,000 N/A Mgcr352 quantitative analysis - 20 of 30

21 Use the above table to answer questions Calculate cross-price elasticity between bread and butter when butter is promoted. 19. Calculate cross-price elasticity between butter and margarine when butter is promoted. 20. Calculate cross-price elasticity between bread and margarine when bread is promoted. Mgcr352 quantitative analysis - 21 of 30

22 BASIC QUANTITATIVE ANALYSIS SOLUTION SET 1. (a) (b),, $. $,,,, $. $,,. 2.78% 9.94% 2. (a) $105,000,000 $800,500, % (b) $21,000,000 $800,500, % (c). 865 $800,500,000 $692,430,000 $105,000, ,430, % d M $108,067,500 $21,000,000 $108,067, or 19.43% (e) While Firm A is probably larger, both firms have sound positions within their respective segments. 3. (a) Contribution margin (CM) tells you how much is left over after accounting for VC, to cover fixed costs and profit. CM % on SP SP VC /SP all per unit CM % on Sales Total Sales Total VC /Total Sales all per total sales CM unit SP VC (b) Absolutely NOT! A contribution margin, as stated before, is what is left over after having accounted for the VC to cover your FC (CM = SP VC). On the other hand, PM is what is left after having accounted for both VC and FC (PM = SP VC FC). CM SP VC all per unit or Total CM Total Sales Total VC PM SP VC FC all per unit or Total PM Total Sales Total VC Total FC (c) CM% Sales = ([$ $8.09]*110,500)/($26.75*110,500) = 69.76% CM% S.P. = ($ $8.09)/$26.75 = 69.76% Mgcr352 quantitative analysis - 22 of 30

23 (d) Salaries => 50*$40,000 = $2,000,000 Equipment => $70,000 Total FC $2,070,000 PM$ = ([$26.75 $8.09]*110,500) $2,070,000 = $-8,070 PM% = -$8,070/($26.75*110,500) = -0.2% *firm loses 0.2% on each unit sold 4. CM$ = $5.89 $2.83 = $3.06 CM% = ($5.89 $2.83)/$5.89 = 51.95% 5. TCM$ = 798, ,660 = $414,840 TCM% = $414,840/798,500 = 51.95% 6. same product line - assuming no VC changes during the year - difference TCM is CM unit * # of units sold 7. (a) CM$ = $2.99 $1.85 = $1.14 CM% = $1.14/$2.99 = 38.13% BE units = $10,600,00/$1.14 = 9,298,246 units BE $ = $10,600,000/ = $27,799,632 To check: BE units * SP per unit (b) BE MS = $27,799,632/$375,000,000 = 7.41% 8. SP = $3.89 Mgcr352 quantitative analysis - 23 of 30

24 VC = $ (0.02*$3.89) = $1.83 FC = $4,500 + $2,500 + $5,000 = $12,000 CM$ = $ $1.83 = $2.06 BE units = 12,000/2.06 = 5,826 units Since Jack is only 1/3 of the way there, and he only has 3 months left of the year it s obvious he should consider closing shop. 9. (a) 1. Calculate total VC Raw material = $ Labour = $ Trans (595*.04) = $ Promo (595*.06) = $ TVC = $ Calculate total FC Rent = $ 96,000 O/H = $890,000 Advertising = $2,950,000 Other FC = $602,000 TFC = $4,538, CM$ = $595 $ = $ CM% = /595 = 36.81% 4. BE units = $4,538,000/$ = 20,718 BE$ = $4,538,000/ = $12,328,171 Mgcr352 quantitative analysis - 24 of 30

25 (b) Total Beer Fridge market = $510,400,000*0.15 = $76, 560,000 Beer Fridge w/ freezer market = $76,560,000*0.46 = $35,217,600 New BE MS = $12,328,171/$35,217,600 = 35% (c) For: 35% is not impossible if you look at other market leaders, but you are launching a product (remember what that implies). Against (stronger argument): might be high because big guys own over 50% of the market. (d) BE new = 0.20*$35,217,600 = $7,043,520 Solve: $7,043,520 = $4,538,000/([SP $ $ SP SP]/SP) $7,043,520 = $4,538,000/([0.9SP ]/SP) $7,043,520(0.9 [$316.46/SP]) = $4,538,000 $6,339,168 (2,228,992,339.2/SP) = $4,538,000 $6,339,168 - $4,538,000 = $2,228,993,339.2/SP $1,801,168SP = $2,228,993,339.2 SP = $1, decrease FC (advertising, salaries, general and administrative expenses) increase SP decrease VC increase scope of launch (increase market size) target more than one segment Analyze BE MS = BE sales$/total Sales (market) BE units = FC/ CM$ (SP VC) BE $ = FC/([SP VC]/SP) Mgcr352 quantitative analysis - 25 of 30

26 11. Solve the following price chains: (a) Manufacturer s Price $15.55 Manufacturer s VC $6.35 Manufacturer s $$ Margin $9.20 Manufacturer s %% Margin 59% (9.2/15.55) Wholesaler s Price $22.21 Wholesaler s VC $15.55 Wholesaler s $$ Margin $6.66 Wholesaler s %% Margin 30% Distributor s Price $25.24 Distributor s COGS $22.21 Distributor s $$ Margin $3.03 Distributor s %% Margin 12% Retail Price $33.65 Retail COGS $25.24 Retail $$ Margin $8.41 Retail %% Margin 25% (b) Manufacturer s Price $80.15 Manufacturer s VC $45.20 Manufacturer s $$ Margin $34.95 Manufacturer s %% Margin 44% Wholesaler s Price $91.08 Wholesaler s VC $80.15 Wholesaler s $$ Margin $10.93 Wholesaler s %% Margin 12% Distributor s Price $ Distributor s COGS $91.08 Distributor s $$ Margin $16.07 Distributor s %% Margin 15% Retail Price $ Retail COGS $ Retail $$ Margin $26.79 Retail %% Margin 20% Mgcr352 quantitative analysis - 26 of 30

27 (c) Manufacturer s Price $20.00 Manufacturer s VC $10.00 Manufacturer s $$ Margin $10.00 Manufacturer s %% Margin 50% Wholesaler s Price $21.98 Wholesaler s VC $20.00 Wholesaler s $$ Margin $1.98 Wholesaler s %% Margin 9% Retail Price $39.96 Retail COGS $21.98 Retail $$ Margin $17.98 Retail %% Margin 45% (d) Manufacturer s Price $ Manufacturer s VC $ Manufacturer s $$ Margin $ Manufacturer s %% Margin 69% Wholesaler s Price $ Wholesaler s VC $ Wholesaler s $$ Margin $40.00 Wholesaler s %% Margin 10% Retail Price $ Retail COGS $ Retail $$ Margin $ Retail %% Margin 25% (e) Manufacturer s Price $85.00 Manufacturer s VC $49.00 (85-36) Manufacturer s $$ Margin $36.00 Manufacturer s %% Margin 42% Wholesaler s Price $ Wholesaler s VC $85.00 Wholesaler s $$ Margin $30.00 Wholesaler s %% Margin 26% Retail Price $ Retail COGS $ Retail $$ Margin $60.00 Retail %% Margin 34% Mgcr352 quantitative analysis - 27 of 30

28 12. Now try solving one that s inverted. If you can do this one, you re all set! Retail Price $ Retail COGS $ Retail $$ Margin $ Retail %% Margin 38% Wholesaler s Price $ Wholesaler s COGS $ Wholesaler s $$ Margin $90.00 Wholesaler s %% Margin 23% Manufacturer s Price $ Manufacturer s VC $ ( ) Manufacturer s $$ Margin $ Manufacturer s %% Margin 61% 13. % change D = (65M 68M)/68M = (-3M)/68M = -4.41% % change SP = ($15 $12)/$12 = 3/12 = 25% PE = (-0.041)/0.25 = < 1 Therefore, price inelastic for increase or decrease in price. 14. Libby s Beans Picasso Painting Clothing Ancient Greek vase Cigarettes YES (price decrease, demand increase) NO (price decrease, demand decrease) - YES (price decrease, demand increase) - NO (price decrease, demand decrease) - NO (inelastic product) Mgcr352 quantitative analysis - 28 of 30

29 15. A) a B) a PE = -2 = change in D%/ change in SP% = (-4%)/2% = -2% = 2 C) b Example: % change D/ % change SP = 2%/15% = < 1 Therefore, price is inelastic. D) b change %D/ change %SP = (-.05)/.1 = -0.5 = 0.5 < 1 Therefore, price is inelastic. 16. (a) % change D = ( )/300 = % change SP = ( )/3.49 = /(-0.34) = > 1 Therefore, price is elastic. (b) % change D = (12,000 15,000)/15,000 = -0.2 % change SP = +0.3 (-0.2)/+0.3 = < 1 Therefore, price is inelastic. (c) % change D = % change SP = ( )/650 = /(-0.38) = > 1 Therefore, price is elastic. 17. Answer: b Hockey sticks and pucks = complements Cassettes and CD players = substitutes Hamburgers and French fries = complements Bread and cheese = complements Perfume and garden hoses = unrelated Mgcr352 quantitative analysis - 29 of 30

30 18. Butter % change SP = ( )/3.09 = Bread % change D = (6,300 4,000)/4,000 = /(-0.10) = negative, therefore complements 19. Butter % change SP = ( )/3.09 = Margarine % change D = ( )/1000 = -0.5 (-0.5)/(-0.1) = 5 positive, therefore substitutes 20. % change SP = ( )/1.89 = % change D = ( )/1000 = /(-0.32) = negative below 1, therefore weak complements Mgcr352 quantitative analysis - 30 of 30