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628 Microsoft Excel 2010: Data Analysis and Business Modeling For prices near the current price, however, the linear demand curve is usually a good approximation of the product’s true demand curve. As a second example, let’s again assume that a product is currently selling for $100 and demand equals 500 units. The product’s price elasticity for demand is 2. Now let’s t a power demand curve to this information. See the le Powert.xlsx, shown in Figure 79-2. FIGURE 79-2 Power demand curve. In cell E3, I enter a trial value for a. Then, in cell D5, I enter the current price of $100. Because elasticity of demand equals 2, we know that the demand curve has the form q ap 2 , where a is unknown. In cell E5, I enter the demand for a price of $100, corresponding to the value of a in cell E3, with the formula a*D5^-2. Now I can use the Goal Seek command (for details, see Chapter 18, “The Goal Seek Command”) to determine the value of a that makes the de- mand for price $100 equal to 500 units. I simply set cell E5 to the value 500 by changing cell E3. I nd that a value for a of 5 million yields a demand of 500 at a price of $100. Thus, the demand curve (graphed in Figure 79-2) is given by q 5,000,000p 2 . For any price, the price elasticity of demand on this demand curve equals 2. What does a demand curve tell us about a customer’s willingness to pay for our product? Let’s suppose you are trying to sell a software program to a Fortune 500 company. Let q equal the number of copies of the program the company demands, and let p equal the price charged for the software. Suppose you have estimated that the demand curve for software is given by q 400–p. Clearly, your customer is willing to pay less for each additional unit of the software program. Locked inside this demand curve is information about how much the company is willing to pay for each unit of the program. This information is crucial for maximizing protability of sales. Chapter 79 Estimating a Demand Curve 629 Let’s rewrite the demand curve as p 400–q. Thus, when q 1, p $399, and so on. Now let’s try and gure out the value the customer attaches to each of the rst two units of the pro- gram. Assuming that the customer is rational, the customer will buy a unit if and only if the value of the unit exceeds your price. At a price of $400, demand equals 0, so the rst unit cannot be worth $400. At a price of $399, however, demand equals 1 unit. Therefore, the rst unit must be worth something between $399 and $400. Similarly, at a price of $399, the customer does not purchase the second unit. At a price of $398, however, the customer is purchasing two units, so the customer does purchase the second unit. Therefore, the customer values the second unit somewhere between $399 and $398. It can be shown that the best approximation of the value of the ith unit purchased by the customer is the price that makes demand equal to i–0.5. For example, by setting q equal to 0.5, the value of the rst unit is 400–0.5 $399.50. Similarly, by setting q 1.5, the value of the second unit is 400–1.5 $398.50. Problems 1. Suppose you are charging $60 for a board game you invented and have sold three thousand copies during the last year. Elasticity for board games is known to equal 3. Use this information to determine a linear and power demand curve. 2. For each of your answers in Problem 1, determine the value consumers place on the two thousandth unit purchased of your game. 631 Chapter 80 Pricing Products by Using Tie-Ins Question answered in this chapter: ■ How does the fact that customers buy razor blades as well as razors affect the prot-maximizing price of razors? Certain consumer product purchases frequently result in the purchase of related products, or tie-ins. Here are some examples: Original purchase Tie-in product Razor Razor b ades Men’s su t Sh rt and/or t e Persona computer Software tra n ng manua V deo game conso e V deo game Using the techniques I described in Chapter 79, “Estimating a Demand Curve,” it’s easy to determine a demand curve for the product that’s originally purchased. You can then use the Microsoft Excel Solver to determine the original product price that maximizes the sum of the prot earned from the original and the tie-in products. The following example shows how this analysis is done. Answer to This Chapter’s Question How does the fact that customers buy razor blades as well as razors affect the prot-maximizing price of razors? Suppose that you’re currently charging $5.00 for a razor and you’re selling 6 million razors. Assume that the variable cost of producing a razor is $2.00. Finally, suppose that the price elasticity of demand for razors is 2. What price should you charge for razors? Let’s assume (incorrectly) that no purchasers of razors buy blades. You determine the demand curve (assuming a linear demand curve) as shown in Figure 80-1. (You can nd this data and the chart on the No Blades worksheet in the le Razorsandblades.xlsx.) Two points on the demand curve are price $5.00, demand 6 million razors and price $5.05 (an increase of 1 percent), demand 5.88 million (2 percent less than 6 million). After drawing a chart and inserting a linear trendline as shown in Chapter 79, you nd the demand curve equation is y 18–2.4x. Because x equals price and y equals demand, you can write the demand curve for razors as follows: demand (in millions) 18–2.4(price). 632 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 80-1 Determ n ng the prot max m z ng pr ce for razors. I associate the names in cell C6 and the range C9:C11 with cells D6 and D9:D11. Next, I enter a trial price in D9 and determine demand for that price in cell D10 with the formula 18-2.4*price. Then I determine in cell D11 the prot for razors by using the formula demand*(price–unit cost). Next, I use Solver to determine the prot-maximizing price. The Solver Parameters dialog box is shown in Figure 80-2. FIGURE 80-2 So ver Parameters d a og box set up for max m z ng razor prot. I maximize the prot cell (cell D11) by changing the price (cell D9). The model is not linear because the target cell multiplies together two quantities—demand and (price–cost)—each Chapter 80 Pricing Products by Using Tie-Ins 633 depending on the changing cell. Solver nds that charging $4.75 for a razor maximizes prot. (Maximum prot is $18.15 million.) Now let’s suppose that the average purchaser of a razor buys 50 blades and that you earn $0.15 of prot per blade purchased. How does this change the price you should charge for a razor? Assume that the price of a blade is xed. (In Problem 3 at the end of the chapter, the blade price changes.) The analysis is in the Blades worksheet, which is shown in Figure 80-3. FIGURE 80-3 Pr ce for razors w th b ade prot nc uded. I used the Create From Selection command in the Dened Names group on the Formulas tab to associate the names in cells C6:C11 with cells D6:D11. (For example, cell D10 is named Demand.) Note Astute readers w reca that I a so named ce D10 of the No Blades worksheet Demand What does Exce do when you use the range name Demand n a formu a? Exce s mp y refers to the ce named Demand n the current worksheet In other words, when you use the range name Demand n the Blades worksheet, Exce refers to ce D10 of that worksheet and not to ce D10 n the No Blades worksheet In cells D7 and D8, I entered the relevant information about blades. In D9, I entered a trial price for razors, and in D10 I computed demand with the formula 18-2.4*price. Next, in cell D11, I computed total prot from razors and blades with the formula demand*(price–unit cost)+demand*blades per razor*prot per blade. Notice that demand*blades per razor*prot per blade is the prot from blades. The Solver setup is exactly as was shown earlier in Figure 80-2: change the price to maximize the prot. Of course, now the prot formula includes the prot earned from blades. Excel shows that prot is maximized by charging only $1.00 (half the variable cost!) for a razor. This price results from making so much money from blades. You are much better off 634 Microsoft Excel 2010: Data Analysis and Business Modeling ensuring that many people have razors even though you lose $1.00 on each razor sold. Many companies do not understand the importance of the prot from tie-in products. This leads them to overprice their primary product and not maximize their total prot. Problems Note In a of the fo ow ng prob ems, assume a near demand curve 1. You are trying to determine the prot-maximizing price for a video game console. Currently, you are charging $180 and selling 2 million consoles per year. It costs $150 to produce a console, and price elasticity of demand for consoles is 3. What price should you charge for a console? 2. Now assume that, on average, a purchaser of your video game console buys 10 video games and you earn $10 prot on each video game. What is the correct price for consoles? 3. In the razor and blade example, suppose the cost to produce a blade is $0.20. If you charge $0.35 for a blade, a customer buys an average of 50 blades. Assume the price elasticity of demand for blades is 3. What price should you charge for a razor and for a blade? 4. You are managing a movie theater that can handle up to eight thousand patrons per week. The current demand, price, and elasticity for ticket sales, popcorn, soda, and candy are given in Figure 80-4. The theater keeps 45 percent of ticket revenues. Unit cost per ticket, popcorn sales, candy sales, and soda sales are also given. Assuming linear demand curves, how can the theater maximize prots? Demand for foods is the fraction of patrons who purchase the given food. FIGURE 80-4 Mov e prob em data. 5. A prescription drug is produced in the United States and sold internationally. Each unit of the drug costs $60 to produce. In the German market, you are selling the drug for 150 euros per unit. The current exchange rate is 0.667 U.S. dollars per euro. Current demand for the drug is 100 units, and the estimated elasticity is 2.5. Assuming a linear demand curve, determine the appropriate sales price (in euros) for the drug. 635 Chapter 81 Pricing Products by Using Subjectively Determined Demand Questions answered in this chapter: ■ Sometimes I don’t know the price elasticity for a product. In other situations, I don’t believe a linear or power demand curve is relevant. Can I still estimate a demand curve and use Solver to determine a prot-maximizing price? ■ How can a small drugstore determine the prot-maximizing price for lipstick? Answer to This Chapter’s Questions Sometimes I don’t know the price elasticity for a product. In other situations, I don’t believe a linear or power demand curve is relevant. Can I still estimate a demand curve and use Solver to determine a prot-maximizing price? In situations when you don’t know the price elasticity for a product or don’t think you can rely on a linear or power demand curve, a good way to determine a product’s demand curve is to identify the lowest price and highest price that seem reasonable. You can then try to es- timate the product’s demand with the high price, the low price, and a price midway between the high and low prices. Given these three points on the product’s demand curve, you can use the Microsoft Excel trendline feature to t a quadratic demand curve with the following formula (which I’ll call Equation 1): Demand=a(price) 2 +b(price)+c For any three specied points on the demand curve, values of a, b, and c exist that will make Equation 1 exactly t the three specied points. Because Equation 1 ts three points on the demand curve, it seems reasonable to believe that the equation will give an accurate repre- sentation of demand for other prices. You can then use Equation 1 and Solver to determine maximum prot, which is given by the formula (price–unit cost)*demand. The following example shows how this process works. How can a small drugstore determine the prot-maximizing price for lipstick? Let’s suppose that a drugstore pays $0.90 for each unit of lipstick it orders. The store is considering charging from $1.50 through $2.50 for a unit of lipstick. The store thinks that at a price of $1.50, it will sell 60 units per week. (See Figure 81-1 and the le Lipstickprice.xlsx.) At a price of $2.00, the store thinks it will sell 51 units per week, and at a price of $2.50, 20 units per week. What price should the store charge for lipstick? 636 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 81-1 L pst ck pr c ng mode . You begin by entering the three points with which you’ll chart the demand curve in the cell range E3:F6. After selecting E3:F6, click the Charts group on the ribbon’s Insert tab, and then select the rst option for a Scatter chart. You can then right-click a data point and select Add Trendline. In the Format Trendline dialog box (see Figure 81-2), choose Polynomial and select 2 in the Order box (to obtain a quadratic curve of the form of Equation 1). Then select the option Display Equation On Chart. FIGURE 81-2 Congur ng the Format Trend ne d a og box for se ect ng po ynom a demand curve. Chapter 81 Pricing Products by Using Subjectively Determined Demand 637 Excel creates the chart shown in Figure 81-1. The estimated demand curve (Equation 2) is Demand –44*Price 2 +136*Price–45. Next, you insert a trial price in cell I2. You compute product demand by using Equation 2 in cell I3 with the formula –44*price^2+136*price–45. (I named cell I2 Price.) Then you com- pute weekly prot from lipstick sales in cell I4 with the formula demand*(price–unit cost). (Cell E2 is named Unit Cost, and cell I3 is named Demand.) Then you use Solver to determine the price that maximizes prot. The Solver Parameters dialog box is shown in Figure 81-3. Note that I constrain the price to be from the lowest through the highest specied prices ($1.50 through $2.50). If you allow Solver to consider prices outside this range, the quadratic demand curve might slope upward, which implies that a higher price would result in larger demand. This result is unreasonable, which is why you should constrain the price. FIGURE 81-3 Congur ng the So ver Parameters d a og box to ca cu ate pst ck pr c ng. The result is that the drugstore should charge $2.04 for a unit of lipstick. This yields sales of 49.4 units per week and a weekly prot of $56.24. The approach to pricing outlined in this chapter requires no knowledge of the concept of price elasticity. Inherently, the Solver considers the elasticity for each price when it deter- mines the prot-maximizing price. This approach can easily be applied by organizations that sell thousands of different products. The only data that needs to be specied for each product is its variable cost and the three given points on the demand curve. 638 Microsoft Excel 2010: Data Analysis and Business Modeling Problems 1. Suppose it costs $250 to produce a video game console. A price from $200 through $400 is under consideration. Estimated demand for the game console is shown in the following table. Price Demand (in millions) $200 2 $300 0 9 $400 0 2 What price should you charge for a game console? 2. This problem uses the demand information given in Problem 1. Each game owner buys an average of 10 video games. You earn $10 prot per video game. What price should you charge for the game console? 3. You are trying to determine the correct price for a new weekly magazine. The variable cost of printing and distributing a copy of the magazine is $0.50. You are thinking of charging from $0.50 through $1.30 per copy. The estimated weekly sales of the magazine are shown in the following table. Price Demand (in millions) $0 50 2 $0 90 1 2 $1 30 0 3 In addition to sales revenue from the magazine, you can charge $30 per one thousand copies sold for each of the 20 pages of advertising in each week’s magazine. What price should you charge for the magazine? [...]... results you want 654 Microsoft Excel 2 010: Data Analysis and Business Modeling I have a sales database for a small makeup company that lists the salesperson, p roduct, units sold, and dollar amount for every transaction I know I can use d atabase statistical functions or COUNTIFS, SUMIFS, and AVERAGEIFS to summarize this data, but can I also use array functions to summarize the data and answer questions... listed in the same row and changes to the original data are reflected in the new arrangement you have created 662 Microsoft Excel 2 010: Data Analysis and Business Modeling 6 Use the data in the Historicalinvest.xlsx file to create a count of the number of years in which stock, bond, and T-Bill returns are from –20 percent through –15 percent, –15 percent through 10 percent, and so on 7 An m by n... for 644 Microsoft Excel 2 010: Data Analysis and Business Modeling rides purchased in cell I3 with the formula I1*C3 In cell J6, I compute profit as revenues less costs with the formula I2–I3 Now I can use a two-way data table to determine the profit-maximizing combination of fixed fee and price per ride The data table is shown in Figure 82-5 (Many rows and columns are hidden.) In setting up the data table,... xn, and you believe that for some values of a, b1, b2,…, bn, the relationship between y and x1, x2,…, xn is given by y a(b1)x1(b2) x2(bn)xn (I’ll call this Equation 1.) 658 Microsoft Excel 2 010: Data Analysis and Business Modeling FIGURE 83 -10 Toy revenue trend and seasona ty est mat on The LOGEST function is used to determine values of a, b1, b2,…, bn that best fit this equation to the observed data. .. the range B4:B10 and obtain the total of 27 FIGURE 83-4 Summ ng second d g ts n a set of ntegers 652 Microsoft Excel 2 010: Data Analysis and Business Modeling An array function makes this process much easier Simply select cell C7 and array-enter the formula SUM(VALUE(MID(A4:A10,2,1)) Your array formula will return the correct answer, 27 To see what this formula does, highlight MID(A4:A10,2,1) in the... profit-maximizing price per ride 642 Microsoft Excel 2 010: Data Analysis and Business Modeling FIGURE 82-3 Profit max m z ng near pr c ng scheme I associate the range names in C8:C10 with cells D8:D10 I enter a trial price in cell D8 and compute the number of ride tickets purchased in cell D9 with the formula 20–(2*D8) Then I compute the profit in cell D12 with the formula Demand*(price–unit cost) I can now... fixed fee between $10. 00 and $60.00 (the v alues in the range K10:K60) and vary the price per ride between $0.50 and $5.00 (the values in L9:BE9) I recomputed profit in cell K9 with the formula J6 I select the table range (cells K9:BE60), and then on the Data tab, in the Data Tools group, I click What-If Analysis and then select Data Table The column input cell is F2 (the fixed fee) and the row input... quarter, the Q1 dummy and the Q2 dummy equal 0 and the Q3 dummy equals 1 Quarterly revenues during this quarter are p redicted to equal 4219.57*(1.0086)qua te numbe *(.468) Finally, during a fourth quarter, the Q1, Q2, and Q3 dummies equal 0 During this quarter, quarterly revenues are predicted to equal 4219.57*(1.0086)qua te numbe 660 Microsoft Excel 2 010: Data Analysis and Business Modeling In summary,... performing complex calculations with Microsoft Excel An array formula can return a result in either one cell or in a 647 648 Microsoft Excel 2 010: Data Analysis and Business Modeling range of cells Array formulas perform operations on two or more sets of values, called rray a arguments Each array argument used in an array formula must contain exactly the same number of rows and columns When you enter an... down on a quarterly basis by using array formulas I want the data summarized (using only array formulas) by company and by quarter as shown in Figure 83-13 664 Microsoft Excel 2 010: Data Analysis and Business Modeling FIGURE 83-13 Format for Prob em 17 answer For example, L7 should contain Quarter 1 (January 1 through March 31) ACS sales, and so on Verify your answer with a PivotTable 18 Explain why . 628 Microsoft Excel 2 010: Data Analysis and Business Modeling For prices near the current price, however, the linear demand curve is usually a good approximation of the product’s true demand. price per ride. 642 Microsoft Excel 2 010: Data Analysis and Business Modeling FIGURE 82-3 Prot max m z ng near pr c ng scheme. I associate the range names in C8:C10 with cells D8:D10. I enter a trial. performing complex calculations with Microsoft Excel. An array formula can return a result in either one cell or in a 648 Microsoft Excel 2 010: Data Analysis and Business Modeling range of cells. Array
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