Question: Background Information: Restaurants have
Background Information: Restaurants have traditionally used bottom-end wines to sell by the glass (BTG) at reasonably low prices per glass. In recent years, there has been a growing trend within the restaurant industry to extend BTG programs to higher-end wines. In doing so, they have greatly expanded the sales of higher-end wines. The typical markup on a bottle of wine is 100 percent or more, meaning that a bottle of wine that sells at retail for $25 in a wine shop can be priced at $100 in a restaurant. To simplify this discussion, suppose that wine is offered at $10 per glass. The size of the serving can be adjusted depending on the price per bottle of the wine being poured. For example, a 4-ounce pour can be offered for wines in the $40 to $50 range and a 2-ounce pour can be offered for wines in the $80 to $100 range. Because a bottle has 25.4 ounces, both examples provide more revenue from BTG sales than from full-bottle sales! Such programs have been quite successful and produce little loss due to unsold wine in the bottle because, with proper storage, a partial bottle can be poured the next evening with no notable change in taste.
The Problem: Suppose you manage a restaurant with a BTG program. You sell 200 glasses per week at $10 per glass. As an experiment, you once raised the price during the week to $11 a glass and found that you sold 20 glasses less than before the price change. Suppose you assume this information as the basis for a full demand curve for wine BTG at your restaurant.
a. Obtain an algebraic and graphical depiction of your restaurant’s BTG demand.
b. How many glasses do you expect to sell at $15 per glass?
c. How would your answers change if the response to a $1 price change is 10 glasses per week or 25 glasses per week?
We now demonstrate how Excel can be used to answer this problem. This allows you to easily conduct a what-if or sensitivity analysis. It also prepares you to use Excel to analyze and estimate more complex demand relationships such as those presented in Chapters 4 and 5. Note: This problem requires three important assumptions.
1. You know a point on the BTG demand curve (e.g., P = $10 and Q = 200).
2. You know the slope of the BTG demand curve at this point is ∆P/∆Q = .05.
3. You know that the slope does not change (i.e., demand for wine BTG is linear). For a review of slopes and equations, go to the Mathematical Appendix on the Companion Website or see Appendix 3A.
Excel Sheet 3.1 shows a screenshot of cells A1:K28 from the Single Demand worksheet of the Demand Excel App. It shows one way to analyze this problem in Excel. The graph is shown next to calculations, and equations are shown next to critical cells, in the worksheet. This is simply done to clarify how each number was obtained: By clicking on a cell, you can check the equations for yourself. This example provides a detailed roadmap for creating a graph in Excel. You are encouraged to open Excel and do this problem yourself.
Notice that the negative slope of the demand curve is represented by the negative sign in cell A4 rather than by writing the equation as P = b - mQ. Both practices work as long as
Excel Sheet 3.1
Source: Demand Excel App, Single Demand worksheet.
Alternate Figures from Excel Sheet 3.1 based on Changing Demand Responsiveness in Cell A4 you follow through with the mathematics consistently. The benefit of not forcing the minus sign into the equation is that a supply curve can readily be modeled with this graph by entering a positive slope in cell A4. Of course, you also want to adjust the labels appropriately.
One quick benefit of doing the problem in Excel is that the new scenarios in part c are analyzed by changing a single cell, A4, on Excel Sheet 3.1(the figures below are from Excel Sheet 3.1 based on new values for A4). Additional scenarios can be examined by varying any of the four pieces of data on which the problem is based (in cells A2:A4 and E2 on Excel Sheet 1).
Transferring Your Excel Work to Other Programs: Once you have a graph you want to use, you can easily insert it into another program by highlighting the graph in Excel and then using the Copy command on Excel’s Home ribbon. To paste in a Word or PowerPoint document, open that software and use Paste Special, Enhanced Metafile, rather than Paste. From this point, the graph can be resized or positioned as needed by right-clicking on the image; it can be adjusted as needed using the Size and Format Picture menus.
Here is a second, related problem: A successful advertising campaign has increased BTG demand by 25 percent at any price relative to pre-advertising levels. Pre-advertising demand is assumed to be the same as was given in the initial 1Demand scenario (200 glasses are sold at a price of $10 per glass, and each dollar price change is associated with a twenty glass-per-week change in sales).
The post advertising demand implies that 250 glasses are sold at a price of $10 per glass, and each dollar price change is associated with a twenty-five-glass-per-week change in sales. This is confirmed by having the P intercept the same for both demand curves. Excel Sheet 3.2 shows how this is analyzed in Excel.
One final scenario: Try doing this problem yourself using the worksheet you created or the 2Demands worksheet. Consider an alternative post advertising scenario. Rather than selling 25 percent more glasses at any price, you find that if you charge 25 percent more per glass, then you are able to maintain the same number of BTG glasses sold. Adjust D2:D4 to model this new scenario and Copy and Paste (using Paste-Special as described above) your answer graph to a fresh sheet of paper; include answers to a and b:
a. Provide a verbal description of demand in this instance by filling in the values of C and D in the following sentence: Post advertising demand shows that 200 glasses are sold at a price of C per glass, and each dollar price change is associated with a D-glass-per-week change in sales.
b. What is the equation for the post advertising demand curve in slope-intercept form?
Excel Sheet 3.2
Source: Demand Excel App, Multiple Demands worksheet
Transcribed Image Text:
A 1 DATA (colored cells) 200 Q Answer for B given: BTG Demand 2 New Price in $ 15 $26 $24 Quantity at this price 100 -A2+A4'(E2-A3) C4 uses point-slope formula 10 Pin $ -20 AQ/AP $22 5 Calculations -0.05 m, slope (-1/A4) $ 20.00 b, P Intercept (= Pg-mQg = A3-A6°A2) 400 Qintercept (=-b/m =-A7/A6) 9 Creating the graph. The easiest way to graph a line 10 is to use the endpoints. This version includes the 11 demand point to increase clarity. $20 A $18 I $16 $14 7 8 $12 * $10 $8 Equations in A14:B16 P. $6 $4 12 (QP) point Paxis Bundle Qaxis 13 Q $2 $0 O 25 50 75 100 125 150 175 200 225 250 275 300 14 20 =A7 15 200 $ 10 =A2 =A3 Number of glasses per week, Q 16 400 $ A8 17 This graph was obtained by following these steps. 18 1. Highlight A13:B16 then click Insert, Scatter, Scatter with Straight Lines and Markers. 19 2. Add axis labels & change the title by clicking on Layout 1 from the Chart Layouts options on the Chart Tools ribbon. 20 3. Change each title by clicking on the title then type the title in the fx area (above the spreadsheet at D). 21 a Three titles were created and font sizes were adjusted using the A^ arrow on the Home ribbon. b The Plegend at the right was removed by clicking on it then pressing delete on the keyboard. c The size of the graph was changed by clicking on the graph and dragging to the preferred size. 22 23 24 4. Change axis formatting by right clicking on either axis then click Format Axis and follow the Format Axis menu. 25 a This Qaxis has a fixed maximum set at 300 with major units set at 20. b This P axis has a fixed maximum set at 26 with major units set at 2. 26 27 5. Vertical major unit gridlines have been added by right clicking on the horizontal axis and click Add Major Gridlines 28 Part B is answered, and a more general solution is provided, in cell CA using the point-slope formula for a line. Price per glass, P Demand given A4 =-10. Q($15) = 150 Demand given A4=- 25. Q($15) = 75 BTG Demand BTG Demand $26 $24 $22 $20 $18 $16 $14 $26 $24 $22 $20 $18 $16 $14 $12 $10 $8 $6 $4 $2 $0 $12 $10 $8 $6 $4 $2 $0 O 25 50 75 100 125 150 175 200 225 250 275 300 O 25 50 75 100 125 150 175 200 225 250 275 300 Number of glasses per week, Q Number of glasses per week, Q Price per glass, P Price per glass, P B D 1 2 demands Pre Adv. Scenario Past-Adv. Two BTG Scenarios 2 Quantity 3 Price 200 250 - Pre-Adv. -Post-Adv. $26 $24 $22 $20 $18 $16 10 Pin$ 10 4 Change in Q 5 Doing repetitive calculations. The slope and 6 intercept caleulations need to be done for each 7 demand curve. Once one set of calculations is done, 8 the other is replicated using Copy and Paste. In this 9 instance, highlight B12:B14, dick Copy, then dick on 10 cell D12 and dick Paste. 11 20 AQ/AP -25 $14 $12 $10 $6 Equations for Bl2:B14 are in C12C14. -0.05 -1/B4 $4 12 13 Pintercept, b s Q intercept slope, m -0.04 $2 $0 O 25 50 75 100 125 150 175 200 225 250 275 300 Number of glasses per week, Q 20.00 =83-B6"B2 $ 20.00 14 400 -B13/B12 500 15 Creating the graph. This version graphs the line from 16 the endpoints in rows 13:14. See 1-5 bekow. 17 Q Pre-Adv. Post-Adv. 18 20 20 19 400 S 500 $ 20 1. Set up the endpoints for the Pre-Demand curve as shown in A17:B19, using B13-B14. 21 2 To create the post-advertising demand endpoints, highlight A17:B19, dick Copy, dick C17 and click Paste. 22 Type Post-Adv. in cell DI7. (This is another example of having Excol do repetitive calculations.) 23 3. Highlight A17:B19, dick Insort, Scatter, Scatter with Straight Lines. In this instance, Excel assumes you have 24 the data oriented by columns. To obtain the Pre-demand curve, dick Switch Row/Column in the Data area of the 25 Chart Tools ribbon. Ignore formating for the moment. 26 4. To obtain Post-Demand, Right dick on the graph (or use the Chart Tools ribbon) and dick Select Data. Click 27 Add. The Edit Series popup menu results. 78 a. Click D17 in the Series Name area. Hit Tab. 29 b. Highlight Cl18:C19 in the Sories X Values area. Hit Tab. 30 c. Hit Delote (to romove -(1). Highlight D18:D19 in the Series Y Values area, hit Tab, Enter. 31 5. To format the graph, add labels and adjust axes and vertical grid lines following steps similar to 2-5 from the 32 Single Demand worksheet (except 3b) shown in Excel 3.1. d'ss8 sad aopa
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