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# Mngrl Dec.Glbl Eco ECO 685

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Economics 685 Managerial Economics Notes David L Kelly Department of Economics University of Miami Box 248126 Coral Gables7 FL 33134 dkelly rniarniedu Current Version Spring7 2005 INTRODUCTION I What is Managerial Economics De nition 1 Managerial Economics is the application of economic theory to decisions made by managers and rms De nition 2 Economics is the study of the allocation of scarce resources Economics is the study of the allocation of scarce resources Because all decisions are essentially about the allocation of scarce resources economics is in fact the study of decision making and problem solving in general So we will simply apply economic rules for decision making to problems faced by managers As an example consider a marketing executive for Tang General Foods considering both TV and guerilla advertising The dollars in the marketing budget are scarce resources that must be allocated to one or the other type of advertising Managerial economics provides a systematic scienti c method for making the where to advertise decision Similarly should Disney add a theme park in France Capital is the scarce resource The capital used to build the theme park could instead be used to build a theme park somewhere else or used to invest in another business perhaps video production II Managerial Economics advice for decision making Managerial economics provides a scienti c method for making business decisions A The Steps 1 Formulate the problem list the objective and the possible decisions 2 Gather data on the objective and the decisions 3 Using statistics estimate the relationship between the objective and the decisions known as the objective function 4 Using calculus or game theory choose the decision that maximizes the objective func tion B Example Consider our Tang marketing executive again Step 1 The objective is presumably to maximizes sales if the advertising budget is xed and the goal is to get as much out of each marketing dollar as possible or pro ts if the executive for example wants to justify a larger budget as positively in uencing pro ts Let us suppose the former It is reasonable to conjecture that diminishing returns exist as more and more adver tisements are made each additional dollar gives less and less additional sales The rst ad is fresh and reaches many previously unaware consumers The 100th ad generates little additional sales everyone is familiar with the product Here is an objective function that has diminishing returns S l b1Aw 7 011431 bgAg 7 02A Here A is advertising expenses S is sales and a b and c are unknown parameters A parameter is a variable which the manager cannot change Step 2 Our executive has data on past sales and advertising expenditures We also of course need to know the cost of a TV ad and the cost of a guerrilla ad In step 3 we use fancy statistics to nd the unknowns a b and c We get sales are in millions of dollars 3 22 5A 7 151 24AM i 0513 2 We also have our budget numbers We have 05 million to spend a block of TV ads costs 5 million while a set of guerilla ads costs 1 million So TV ads are more expensive but reach a wider audience 05 5A HA 3 In step 4 we use calculus to nd the values of Am and Ag that maximize S given our scarce resources budget dollars We would nd that An 0086 ad blocks or about 430000 and Ag 007 ad blocks or about 70 0001 Although TV ads are more expensive the extra expense is more than o set by the larger audience C Alternative Methods of Making Decisions Believe it or not the vast majority of you despite this class will not make decisions this way Instead most of you will guess timate or blu your way through the problem Let us be generous and call guessing relying on experience or expertise One can actually do a pretty good job relying on experience if you have it With enough practice a squirrel can gure out how many acorns to save without knowledge of internal rates of return However the scienti c method requires no practice other than data collection and gives a better decision Both decision methods require common sense to work The data used above may have been collected in a record year giving numbers that are unlikely to be repeated The executive may have data on TV advertising in one state and falsely suppose all states work the same III Decisions Studied in Managerial Economics Although managerial economic principles can be applied to any decision and in fact are applied elsewhere in for example your nance class managerial economics typically focuses on three types of decisions 1 How much to produce How many calculators should the Rondo Corp produce per day 2 What inputs to use How many workers and how many machine tools should Rondo employ 1By the way this executive should be arguing for a larger budget spending 2 million on guerilla marketing and 128 million on TV ads total budget of 130 million would maximize pro ts 3 What price to charge Should Rondo use cost plus pricing or some other method Notice that these decisions are very high level decisions typically made by CEOs and senior management not newly minted MBAs unless they are entrepreneurs or work in a small rm This is one reason why the most common major among CEOs is economics Nonetheless as our Tang example demonstrates even junior marketing executives can use these methods Further some of you no doubt aspire to be CEOs and so will eventually need this information IV Theory of the Firm A Objective of the rm What is the objective or goal that a manager has in mind when making decisions At the most general level managerial economists suppose that managers try to maximize the value of a rm De nition 3 The value of a rm is the present value of the rm s cash ows In a rough sense cash ows are pro ts which are revenues less costs Thus yawi 7 lt4 7r TR 7 To 5 Here pv is the present value of the rm n is the planning horizon 239 is the appropriate interest rate or the rate of return that could be earned if the pro ts were invested elsewhere Here 7r is pro ts and TRt and TC are total revenues and total costs B Economic Pro ts Note that pro ts here are economic pro ts De nition 4 Economic Pro ts are pro ts after taking into account capital and labor provided by owners Pro ts as normally recorded are known as accounting pro ts Economic pro ts are lower they subtract from total revenues opportunity costs That is they subtract the value of time and capital that could be spent elsewhere Example Suppose the market rate of return is 10 A shoe store owner is considering buying an additional factory for 240000 The owner values the additional time required to supervise the new plant at 40000 per year or suppose he could hire someone at this price but prefers to do it himself He gures the accounting pro t is 60000 per year To get the economic pro t Economic Pro t accounting pro t 7 return on capital used 7 owners labor 6 So here the economic pro t is 60000 7 24000 7 40000 74000 Although the additional factory would make money the owner would do better by investing the 240000 in the market Thus the optimal decision would be not to buy the factory Clearly accounting pro ts are good for maintaining records but economic pro ts are needed to make decisions Finally in the long run economic pro ts are generally driven to zero If economic pro ts are negative rms will drop out of the market and prices will rise increasing pro ts Conversely if economic pro ts are positive rms will enter the market and competition will drive prices down Thus unless the industry has barriers which prevent rms from entering and exiting eg monopolies or their are regulations on price setting eg electricity prices economic pro ts tend to zero C Other objectives 1 Objectives of rms and managers We claim that rms maximize pro ts although individual managers may not Firms that do not tend to go out of business CEOs who do not maximize pro ts tend to be replaced since shareholders clearly desire pro ts to be maximized Many other objectives such as maximizing market share are just intermediate goals toward the nal goal of maximizing pro ts remember by setting a price of zero one could always maximize market share so it is doubtful if any rms despite their claims really do this Similarly satis cing or meeting pro t goals are approximations to maximizing pro ts done when it is not clear what maximum pro ts are It is important to realize that individual managers or CEOs may have other objectives as our Tang example indicates unless motivated by stock options or other incentives 2 Pro t maximization ethics and welfare Maximizing pro ts improves the welfare of society in two ways 1 The rm provides products and services that consumers want as evidenced by their willingness to pay for the products and thus add to rm pro ts 2 The rm stays in business thus providing income to workers and stockholders Famous theorem in economics in general maximizing pro ts maximizes the welfare of society this is not usually what is heard in the news For example consider price gouging77 of gasoline By charging high prices when supply is low gas retailers insure that the consumers who most need the gas as evidenced by their willingness to pay high prices get it Further the retailer generates income in the form ofwages and pro ts for stockholders Charging a low price means that whoever gets the small supply of gas is whoever gets to the station rst for example Second example is electricity in California During the recent shortage retail prices were xed Thus hospitals and swimming pools paid the same price for electricity and rolling blackouts determined who got electricity By raising prices hospitals would have a chance to out bid swimming pool owners for the needed electricity raising welfare Thus in most cases the most ethical practice is to maximize pro ts PRODUCTION THEORY Production Theory helps managers decide what inputs to use The book presents the material largely from a manufacturing prospective7 for example how many machines and how many laborers to use But the material could equally apply to7 say7 a nancial planning rm deciding how many assistants should be assigned to each nancial planner I The Production Function De nition 5 The Production Function is a graph table or equation showing the maxi mum output rate that can be achieved by any speci ed set of inputs For example7 consider the production function in the book7 for Thompson Machine Co Thompson has ve machines in a shop that produces machine parts Let7s suppose the number of machines input is xed in the short run Let Q be hundreds of parts produced per year7 and let L be the number of full time workers7 again per year Then Q 30L 20L2 7 L3 7 Here we have the information in table form Full time laborers L Parts Produced Q 0 0 1 49 2 132 3 243 6 684 9 1161 12 1512 14 1596 15 1575 What can we do with the production function H Set inputs to produce a speci ed quantity of outputs If the manager expects 700 orders this year7 he knows to hire 7 workers from the table7 6 produces only 684 N Hire workers to meet objective of maximizing production See below 03 With information on wages7 hire workers to meet objective of maximizing pro ts See below Where does the production function come from We estimate a production function statistically7 see below What are the properties of the production function It is helpful to understand the production function by studying its properties 1 Zero inputs implies zero output Product cannot be produced without inputs 2 De nition 6 Law of diminishing marginal returns if all other inputs are held constant then the additional output from increasing one input eventually falls Hold the number of machines constant at ve Then going from four to ve workers is no problem each can use one machine Adding one more worker has a lower marginal return he can only assist one of the machine operators Adding in this case the 15th worker results in zero additional output he can only stand and watch Adding still more workers decreases output these workers simply get in the way 3 Positive marginal product Up to a point7 adding additional workers increases output The graph below illustrates these concepts Output ofThompsorv Machine C0 Parts Produced PerYear Q 6 8 10 l LFull Time Laborers Per Year II Application 1 Maximizing Production Let us now back up and do a step by step application Suppose you a manager assigned to a particular shop with ve machines A shortage of machine parts exists The orders are to crank out as many parts as possible 1 Formulate the problem The objective is clearly to maximize output of parts The decision is in fact how many workers to hire N Gather data on the objective and the decisions 03 Using statistics estimate the objective function The objective function here is the production function which relates choices how many workers to hire to the objective how much is produced We cannot yet do these steps Therefore let us instead assume we have completed these steps and have thus come up with the production function Q 30L 20L2 7 L3 4 Using calculus determine the optimal decision So mathematically the problem is mLax30L 20L2 7 L3 8 By looking at the graph we can see that output is maximized when adding an additional worker adds zero output the marginal product is zero De nition 7 The Marginal Product is the additional output from an additional unit of an input If we view units as full time workers77 then by following the graph we see that the maximum occurs at about 14 workers 1596 parts Alternatively if through overtime or part time we can hire part of a worker we could use calculus Notice that when output is maximized the slope of the tangent line the derivative is zero Thus 8 marginal product of labor g 0 9 The derivative is mi 27 73040L73L 0 10 73L240L300 11 The solution is given by the quadratic formula page 62 i 7b i xbz 470 i 740 i 1600 7 473 30 L 2a 2 73 1405 12 Notice I have discarded the negative solution So in fact if possible the manager should pay some overtime so that the equivalent of 1405 full time workers are employed to maximize production I submit to you that coming up with 14 workers would be di cult to come up with relying solely on expertise III Application 2 maximizing productivity Let us suppose now that there is no shortage7 but the manager is paid a bonus based on the productivity of the workers De nition 8 The Productivity or average product of an input is the output divided by the number of inputs So we have 7 Q average product of labor 7 Z 13 Follow the steps 1 The objective is to maximize the average product of labor The choice is once again how many full time workers to hire 2 The objective function is QL 30 20L 7 L2 3 We do not need to estimate this function7 we have it already 4 The last step is to maximize So mathematically mLax30 20L 7 L2 14 We can create another table or use calculus again Set the slope or derivative equal to zero 830 20L 7 L2 2072L0 L10 15 BL So hiring 10 workers maximizes productivity7 with QL 130 On average7 the workers produce at most 130 units each IV Application 3 Maximizing Pro ts A Example Suppose now the manager is paid a bonus based on the pro ts of the company To maximize pro ts we need to know how output a ects total revenues and how inputs a ect total costs Suppose the parts can be sold for 500 each and workers earn a salary of 45000 per year Total revenues are thus TR 500 Q 500 30L 20L2 7 L3 16 Total costs are TC 45 000L 17 Follow our steps again 1 The objective is to maximize pro ts the choice is the number of full time employees 2 The only data we need are the cost of labor 45000 and the price of the parts 500 Pro ts are 7139 TR 7 TC 500 30L 20L2 7 L3 7 45 000L 18 3 We again do not need to do any estimation beyond the production function 4 Maximize We have mLax500 30L 20L2 7 L3 7 45 000L 19 15 000 20000L i 1 500 L2 i 45 000 0 20 Divide by 1000 20L715L27300 21 720 11202 7 4 715 730 L W 116 22 Either answer works 1 have chosen the larger So to maximize pro ts we should hire 116 workers Again 1 don7t know of a way to obtain this without using math B Marginal Revenue Product To help with the intuition note that aw i 8TB i 8T0 i 23 ainput 7 ainput ainput 7 7rTRiTC 8TB 8T0 24 ainput ainput We call the rst term the marginal revenue product MRP De nition 9 Marginal Revenue Product is the amount of additional revenue from an additional unit of an input The second term is the marginal expenditure De nition 10 The Marginal Expenditure is the amount of additional costs from an additional unit of input So we hire additional inputs until marginal revenue product equals marginal expenditure Ignoring the fancy jargon we see that we should hire a worker if the worker produces more revenue than the cost of hiring that person Such a worker makes money for the rm Finally notice that am 7 am 8Q 7 7 MR MP 25 ainput 8Q ainput MRP 13 Thus the additional revenue from an additional unit of input is equal to the marginal revenue times the marginal product V Multiple Inputs A Marginal Product and Price Ratios We now suppose there is more than one input to choose from in principle7 everything is the same Let L and K denote the two types of inputs7 for example workers and machines capital7 or workers and managers The price of capital is PK and the price of labor is PL Let us suppose again our desire is to maximize pro ts r aLleuL7 K 7 PKK 7 PLL 26 ldentical to the one input case7 we are looking for a maximum7 we nd the place where the slope derivative is zero 8TB W Pk 0 27 8TB 8L 7 PL 0 28 Notice that we have two equations for the two unknowns7 the amount of labor and capital aTR MRP 7 P ME 29 K k K aTR MRPL W PL MEL 30 Notice that we have the exact same result as before the marginal revenue product equals the marginal expenditure Hire additional workers until adding one more worker costs more in salary then the revenue that worker brings in Buy one more machine until the cost of the machine is higher than the value of the product produced Now divide the two equations MRPKiMPIVMRi Pk 31 MRPL i MPL MR 7 PL Cancelling out the MR7 we see that MPK angQ 7 8K MPL Lg PL 32 So after all this math7 we see that the ratio of marginal products must equal the price ratio This combination of inputs minimizes the costs of production and maximizes pro ts We can give a graphical intuition of this result K allows IiPK extra K to be used at same cost l But less than Optimal L 6 L PLPKadditional capital is reduce required to produce by 1 unlt 10 units when labor is reduced by one thus either save costs or increase production by reducing L Suppose the manager has two inputs K and L and a total budget of 8 million Draw all of the possible ways to spend the 8 million For example7 we could spend 8 million on labor7 which at price PL results in L 8PL units of labor Reduce the number of laborers 15 by one Then we have PL extra dollars to spend on K Thus we can buy PKK PL or K PLPK units of capital So the slope is iPLPK This line is called the isocost line Now draw all of the input combinations that produce 10 units The curve is convex because of diminishing returns7 when a lot of labor is used and very little capital7 it takes a lot of labor to keep production at 10 units when we reduce the capital used by one unit Now consider a point where the price ratio is not equal to the ratio of the marginal products7 like the red point At that point7 PLPK gt MPLMPK Reduce L by one unit That means we can buy PLPK additional K But we need less than this amount of K to continue producing 10 units7 since the marginal product of labor is small relative to the marginal product of capital at this point So we can either spend all of the money on K7 increasing production to 15 units7 or we can reduce costs and continue to produce 10 units Thus the optimum is reached when the ratio of marginal products equals the price ratio B Example Multiple Inputs Suppose an engineering analysis rm uses engineers and technicians to do their consulting Engineers are paid 47000 per month and Technicians 2000 The production function was found to be Q 20E7E212T705T2 33 The rm charges 17000 to do an engineering analysis 1 How many engineers and technicians should be hired if the manager is given a maximum wage bill of 28000 We can skip many of the steps here7 we know that pro t and production maximization and cost minimization all say the marginal product and price ratios must be equal We have MPE Lg 7 PE MPT T 73435 7 P7 34 Or 20 72E 7 4000 7 2 127T 2000 2072E2127T 72E472T ET72 The rm should always have two fewer engineers than technicians Thus since the wage bill is 28000 28 000 4000E 2000T 14 2E T 14 2 T i 2 T 183T 7gt T6 7gt E4 3 How many engineers and technicians should be hired to maximize pro ts We know already that we need two fewer engineers than technicians rrTiaEx17000 lt20E 7 E2 12T 7 05 T2 7 4000E 7 2000T So set the slope equal to zero With respect to E 1000 20 7 2E 4000 35 36 37 38 39 40 41 42 43 44 20 4 2E 4 45 E8aT10 46 So we have 8 engineers7 two fewer than the 10 technicians 4 How many engineers and technicians should be hired if the rm needs to perform an output of 166 engineering analysis We need Q16620E7E212T705T2 47 166 20 T727T72212T705T2 48 166 20T7407T24T7412T705T2 49 166 36T i 44 715T2 50 0 15T2 i 36T 210 51 364362 44210 15 T 42314aE12 52 2 15 VI Mergers and Spinoffs A Returns to Scale Here we think about the size of our production processes Should the rm expand say through a merger or contract say through a spin o Should the rm build a second factory or increase the size of the current factory Should the rm close one plant and move operations to another Should the rm outsource some production processes The production function tells us the answer De nition 11 The production function exhibits Increasing decreasing constant re turns to scale if a doubling of all inputs more than less than exactly doubles output Doubling all inputs can be thought of as building an identical factory or merging with an identical rm lf increasing returns to scale exists than the merger is bene cial since the total costs do not change the costs are the same as the costs of the two rms acting separately but output is greater Thus the cost per unit falls Similarly with decreasing returns to scale if half the rm is spun o then costs are split in half but output falls by less than half Thus cost per unit falls Consider the above production function and let us double all inputs Q 20 2E 7 2E2 12 2T 7 05 2T2 53 40E 7 4E2 24T 7 2T2 54 On the other hand if we double output we get 2Q 2 20E 7 E2 12T i 05 T2gtgt 55 2Q 40E 7 2E2 24T i T2 56 So Q lt 262 doubling all inputs resulted in less than double the output This rm has decreasing returns In the long run I would recommend splitting this plant into two smaller units Why returns to scale The primary reason for decreasing returns is well too much management Coordination of a large enterprise requires many employees who do not directly contribute to the overall production lnformation does not ow well each individual worker has little impact on pro ts and therefore little incentive to engage in pro t maximizing Conversely increasing returns to scale can occur for many reasons 1 lndiVisibilities It may be di cult to hire part time accountants one full time ac countant must be used But then doubling the size might not require any additional accountants N Engineering Reasons It may be the case that doubling the size of the warehouse might not require double the steel electricity etc 03 Specialization Large rms can have employees be more e icient by specializing A larger rm can hire an accountant rather than have the head sales guy also do the accounting B A special production function and output elasticity De nition 12 The output elasticity is the percentage increase in output from a one per cent increase in inputs Consider the telephone industry in Canada The production function was found to be Q 070L070K041 57 A one percent increase in inputs gives Q 070 101L03970 101K03941 58 0397013901070 L07013901041 K041 5g 1390107013901041 03970L070K041 60 13901070041 Q 61 10111Q 62 Thus if inputs increase by 1 outputs increase by 111 so the output elasticity is 111 The above production function has the special feature that the output elasticity is constant Further for this production function the output elasticity is simply the sum of the coe i cients 071040 111 Does this function have increasing decreasing or constant returns to scale How could a telephone monopoly increase or decrease its size VII How Do We Find the Production Function We can do many great thing with the production function However l7m willing to bet none of you have come across one in your business career How do we obtain the production func tion Several ways exist all of which involve gathering company data or even competitors data and then using statistics regressions What we need is data on inputs used and how much output was obtained A Obtain inputoutput data The rst step is to obtain some data Here are several possibilities H Time Series Data Get historical data of the rms inputs and outputs N3 Cross Section Data Get data of all plants or factories owned by the rm in a single time frame Or get data on all of the rms in the industry 03 Use technical information supplied by engineers Hgt Conduct a randomized study Select a random factory or factories and change the inputs 5quot Benchmarking Observe rms outside the industry that specialize in this type of pro duction Each has advantages and disadvantages Time series data is often easy to come by The manager does not need to request data from other managers or look up data on other rms However things change over time Suppose the time series data is something like 21 Date Full time laborers L Parts Produced Q April 3 6 684 April 4 7 681 One might look at this data and think that the MP becomes negative after 6 workers that is the rm should never hire more than six workers But it is also possible that something odd happened on April 4 that did not happen on April 3 For example it could have been someone7s birthday on April 4 and the rm wasted a few hours giving out cake Cross sectional studies take more time to acquire the data To a lesser degree cross sectional data has the same problem There might be something special about one factory that the manager does not know about Plant Full time laborers L Parts Produced Q West Palm Beach 6 684 Miami 7 681 With this data we would again conclude that hiring more than 6 workers is a mistake But it could be that the Miami plant uses older equipment and so the workers are not as productive The randomized study as is done in medicine does not su er from these problems but is the most expensive way to obtain data Because the plant selected is random differences between plants are random and tend to average out But you have to make the plant use odd combinations of inputs possibly resulting in low production just to gather data B Choosing a production function The second step is to choose a production function Suppose we have two inputs K and L again We would like our function to have all of the properties listed above like diminishing marginal products Here are two that have these properties Q aLK WK cLK2 i dLgK i eLK3 63 Q aLbKC 64 C Regression We now use the data to nd values for 1 b7 07 17 and e No production function is exactly like the above two What the regression tells us is what values of 1 6 make the above production function closest7 to the data ie closest to the real world Excel has a simple function linest which will be su icient On the website is an example Excel le that demonstrates how to do a linear regression Statistics can tell us many things besides the values a e We will focus on two other things the Excel le tells us H T stat The T stat tells us if K7 L7 K27 etc likely have any e ect on Q If the T stat for d is small7 then we may want to drop the term LBK from the production function N3 R2 This tells us the percentage of the variation in output that is explained by variation in the inputs If the number is close to one7 the production function is doing a good job describing the real production process If the number is close to zero7 there are some aspects of production being missed Perhaps another input We now have all the pieces in place The steps are as follows 1 Determine the objective and the decision 2 Gather data on inputs and outputs 3 Choose a production function and estimate the coe icients 4 Use calculus to nd the decision which maximizes the objective I have provided an example problem7 with all steps complete COST THEORY Cost theory is similar to production theory they are often used together However the question is usually how much to produce as opposed to which inputs to use That is assume that we use production theory to choose the optimal ratio of inputs eg 2 fewer engineers than technicians how much should we produce in order to minimize costs andor maximize pro ts We can also learn a lot about what kinds of costs matter for decisions made by managers and what kinds of costs do not I What costs matter A Opportunity Costs Remember from Section IV of the Introduction that in addition to accounting pro t managers must consider the cost of inputs supplied by the owners owners capital and labor De nition 13 Explicit Costs Accounting Costs or costs that would appear as costs in an accounting statement De nition 14 Implicit Costs Other costs such as the cost of the owners capital and labor andor the cost of alternative uses of each input De nition 15 Opportunity Costs The value of all inputs to a rm s production in their most valuable alternative use Recall the example from Section IV where the decision was whether or not to buy the shoe factory the implicit costs were the 24000 per year the money could be earning elsewhere and the owners time cost of 40000 which exceeded the accounting pro t of 60000 Another example suppose we run a nancial planning rm with one planner making 60000 Each account takes 10 of her time and she already has 9 clients Our valued sales force gets us two new accounts one is a restaurant owner with 2 million to invest assume a 1 management fee the second is a doctor with 1 million to invest What 24 are the opportunity costs of managing the restaurant owners account The costs are of course the explicit cost of 6000 in salary 10 time7 but also the opportunity cost of 107000 that could be earned managing another account Similarly7 the opportunity cost of the doctors account is 207000 and 6000 The choice is obvious7 manage the restaurant owners account7 but just measuring the accounting costs of 6000 in either case tells us nothing about which account we should manage For fun7 calculate the economic pro t for each account Digression about nancial planning and keeping an eye on the valued customers Do you consider the opportunity cost of your time when you respond to questions from a low value account often the low value accounts are the most time consuming B Fixed costs variable costs and sunk costs The short run is a time period such that some inputs cannot be changed We will de ne the short run as a period of time in which capital and much professional or salaried labor cannot be changed We also assume the short run is long enough so that production workers or non professional labor inputs can be changed We call inputs that can be changed in the short run variable inputs7 and inputs that cannot be changed xed inputs De nition 16 Total Variable Cost The total cost of all inputs that change with the amount produced all variable inputs De nition 17 Total xed costs The total cost of all inputs that do not vary with the amount produced all xed inputs Consider the Thompson machine company The cost of the 5 machines used to make machine parts was xed in the short run7 and therefore a xed cost7 while the number of workers could change and varied with the amount produced These were variable costs A xed cost cannot be changed and thus cannot vary with the amount produced De nition 18 Sunk costs Are costs that have been incurred and cannot be reversed Any costs incurred in the past7 or indeed any xed cost for which payment must be made regardless of the decision is irrelevant for any managerial decision Whether you pumped 2 25 or 2 million trying to break into a new market last year is irrelevant the only question is whether an additional dollar investment will make su icient return The principle of sunk costs is equivalent to the saying don7t throw good money after bad77 in poker Sometimes a decision can be made to recover part of a xed cost Perhaps one could sell a factory and recover part of the xed costs Then only the di erence is sunk For example if we can sell a building for which we paid 500000 for 300000 then only 200000 is sunk Conversely once we pay a signing bonus the bonus is sunk and should not a ect our decision about ring the employee Sunk costs are perhaps one of the most psychologically di icult things to ignore Last night I watched the world series of poker In one instance the odds of drawing a ush and almost for sure winning the hand was 1 in 5 The pot was huge say about 200000 So the player should call any bet less than or equal to 40000 Yet the commentator advised that the player would call regardless of the bet because he already had so much money in the pot sunk costs Another example the Iraq war We have sunk billions but that should not enter our decision about whether or not to stay Another example Consider restaurants in a high rent district say an airport Should they take the rent into account when setting prices No II Short run costs We use short run costs primarily to compute how much to produce while minimizing costs or maximizing pro ts We use long run costs to answer questions like should the rm expand contract merge etc De nition 19 Average Costs Costs divided by output De nition 20 Marginal Costs The cost of one additional unit of an input Here is the notation Type of Cost Total Cost equals Variable Costs Plus Fixed Costs Total TC TVC TFC Average ATC AVC if AFC T570 Marginal MC Properties of cost functions in the short run 1 Total costs of course increase with Q7 the quantity produced 2 Average Costs decline with Q7 but eventually rise The xed costs are spread over many more units of production at high Q7 reducing average costs All of the extra workers required for producing additional units when the factory is near capacity starts to increase average costs eventually 03 producing one additional unit is cheaper than the last unit Suppose the rm goes from one to two workers The workers can now specialize increasing e iciency How ever7 eventually diminishing returns sets in and the workers just get in each others way Then a very large number of additional workers might be needed to produce an additional unit Marginal costs usually decline then increase7 but must eventually increase At rst7 Here is a graph of the cost curves Tota Cost Funct ons x 0ta Costs 5 FM ed Costs 4 Tota Var ab e Costs Costs perumtm III Examples of using Short run cost curves A Pro t maximization Let us suppose that you are a hypothetical manager of a group of sugar cane farms Using data from your horticulturalists have estimated the short run cost function to be we will see how to do this estimation below Q2 TC 60 7 65 20 Some costs are xed and in the short run7 sunk regardless of Q7 you must pay 60 in xed costs7 so this will not enter your decision Suppose the futures price of sugar cane is 3 per basket7 so you can sell any reasonable amount of sugar cane at this price Maximize pro ts 2 max7rTRiTC393Qi607El0 66 Take the derivative to get the slope and set the slope equal to zero 3700rMRMC 67 Notice that the xed costs have dropped out The math agrees xed costs do not matter for our decision Solving for Q we see that Q 30 Producing the 30th basket gives us 37 just enough to cover our costs of producing the 30th basket7 3 However7 the 31st basket requires more labor than previous baskets due to diminishing returns Producing any more is not pro table Management costs7 taxes7 rent on the farm7 and other xed costs are irrelevant The rm is losing money here TR lt TC But that is irrelevant We have already paid the xed costs7 so we might as well lose as little as possible B Break Even Analysis An important consideration When deciding Whether to continue operations in a particular market expand into a market or start a new business is a break even analysis We can do a break even analysis very easily With our cost functions In a break even analysis the question is how much pro t is required to exactly pay o all xed costs Alternatively how much revenue is required to pay o the average variable costs and the xed costs 7r0TR7TC 68 0PQ7TF07TVC 69 0PQ7TF07AVCQ 70 Here I have assumed linear total costs so that average variable cost is constant One could assume more realistically that total costs are quadratic and then solve for Q using the quadratic formula C Minimizing Average Costs The book pays attention to minimizing cost per unit or average costs Consider a consulting rm With the total cost function TC 10Q 7 6Q2 Q3 72 The rm has no xed costs Average costs are ATC1076QQ2 73 So here is the problem rrgnATC 10 7 6Q Q2 74 Find the slope and set equal to zero 62Q0 Q3 75 When two units are produced AVC1076QQ21076391 76 MC10712Q3Q2107123391 77 So AVC MC when AVC is minimized IV Long Run Costs We use long run costs to decide scale issues7 for example mergers We assume the long run is long enough for all costs to be variable In the long run7 we can build any size factory we wish7 based on anticipated demand7 pro ts7 and other considerations Once the plant is built7 we move to the short run as described above Therefore7 it is important to forecast the anticipated demand Too small a factory and marginal costs will be high as the factory is stretched to over produce Conversely too large a factory results in large xed costs eg air conditioning7 or taxes and low pro tability De nition 21 Long Run Average Costs The minimum cost per unit of producing a given output level when any sized plant can be built Graphically Average cost unit Short Run Average Costs Long Run Average Costs Q Long run average costs may be increasing and then decreasing7 but also may be strictly decreasing Here are some LRAC curves for some industries 1 Nursing Homes have decreasing LRAC Nursing homes have many xed management costs Further7 larger nursing homes are able to negotiate lower prices for many raw materials 2 Cruise Ships Huge cruise ships have lower average costs than small cruise ships7 economizing on many services provided on the ships When the LRAC curve is decreasing7 it is often in the interest of the industry to consol idate A merger with another rm can increase the customer base but reduce the cost per unit7 thus increasing pro ts One reason for increasing long run costs is coordination and information problems In a large rm7 many individuals do not meaningfully a ect pro ts7 and thus have the wrong incentives Smaller operations may know their customers and production processes better In this case7 spin o s and divestments may be optimal A compromise is franchising Nationalize just the parts for which increasing returns works Another reason for increasing LRAC curves is regulation In many countries large rms are taxed to a much greater extent ln addition7 large rms are attractive targets for lawsuits 32 the ladder industry is small Unions may drive up costs in large rms In such industries7 smaller may be better Consider the taxi industry in Peru7 dominated by one employee rms Why not large rms like in the US Because of taxes and other regulations V Application Banking mergers Consider two banks The rst bank services Q 15 customers and the second smaller bank services Q 5 customers The long run average cost function in the industry is LRAC 7 700 7 40Q Q2 78 Revenue is constant at 300 dollars of loan revenue per customer Should these two rms merge The size of the customer base Q which minimizes long run average costs is min LRAC 7 700 7 40Q Q2 79 7402Q0 7Q720 80 Costs per unit fall until Q 20 Thus these two rms can reduce costs by merging from two rms of size Q 15 and Q 5 into one rm with Q 20 Pro t per unit in each case are 7r 7 300 7 700 7 40Q Q2 7 7400 40Q 7 Q2 81 7rQ 7 15 7 7400 4015 7152 7 725 82 7rQ75774004055277225 83 7rQ20 740040207202 70 84 lndiVidually7 the two banks lose money but together they break even VI Measuring Cost Functions We use the same procedure as With production functions Obtain data on total costs and quantity produced7 and use Excel to t the data Both total cost and total quantity produced may appear to be easier to obtain than input data However7 one must remember that costs represent opportunity costs7 Which are not always straightforward Some additional issues A Choice of Cost Function One choice is Whether to use a linear7 quadratic7 or cubic function TC a Mg 85 TC aquQnLcQ2 86 TC a bQ co dQ3 87 Under most circumstances7 the linear cost function does a reasonable job over a narrow range of Q for example in the short run7 but the quadratic and cubic terms must matter theoretically7 especially for a Wider range of Q A good strategy might therefore be to estimate the cubic or quadratic If the t stats are low for the quadratic and cubic terms7 then predictions are likely to be unreliable for Q that falls outside the data This indicates using some caution before7 for example7 committing to large mergers The following graph illustrates the problem Possible Problem Estimating Cost Functions Data is to homogeneous l l l l l 9 data Cost Function 63 5 Estimated Cost Function Estimate 5 inaccurate here 7 Cost B Data issues Some problems with the data that often need correcting H N3 03 Hgt 5quot De nition of cost as mentioned earlier7 we use opportunity costs not accounting costs Price level changes Historical data is likely to be inaccurate if the price of some inputs or outputs have changed dramatically What costs vary with output Some costs have a very limited relationship with output For example7 the number of professionals required may vary in some limited way with output A rm with 1 million in sales may have two accountants The rm can obviously increase output to some degree without needing more accountants so the cost would be xed But for larger Q additional accountants are needed like a variable cost The cost data needs to match the output data Often the cost of producing some output may be accounted for in some other period The rms technology may change over time 35 When estimating long run costs7 it is usually preferable to use a cross section of rms across an industry An individual rm is unlikely to have changed size signi cantly enough to generate data for a Wide range of Q First Quiz Managerial Economics Eco 685 Friday7 February 47 2005 The test is closed notes and goes until 915 Good luck pvZ m2 mTRtiTCt Economic Pro ts accounting pro t 7 return on capital used 7 owners labor abLC 7 671 8a bLC i 8 objective 7 8L 7 bcL 7 T i 7 m i 0 at the rnax1rnurn 8TB 8T0 8TB MRP ainput MR 39 MP7 ME ainput7 8Q ATR ATR MRP Ainput7 Ainput 8Q MPK i p ainput 7 MPL PL TC TFO TVC ATC AFC E AVG TgC MC 8T0 TFO 3Q 7 Qbreak even PiAVC 7 Short Answer 13 sentences Question 1 10 points Give two reasons Why in general maximizing pro ts bene ts society Question 2 10 points Suppose the ratio of marginal products is greater than the price ratio MP5 gt 5 MPH Pu Here 3 is skilled labor and u is unskilled labor Give one strategy to increase pro ts Question 3 5 points Explain Why the marginal product of labor tends to diminish7 holding other inputs xed Question 4 10 points In Peru the median rm size is one employee a Are Long Run Average Costs likely increasing7 decreasing7 or constant b Give one likely reason Why Question 5 5 points A rm paid 5007000 for an option to buy a building for 570007000 The total cost if it buys is 575007000 The rm nds an alternative building for 572507000 Which should it buy Problems Question 6 20 points Broiler chickens are sold for 3 per pound A regression analysis done by the OECD in 1966 determined that the weight in pounds7 Q7 is determined by the pounds of corn7 C7 and soybean oilmeal7 S7 the chickens eat The production function is thus Q 003 0480 064s 7 00202 7 00532 2 The price of corn is 040 per pound and the price of soybean oilmeal is 030 per pound a Calculate the amount of corn and soybean oilmeal that maximize pro ts b Calculate the maximum pro ts c Calculate the quantity of corn and soybean Which maximize production Question 7 20 points Enterprise Corporation makes speedboats Their annual costs are TC Q2 my 150 3 Here Q is the number of speedboats Assume the market for speedboats is competitive7 so that Enterprise can sell any number of speedboats for a price of 50 The 150 in the total costs corresponds to maintenance costs on a warehouse7 that Enterprise has already paid 9 Calculate how many speedboats Enterprise should make to maximize pro ts V Calculate the pro ts of Enterprise Corp 5393 Suppose Enterprise can sell the warehouse for 500 and close operations Should En terprise do so Question 8 20 points Econ students S and co ee C are inputs to the production of economics homework solution sets The production function is Q C s 4 Suppose the price of co ee is 3 and econ students earn a wage of 9 a Explain how co ee a ects the additional production that results from a small increase in the number of econ students b Compute the optimal ratio of co ee per student ie how many cups of co ee should each student consume7 c Suppose the operation has a budget of 36 Compute the optimal amount of co cee7 students7 and solutions sets PRICING So far we have supposed the price of the rms output is xed That is7 the rm can sell as many units as it desires at a xed price Alternatively7 the rm has no pricing power it cannot o er a price above the competition without losing all customers This is reasonable7 for example7 when customers can nd close substitutes when many competing rms exist and the product is a commodity For example7 the sugar farmer who creates a futures contract to sell all output at a xed price can be viewed this way For many most goods the rm has some pricing power Pricing power arises from lack of availability of close substitutes lack of competitors andor from producing a di erentiated product If the rm has some pricing power7 the rm can set a price that is high relative to competitors In this case7 the rm makes more money on each unit7 but of course sells less units only those customers who really like the rms product will buy it7 the rest buy imperfect alternatives from competitors Alternatively7 the rm can cut prices and try to sell more units to make higher pro ts Which is better of course depends on the properties of demand for the rms product which is what we are going to study here We will also evaluate many common pricing strategies Does 99 cent77 pricing pricing something equal to 199 instead of 2 work When should we use coupons or rebates What about setting the price equal to a xed mark up over costs Why do some rms charge 1 for a coke that costs 5 cents to make and 2 for a burger that costs 185 to make We will also study price wars77 and other games rms play against each other I Market Demand Function Quantity demanded is the number of the rms product customers wish to purchase What a ects the quantity demanded 1 Price of the product inversely related to demand 2 Income of consumers positively related to demand 3 Price of competitors positively related to demand 4 Advertising positively related to demand 5 Price of complementary goods inversely related to demand For example the price of cruises is certainly affected by the price of a cruise the rm charges income the price of other cruise lines and other competitors such as vacation packages advertising and the price of goods like sun tan lotion which are complementary with cruises De nition 22 The Market Demand Function is the relationship between the quantity demanded of the product and the various factors that in uence the quantity demanded For example the market demand for Dell computers might be Q i700P 500 7 2003 001A 88 Here A is advertising P is the price of a Dell computer I is income S is the price of software and Q is the quantity demanded Apparently if Dell raises the price by 1 then the quantity demanded falls by 700 units per year How do we nd the market demand function Similar to cost functions we use company data and statistics See below II Price Elasticity and the Optimal Pricing Policy Price elasticity measures how sensitive the market demand function is to changes in the price the rm charges A Price Elasticity of Demand De nition 23 The Own Price Elasticity of Demand is the percentage change in quan tity demanded from a one percent change in price The price elasticity is our primary measure of the rms pricing power Formula eplt2gtlt3gt Alternative formula 7 percent change in Q 90 p percent change in P As elasticity becomes more negative rms lose pricing power Even a small rise in price would mean no goods are sold As 6p gets larger approaches 07 pricing power increases Such rms may increase the price quite a bit and lose little customers elasticity economics term pricing power level of competition 6p foo perfectly elastic none perfect competition 6p lt 71 elastic little competitive 6p 71 unitary elastic moderate moderate competition 71 lt 6p lt 0 inelastic strong imperfect competition 6p 0 perfectly inelastic in nite no competition B Examples Consider the example from Dell computer7 with S A 0 and I 1 Q 500 i 70013 91 i P 8Q ilt P gt 7007 7700P 92 6 7 Q 8P 7 500 i 700p 7 500 i 700p ln general7 the price elasticity varies with P if P 0 then 6p 0 If P then 7 7350 7 ep 7 W 7 7233 Suppose instead the company raises the price from 2 to 3 and the quantity sold falls from 4 units to 2 units Then using the alternative formula 71 93 C Examples and Determinants of Elasticity Determinants of elasticity 1 Level of competition decreases elasticity 2 Degree of product di erentiation increases elasticity 3 Level of income decreases elasticity 4 Length of time decreases elasticity lndustry Price Elasticity Beer 283 Wine 112 music CDs 63 Domestic Cars 078 Foreign Cars 109 Cigarettes 042 everyone 08 young adults Elasticities of products by an individual rm are generally lower less pricing power For example the book quotes Phillip Morris price elasticity for cigarettes at 069 Cigarettes are addictive One might think you can raise the price inde nitely and addicts will continue to buy the product But it is not so makers of discount cigarettes will take your business In addition teenage consumers have little income and therefore cannot a ord large price increases Remember the own price elasticity is a ected largely by the availability of close substitutes which is in turn determined by the number of competitors and how di erent their products are product di erentiation The table indicates demand for Beer to be elastic Products are di erentiated helped by prodigious amounts of advertising but many competitors exist as well Wine sales are more inelastic perhaps wine drinkers have more income Entertainment music CDs tend to be very elastic A host of substitutes and competitors including down loaded music and movies exist D Example Set the price to maximize pro ts Suppose the rm is interested in maximizing pro ts but now we allow the rm to change the price For each price the rm may choose there is a corresponding quantity that consumers 40 will demand Conversely7 for each level of quantity demanded7 there is a corresponding price For example if Q 5 i 2P 94 Then P Q Q77 lt95 In other words if we wish to sell 4 units7 then we need to charge 3 050 Suppose total costs are TC 10 7 Q Q2 We are maximizing pro ts max7r TR 7 TC 96 Notice now total revenues are more complicated7 since the price we can charge changes with the quantity produced max ijQ i 10 i Q Q2 97 max7Q225Q710Q7Q2 715Q23Q710 98 7152Q30 Q1 99 The optimal price to charge is then Pa 2 2 100 What is the elasticity BQP 7n234 101 81 1 6p Notice that the optimal pricing policy is one in which demand is elastic7 where the rm has little pricing power If the rm had pricing power 6p gt 71 then the rm could raise prices With a relatively small decrease in sales Thus it makes sense to raise prices When 6p gt 717 so the optimal price has 6p 3 71 E Optimal pricing policy I Will now derive a formula that determines the optimal price and quantity produced max7r TR 7 TC 102 Substitute in for Q max7r P Q Q 7 TC 103 Take the derivative With respect to Q here I am using an additional rule of calculus and set equal to zero 813 QHwQ 7M0 0 104 Notice that the derivative is part of the formula for elasticity 1 PQ if P 7M0 6p Q 0 Q o 105 MR P i 1 MC 106 6p P 7 71 MC 107 i1 Notice that the rm never chooses a price Which results in an inelastic price elasticity lf 6p gt 71 then marginal revenue is negative and so MR lt MC If the rm increases prices7 then revenues rise because prices increase but the quantity sold falls only a little Further costs fall since we are producing less The price is a constant mark up over marginal costs P 7 t Mark up amp 108 cost lMC 7 MC M k ep 109 ar up MC 1 71 Mark up 1 71 110 7 1 ep 1 Examples If the price elasticity is 72 then P ill MC or P 2M0 so we charge a mark up of ii 1 100 over marginal costs As ep a 700 the rm has no pricing power and we must charge the minimum price possible P MC no mark up Consider a swimming pool company who charges a 100 mark up over the wholesale price for example if the manufacturer charges 10 for chlorine then charge 20 This is a mistake Our mark up should be over marginal costs which include things like labor Further the rm is not taking into account the elasticity the pool store down the street sold the same stu so price elasticity was low III Other Elasticities De nition 24 The Income Elasticity of Demand is the percentage change in quantity demanded from a 1 change in consumers income Formula 8Q I 61 7 g 111 We can think of income as the income of the consumers who buy the product But we can also think of income as the state of the economy as a whole If the income elasticity is positive a high income elasticity corresponds to quantity demanded being very sensitive to income Consider two examples Milk eI 005 and European cars 61 193 The economy income grew by 4 last quarter We can expect demand for milk to rise by 43 4 005 02 while demand for European cars should rise by 4 193 772 European cars are sensitive to income because they are not necessities In good times when income is rising products with a high income elasticity do better luxuries however products with a low income elasticity do better in bad times necessities A primary use of the income elasticity is thus in forecasting demand Here is the economic jargon for income elastiticty income elasticity economics term 61 gt 1 Luxury Good Normal Good 0 lt 61 lt 1 Necessity Normal Good 61 lt 0 lnferior Good Other elasticities can also be computed for example the advertising elasticity IV Estimating Demand To nd the market demand function we use the same technique as when we nd the cost and production functions We need to assemble data on quantity demanded and the various factors that a ect quantity demanded such as price and income The data sources are similar 1 Time Series Data Get historical data on demand and price income etc 2 Cross Section Data Get data from various geographic locations 3 Conduct a randomized study Select a random set of consumers and change the price Note that the randomized study is easier here than in the case of estimating the produc tion function A famous example is Amazoncom which recently randomized prices o ered to consumers who went to their website although there was a lot of uproar Market demand functions need to be constantly re estimated Consumers sometimes buy without shopping around based on say a reputation for low prices This can make demand look inelastic But after a price change consumers slowly learn the rm does not have the lowest price and switch making demand elastic V Evaluating Pricing Strategies Cost plus pricing Now we will look at various pricing strategies and what economists think about them Cost plus pricing similar to that used in the pool store example above is setting the price equal to a constant mark up over average costs Examples Onsalecom sells at the wholesale price plus a xed transaction fee77 Auto dealers sell at dealer cost77 Of course we want to set a constant mark up over marginal costs not average costs Further wholesale costs ignore costs like labor But on occasion wholesale costs and marginal costs can be close For example the auto dealer The cost of rent etc are sunk costs Even part of the inventory cost is sunk The salesperson is paid with commission Thus for retail cars the marginal cost is close to the wholesale price VI Evaluating Pricing Strategies Price Discrimination De nition 25 Price Discrimination is selling a product at more than one price Examples of price discrimination coupons rebates college discounts senior citizen dis counts and even selling products with the same cost at di erent prices in wealthy and poor neighborhoods Consider the market demand function Q 50 7 2P At P 5 40 units are demanded At P 10 30 units are demanded We lose 10 customers assume each customer buys 1 unit when we raise the price from 5 to 10 Who are the 10 price sensitive customers Quite possibly these customers might be college students seniors or the poor If we instead charge 10 but with a senior citizen discount of 5 then we can still sell to 40 customers but raise the price for 30 of them A Example Airline Suppose demand for business travel b consumer travel 0 are PC 107Qc 112 Pb 20 715Qb 113 Total costs are To 42Q0Qb 114 We choose a price in each location to maximize pro ts rnaX7r TR 7 TC 115 maxPch Pbe i 4 2 Q Qb 116 rnaxlOQcngjLZOQbi15le7 7472Q672Qb 117 rnaX8QciQ 18Qbi 15g 74 118 872Qc0 an4 119 1873Qb0 a Qb6 120 The prices are Pc10746 121 Pb20715611 122 We discriminate against the business traveler7 by say7 charging 6 dollars for a ight that stays over on a Saturday7 and 11 for a ight that does not Pro ts are 7r1166474724666 123 With no price discrimination7 total costs are TC 4 2Q 124 Demand With a single price is P 10 7 QC 125 P 20 715Qb 126 Thus Q6 10 7 P 127 40 2 Qb 3 7 gP 128 QQ0Qb P 129 3 P 14 7 gQ 130 Now doing the problem Without price discrimination7 we charge P 87 sell Q 10 units7 and make pro ts of 8 10 7 4 7 2 10 567 less than in the case Where we can discriminate B Degrees of discrimination H First degree discriminate against every customer Example negotiated prices such as cars7 Pricelinecom N Second degree discriminate based on quantity purchased Example buy one7 get second one at half price 03 Third degree discriminate against a group Example senior discounts 47 First degree discrimination has the highest revenues However7 you have to pay your sales force more when they negotiate More information about the customers are required C Pitfalls of discrimination So discrimination raises pro ts if you can do it Discrimination does not always work though H Discrimination requires a lack of competition If two auto dealers exist on the same block7 the customer can negotiate the price down to marginal cost N There are information costs For example7 the need to hire commission based sales people 03 A target group is not always easy to identify Some seniors and college students are wealt hy7 for example 4 Arbitrage can sometimes result Those with discounts can buy and resell to those who do not 5quot Legal restrictions Price discrimination can be illegal Example minority scholarships VII Evaluating Pricing Strategies 99 cent pricing A common pricing strategy is 99 cent pricing77 or charging 199 instead of 2 The rst thing to remember is that this strategy entails certain time costs Lines say at the cash register build up when the sale amount is not a round number If the purchase is time sensitive7 say lunches or snacks at an arena7 then the manager must either hire additional clerks or lose sales What are the bene ts One advantage is theft prevention A clerk must make change and therefore open the cash register7 creating a paper trail 99 cent pricing originated at the same time as the cash register No evidence exists that consumers believe 199 is really 1 VIII Evaluating Pricing Strategies Flat rate pricing and price confusion The pricing system above equates supply and demand However the price system at say an airline can get extremely complicated Each ight has a di erent demand curve and price discrimination increases the number of prices for each ight In some cases rms will use at rate prices one price for many similar goods to attract customers Flat rate pricing cannot equate supply and demand for all goods Therefore shortages and surpluses often result When the rm has a shortage or surplus of goods pro ts fall o setting the gains made by attracting customers In general consumer7s pay by having to buy earlier than desired or face the possibility of a shortage For example AOL charges a at rate rather than increase the price of the Internet during high tra ic business hours and reducing the rate at night like cell phones do Consumers still pay by dealing with a slow Internet during the daytime AOL hopes that the at rate price attracts more customers than are lost due to slow tra ic Other industries like cell phones introduce a complicated pricing scheme on purpose to confuse customers This is price discrimination Like a coupon only the most price sensitive customers will search for the lowest rate However a simple rebate system would likely create the same e ect and not annoy the customers as much IX Evaluating Pricing Strategies The popcorn problem Sometimes the pricing of certain related products is very di erent Consider popcorn at the Movies Movie tickets are sold at a relatively small markup over marginal costs but popcorn which costs next to nothing to produce is sold for very high prices Similarly for a hamburger and a coke Let us examine the possibile explanations First let us dispense with the obvious answer Unlike airports which have a monopoly on air travel one has a choice for resturants and movie theaters Movie theaters cannot charge more for popcorn because consumers are trapped at the movie theater Competition usually erce exists since most customers can go to the theater with the lowest combined price of popcorn and tickets A theater which lowered the price of popcorn could presumably increase sales dramatically 49 One possible explanation is price discrimination against popcorn lovers Are popcorn lovers less price sensitive Perhaps7 but again high cornpetition tends to reduce price dis crimination In the end7 no fully satisfactory explanation has been put forward This pricing strategy remains a mystery to econornists X Evaluating Pricing Strategies Other We Will look at price wars77 and discount pricing in the next section

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