Economics of Strategy (ECON 4550) Maymester 2015 Overview of Alternative Competitive Environments

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1 Economics of Strategy (ECON 4) Maymester 2 Overview of Alternative Cometitive Environments Definitions and Concets: Profit Total Revenues minus Total Costs. Primary objective of most rivate enterrise is to maximize rofit Cost-Benefit Princile a rational decision maker should undertake an action if and only if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so. For rofit maximization, think about increasing uantity roduced/sold and comaring Marginal Revenue to Marginal Costs In general, if a firm sells (Q) units of outut each at a rice of (P), then Total Revenue is eual to (Q)(P) => but, the behavior of Marginal Revenue deends greatly uon the Market Structure in which the firm oerates Continuum of Market Structure: Perfect Cometition Intermediate Market Structures (e.g., Duooly, Oligooly, Monoolistic Cometition) Monooly Market Power a firm has market ower if: (i) it can increase the rice of its roduct without losing all customers, or euivalently (ii) it must decrease the rice of its roduct in order to sell additional units. Market Power control over rice Firms in erfectly cometitive markets have no market ower [face a horizontal demand curve at the market rice determined by the interlay of market demand and market suly] Firms in imerfectly cometitive markets (i.e., all other market structures) have at least some market ower [ downward sloing demand curve ]

2 Marginal Revenue the change in Total Revenue as uantity sold is increased If demand is given by the Inverse Demand Function P D (, then R( PD (, and it follows that MR( P ( P ( Price Elasticity in terms of Inverse Demand: From here, P D ( P ( D D D % Q % P Q Q P P => Marginal Revenue can be exressed as P PD ( P Q P D( Q MR ( ) P D ( ) Fixed Costs costs that do not vary in magnitude as the uantity of outut roduced is changed Variable Costs costs that do vary in magnitude as the uantity of outut roduced is changed Total Costs are eual to the sum of Variable Costs and Fixed Costs: C( VC( F. Average Total Costs Total Costs divided by uantity of outut roduced => C( ATC( Average Variable Costs Variable Costs divided by uantity of outut roduced => VC( AVC( Average Fixed Costs Fixed Costs divided by uantity of outut roduced => F AFC( Average Total Costs are eual to the sum of Average Variable Costs and Average Fixed Costs: C( VC( F VC( F ATC( AVC( AFC( Marginal Costs the change in Total Costs as uantity of outut roduced is increased => MC( C( VC( Efficient Scale the efficient scale of roduction refers to the uantity of outut at which Average Total Costs of roduction are minimized. Short Run a eriod of time sufficiently short so that the amount hired/used of at least one inut is eual to some redetermined level (based uon a revious decision) In the short run, the fixed inuts are being hired in redetermined uantities => fixed costs reresent the redetermined costs of hiring these fixed inuts in their redetermined uantities

3 Long Run a eriod of time sufficiently long so that the amount hired/used of every inut can be varied In the Long run the firm has the flexibility to hire zero units of every inut => incur zero costs of roduction => fixed costs are eual to zero => all costs are variable Otimal Choice of Outut in Short Run by a firm in a Perfectly Cometitive Market: a firm in a erfectly cometitive market (in which the revailing rice for outut is ) maximizes rofit by: (i) shutting down and roducing units of outut if AVC min (ii) roducing the ositive uantity of outut for which MC ( ) (with MC intersecting MR from below ) if AVC min Long Run Dynamics of Perfectly Cometitive Market => recall, a Perfectly Cometitive Market is characterized by Free Entry/Exit in the Long Run If firms currently in the market are earning ositive rofits in the Short Run, then: o New firms will enter the market, increasing market suly o Increase in suly leads to a decrease in euilibrium rice, driving down rofits of firms in the industry o Entry will continue and rice will gradually decrease until rofit of firms in the industry is driven down to zero If instead firms currently in the market are earning negative rofits in the Short Run, then: o Some existing firms will exit the market, decreasing market suly o Decrease in suly leads to an increase in euilibrium rice, driving u rofits of firms in the industry o Exit will continue and rice will be gradually increase until rofit of firms in the industry is driven u to zero In either case, the outcome of this rocess is one in which firms in the industry are earning zero rofit Since ( C( ATC( this condition of zero rofit imlies ATC( at the Long Run euilibrium o If rice is driven to ATC( in the Long Run and firms are still maximizing rofit in the Short Run (i.e., MC( ), it follows that in the Long Run we must have MC( ATC( => firms are oerating at the oint where ATC ( is minimized (i.e., at the Efficient Scale of roduction), thereby minimizing the industry s total costs of roduction Inverse Elasticity Pricing Rule to maximize rofit, a firm must be oerating where the marku of rice above marginal costs as a ercentage of rice is eual to minus the inverse of rice elasticity of demand. When demand is less elastic (i.e., closer to zero consumers not very sensitive to rice), a firm with market ower will set a rice for which the ercentage marku of rice over MC is greater

4 Total Social Surlus a measure of the total gains to society from economic activity in a market As long as there are no external effects, Total Social Surlus is eual to the sum of Total Consumers Surlus and Total Producers Surlus Deadweight Loss (DWL) the difference between the maximum ossible level of Total Social Surlus and the realized level of Total Social Surlus. DWL is zero at the efficient level of trade DWL is ositive at all other levels of trade. Inefficiency from too little trade there are some units that are not traded for which trade would generate a ositive net gain for society i.e., we don t trade all units that we should trade (absent external effects) these are units that are not traded even though buyer s reservation rice is greater than seller s reservation rice Inefficiency from too much trade there are some units that are traded for which trade generates a negative net gain for society i.e., we trade some units that we should not trade (absent external effects) these are units that are traded even though seller s reservation rice is greater than buyer s reservation rice Monooly a market structure in which there is one single seller of a uniue good (for which there are no close substitutes) and in which there are significant barriers to entry which revent rival firms from entering the market in many resects, Monooly is the olar oosite of Perfect Cometition in the Long Run (since entry barriers revent new firms from entering the market) a monoolist can otentially earn a ositive rofit eriod after eriod Monoolistic Cometition market structure in which cometing firms sell differentiated roducts (and thus, each firm has some market ower in the Short Run) and in which there are no substantial barriers to entry examles: gas stations, harmacies, restaurants, and grocery stores; novels; movies in the Long Run free entry will result in many firms bring in the market (with rofit of each firm being driven to zero) [we ll exand uon this below] Oligooly market structure in which firms sell very similar roducts (i.e., slight differentiation ), but in which there are significant barriers to entry which revent most otential rivals for entering the market Examles: Coke/Pesi, XBox/Playstation/Wii In most resects, closer to Pure Monooly than to Perfect Cometition Because of entry barriers, there will end u being relatively few firms in the market in the Long Run There is no one-size-fits-all model of Oligooly => will develo and analyze multile models later in the course

5 Four Firm Concentration Ratio (C4) a measure of industry concentration defined as the ercentage of total industry sales made by the four largest firms in the industry (C4 ranges between and a higher value suggests the industry is more concentrated or less cometitive). Herfindahl-Hirschman Index (HHI) a measure of industry concentration defined as the sum of the suared values of market shares over all firms in the industry (HHI ranges 2 between and, a higher value suggests the industry is more concentrated or less cometitive). Selected Real World Values of C4 and HHI: Industry: C4: HHI: Electric Light Bulbs Breakfast Cereals Automobiles Aluminum Sheet/Plate/Foil Telehone Euiment.3 6. Women s Footwear Soft Drink Manufacturing Semiconductors Comuters and Periherals Cement Manufacturing Petroleum Refineries Paer Manufacturing Textile Mills

6 Relation between Marginal Revenue and Price for (i) Firm with no market ower faces horizontal demand curve => erfectly elastic demand or MR P ( P ( ( => Marginal Revenue is constant and eual to rice D D Intuitive: when rice is simly eual to some constant regardless of uantity sold, then selling one more unit always increases revenue by exactly dollars $ P D ( => MR( (ii) Firm with some market ower or control over rice Faces downward sloing demand => MR( P D ( => Thus, for a firm with market ower Marginal Revenue is: Less than Price. Visually: $ ( P D Positive (droing rice and increasing uantity demanded leads to greater revenue) Negative (droing rice and increasing uantity demanded leads to less revenue) Eual to zero (which must be true if total revenue is maximized) MR (

7 Grahical illustration of Costs of Production: Minimum level of Average Total Costs $ MC( ATC( AVC( Minimum level of Average Variable Costs Quantity of outut which minimizes AVC( Efficient Scale Quantity of outut which minimizes ATC( Efficient Scale the efficient scale of roduction refers to the uantity of outut at which Average Total Costs of roduction are minimized. For the first unit of outut, Variable Costs are eual to simly marginal costs of the first unit => AVC( must start out eual to MC( But total costs for the first unit consist of more than just variable costs of the first unit => ATC( will start out above MC( Since ATC = AVC + AFC => AFC = ATC AVC AFC is the vertical distance between ATC and AVC Since AFC decreases as ( increases => red curve and blue curve must get closer to each other as ( increases

8 Short Run choice of outut and rofitability of a firm in a Perfectly Cometitive Market: Thus, the short run suly curve of this firm is essentially: the ortion of the Marginal Cost Curve which lies above the Average Variable Cost Curve. Minimum value of AVC $ Short Run Suly Curve of Firm => curve illustrating uantity sulied as a function of rice (at all ossible market rices) MC( AVC( uantity uantity at which AVC are minimized For all ossible ositive rices we have that a rofit maximizing firm oerating in a erfectly cometitive market in the short run will: Minimum Value of Average Variable Costs Minimum Value of Average Total Costs Price of Outut Shut Down and roduce zero units of outut Earn a rofit of ( F) Produce a ositive uantity of outut Maximum rofit is negative, but greater than ( F) Produce a ositive uantity of outut Able to earn a ositive rofit

9 Short Run Profit Maximization for firm with Market Power: $ MC( P* ATC( ATC(Q*) Demand Q* MR( uantity maximize rofit by charging P* er unit and selling Q* units of outut (Profit) = (Total Revenues) (Total Costs) = [P*][Q*] [Q*][ATC(Q*)] = [Q*][P* ATC(Q*)] = ( light green area above ) In the grah above (Profit)> => but, even a firm with market ower is not guaranteed a ositive rofit (if the height of the ATC( curve was greater than the height of the Demand curve at every uantity, then maximum rofit would be negative) In fact, it may be best for a firm with market ower to shutdown and roduce zero units of outut in the Short Run => if the height of the AVC( curve was greater than the height of the Demand curve at every uantity, then the firm would maximize rofit by roducing zero units of outut in the Short Run (and realizing a rofit of ( F)) When a firm with market ower maximizes rofit, a ositive Deadweight-Loss results: P* $ CS PS DWL MC( MR( Demand Q* Q E uantity

10 Numerical Examles of Industry Concentration Measures: Suose we observe the following market shares (i.e., fractions of total industry outut or of total industry revenues across several different industries) Industry A Industry B Industry C Industry D Industry E A: (C4) = ( ) = (HHI) = ( ) =,66 B: (C4) = (3+++8) = (HHI) = ( ) =,44 C: (C4) = (6+++) = (HHI) = ( ) = 4,37 D: (C4) = ( ) = (HHI)=( )=4,966 E: (C4) = ( ) = (HHI) = ( ) = 2, Observations from the receding numerical examle Value of (C4) does not deend uon anything beyond the 4 th firm => comare Industry A to Industry E Value of (C4) does not deend uon how the market shares are distributed among the To 4 firms => comare Industry A to Industry C Across two different industries: there can be big differences in structure with only small differences in the value of (C4) ; and further the ordinal values of (C4) might run counter to our intuition => comare Industry D to Industry A or E (clearly D is closer to Monooly, but it has a smaller value of (C4) ) (HHI) and (C4) can give different orderings C4: A, C, and E are tied for closest to Monooly, and are closer to Monooly than D HHI: ordering from closest to Monooly to closest to Perfect Cometition of: D, C, E, A, B

11 Monoolistically Cometitive Market in Long Run: (i) Suose Short Run Profits are Positive (i.e., ATC( dis below demand) => new firms want to enter (and can since there are no barriers to entry ) Entry of new firms increases the available otions for consumers => thereby reducing demand for all individual firms initially in the market Continued entry occurs until demand for each firm decreases enough so that rofit of the firm is driven down to zero (ii) Suose Short Run Profits are Negative (i.e., ATC( is above demand everywhere) => existing firms want to exit Exit of existing firms decreases the available otions for consumers => thereby increasing demand for all firms which remain in the market Continued exit will occur until demand increases enough so that rofit of each firm is driven u to zero Short Run situation after entry or exit has occurred to the oint where rofit of the firm is driven to zero => whether we start with ositive rofits or start with negative rofits, the market will reach the same state in the Long Run $ MC( ATC( ATC(Q*)= P* Q* MR( Demand uantity Demand just barely touches (and is everywhere else below ) the Average Total Cost Curve => zero rofit This oint of tangency between Demand and ATC occurs at the one uniue uantity at which Marginal Revenue is eual to Marginal Costs Two notable features of the Long Run Euilibrium in Monoolistically Cometitive Market:. due to the cometitive nature of the market (i.e., entry is ossible), Long Run rofits are driven to zero => rice is eual to Average Total Costs 2. because firms have market ower, demand is downward sloing and marginal revenue is therefore less than rice => firms roduce a uantity of outut for which rice is greater than Marginal Costs (ositive DWL from too little trade )

12 Comarison of Monoolistic and Perfect Cometition in LR: ATC ( Q*) P * $ MR( MC( ATC( MC( Q PC ) P PC ATC( QPC ) Q * Q PC Demand uantity Excess Caacity Monoolistically Cometitive Market: in the Long Run, sell Q *, each at a rice of P* ATC( Q*) MC( Q*) Perfectly Cometitive Market: in the Long Run, sell Q PC, each at a rice of PPC MC( QPC ) ATC( QPC ) Excess Caacity amount by which the outut of a firm is less than the efficient scale of outut a firm with excess caacity could decrease ATC of roduction by increasing outut => in a monoolistically cometitive market, the industry s total costs of roduction are not minimized Marku: Monoolistically Cometitive firm charges a rice above marginal costs of the last unit roduced (a Perfectly Cometitive firm charges (rice)=(mc) ) Would you want another customer come through the door ready to buy at your current rice? yes for Monoolistically Cometitive firm but don t care for Perfectly Cometitive firm

13 Multile Choice Questions:. is a market structure in which firms sell differentiated roducts (and thus, each firm has some market ower in the Short Run) and in which there are no substantial barriers to entry in the Long Run. A. Monoolistic Cometition B. Oligooly C. Monooly D. Perfect Cometition 2. Suose that as the rice of shoes decreases from $4 to $3 Total Consumer Exenditures on shoes increases from $8, to $84,. From this information we can infer that over this rice range demand is A. Inelastic. B. Unit Elastic C. Elastic. D. None of the above answers are necessarily correct (based uon the given information). 3. Consider a market in which the efficient level of trade is 28, units. If 3, are traded, then Deadweight Loss A. would be ositive. B. would be eual to zero. C. would be negative. D. could ossibly be ositive or negative (it deends uon how elastic demand is). 4. In Industry X : the largest firm roduces 2% of total industry outut, the second largest firm roduces % of total industry outut, and the third largest firm roduces 9% of total industry outut. From this information alone we know that A. this market is Perfectly Cometitive. B. the value of the Four Firm Concentration Ratio is greater than 49. C. the value of the Herfindahl-Hirschman Index in this industry is exactly eual to 93. D. More than one (erhas all) of the above answers is correct.. The Efficient Scale of Production refers to A. the level of outut above which all Fixed Costs can be avoided. B. the level of outut which minimizes Average Fixed Costs of roduction. C. the level of outut which minimizes Average Total Costs of Production. D. the level of outut at which Marginal Costs of Production become negative. 6. In which of the following industry structures is there free entry? A. Monoolistic Cometition. B. Oligooly. C. Perfect Cometition. D. More than one (erhas all) of the above answers is correct.

14 7. rovides a direct, general measure of the total gains to society from economic activity in a market. A. Deadweight-Loss B. Monooly Surlus C. Total Social Surlus D. Profit 8. For a firm with market ower, while for a firm in a erfectly cometitive market. A. Marginal Revenue is eual to Price; Marginal Revenue is less than Price. B. Marginal Revenue is less than Price; Marginal Revenue is greater than Price. C. Marginal Revenue is less than Price; Marginal Revenue is eual to Price. D. Marginal Revenue is greater than Price; Marginal Revenue is eual to Price. 9. The is defined as a eriod of time sufficiently long so that the amount hired/used of every factor of roduction can be altered. A. Profitability Stage B. Efficient Scale of Production C. Short Run D. Long Run. Excess Caacity refers to A. the difference between Revenue and Variable Costs of Production. B. the maximum ossible amount of outut that a firm can roduce. C. the amount by which the outut of a firm is less than the efficient scale of outut. D. the amount by which the outut of a firm has increased between the last eriod of roduction and the current eriod of roduction.. According to the Inverse Elasticity Pricing Rule, when maximizing rofit a firm must be oerating in a manner so that is eual to A. P. B. P MC. C. P. MC D. P MC. P 2. The states that a rational decision maker should undertake an action if and only if the Marginal Benefit from taking the action is at least as great as the Marginal Cost of doing so. A. Cost-Benefit Princile B. Incentive Princile C. Inverse Elasticity Pricing Rule D. Herfindahl-Hirschman Index

15 3. In which of the following industry structures should a firm exect to earn zero rofit in the Long Run? A. Perfect Cometition. B. Monoolistic Cometition. C. Monooly. D. More than one (erhas all) of the above answers is correct. For uestions 4 through 7, consider a firm with costs of roduction as illustrated below: $ ATC min ATC( AVC( AVC min.6 uantity 2 8, 4. Based uon the grah above, this firm is currently oerating in the A. Long Run, since no Marginal Cost Curve has been drawn. B. Long Run, since Average Fixed Costs clearly increase as more outut is roduced. C. Short Run, since Marginal Costs of roduction are clearly ositive. D. Short Run, since Fixed Costs of Production are clearly ositive.. The Marginal Cost of roducing the 9 th unit of outut must be A. exactly eual to $.6. B. greater than $.6, but less than $7.2. C. exactly eual to $7.2. D. greater than $ The Efficient Scale of roduction is eual to units of outut. A. B. 2 C. 8 D., 7. If this firm were to roduce, units of outut, Average Variable Costs of Production would be eual to A.. B. $.6. C. $.7. D. $8.7.

16 8. Consider the automobile industry and the textile mills industry. The value of the Herfindahl-Hirschman Index for automobiles is (2,862.8), while the value of the Herfindahl-Hirschman Index for textile mills is (94.4). These values directly suggest that A. both the textile mills and automobile industries are Pure Monoolies. B. roducers of automobiles incur roduction costs which are over 3 times greater than the roduction costs incurred by textile mills. C. the total value of outut roduced by automobile factories is over 3 times greater than the value of outut roduced by textile mills. D. the automobile industry is less cometitive than the textile mills industry. For uestions 9 through 2, consider a monoolist oerating in the market illustrated below. Suose throughout that the monoolist is restricted to charging a common rice for every unit of outut sold $ 4 6, 9. In order to maximize rofit this monoolist should A. sell, units of outut. B. sell 4 units of outut C. charge a rice of $2 er unit. D. More than one (erhas all) of the above answers is correct. 2. The efficient level of trade in this market is A. 4 units. B. 6 units. C., units. D.,2 units. MC( MR( AVC(,2 Demand uantity 2. The maximum rofit of this monoolist would be exactly eual to $ if Fixed Costs were A. exactly eual to $6 B. exactly eual to $, C. exactly eual to $,4 D. None of the above answers are correct (since a monoolist is always able to earn a ositive rofit).

17 22. Scott sells turnis in a small, rural town in Oklahoma. Since he is the only turni seller in town, he has some market ower. He is currently charging $.7 for each five ound bag of turnis, a rice at which he sells 4 bags er month. If he were to increase his uantity sold to bags er month A. he would have to decrease the rice he charges. B. his Average Total Costs of roduction would have to be lower. C. his Total Revenue would have to increase. D. More than one (erhas all) of the above answers is correct. For uestions 23 through 2, consider a firm in a erfectly cometitive market with costs of roduction as illustrated below: 2. $ MC( ATC( 9. ATC min 8. AVC( 6.. AVC min 4.3 MC min 3. uantity 8,4 2, 2,4 23. If this firm were to roduce zero units of outut in the short run, then A. it would earn zero rofit. B. it would earn a rofit of $( 2,2). C. it would earn a rofit of $( 6,). D. it would earn a rofit of $( 6,9). 24. If the er unit rice of outut in this market were $2., then this firm would A. roduce 2,4 units of outut. B. incur Variable Costs of Production eual to $,6. C. earn a rofit of $3,2. D. More than one (erhas all) of the above answers is correct. 2. This firm will roduce a ositive uantity of outut in the short run but earn a negative rofit if and only if the er unit rice of outut is A. less than $3.. B. less than $4.3. C. exactly eual to $4.3. D. greater than $4.3 but less than $8..

18 26. Average Total Costs of Production A. are eual to Average Variable Costs of Production lus Average Fixed Costs of Production. B. are defined as Fixed Costs of Production divided by uantity of outut roduced. C. can never be less than Average Variable Costs of Production. D. More than one (erhas all) of the above answers are correct. 27. The short run suly curve of a firm in a erfectly cometitive market is A. a horizontal line at the revailing market rice. B. a horizontal line at the minimum value of Average Total Costs of Production. C. the ortion of the Marginal Cost curve which lies above the Average Variable Cost Curve. D. the ortion of the Marginal Cost curve which lies above the Average Total Cost Curve. 28. Consider a firm with costs of roduction given by C ( 3,, facing demand of 94, D( ) (i.e., uantity demanded as a function of rice is eual to 94, (3 / 2) divided by rice raised to the ower of three-halves). When maximizing rofit this firm A. is not able to earn a ositive rofit. B. should charge a rice of $3 er unit. C. should sell 3, units of outut. D. More than one (erhas all) of the above answers is correct. 29. Consider a firm in a erfectly cometitive market with: outut rice of $4.9 er unit; AVC min $.2; and ATC min $6.8. When maximizing rofit in the short run, this firm A. will shut-down and earn a negative rofit. B. will shut-down and earn zero rofit. C. will roduce a ositive uantity and earn a negative rofit. D. will roduce a ositive uantity and earn a ositive rofit.

19 Problem Solving or Short Answer Questions:. Consider a market in which demand is given by the demand function D( ) 6, 2,. A. Is demand Elastic, Inelastic, or Unit Elastic at a rice of 2? Exlain. B. If rice were to decrease from to. 89 would Total Consumer Exenditures on this good increase, decrease, or remain constant? Exlain. C. Is it ossible for Total Consumer Exenditures on this good to eual $3,? Clearly exlain why or why not. 2. Consider a firm oerating in a erfectly cometitive market with roduction costs of 2 C ( 8 2,. 2A. Determine exressions for MC (, AVC (, and ATC ( for this firm. 2B. Determine an exact rice above which the firm will choose to sell a ositive uantity of outut in the Short Run and below which the firm will choose to shutdown in the Short Run. 2C. Determine a function which secifies the uantity of outut that this firm will choose to roduce in the Short Run (as a function of market rice, ). 2D. For what range of values of is this firm able to earn a ositive rofit in the Short Run? For what range of values of is this firm not able to earn a ositive rofit in the Short Run? Exlain. 3. Consider a firm oerating in a erfectly cometitive market with roduction costs of 3 2 C ( 22,. 3A. Determine the functional form of MC (. 3B. Determine the functional form of AVC (. 3C. Determine the functional form of ATC (. 3D. Determine an exact rice above which the firm will choose to sell a ositive uantity of outut in the Short Run and below which the firm will choose to shutdown in the Short Run Consider a firm with roduction costs of C( F, facing demand of 648,8 D( )..2 4A. Determine the er unit rice that this firm would set and the uantity of outut that this firm would sell in order to maximize rofit. 4B. For what range of values of F is this firm able to earn a ositive rofit in the Short Run? For what range of values of F is this firm not able to earn a ositive rofit in the Short Run? Exlain.

20 . Consider a firm oerating in a erfectly cometitive market in the Short Run. The table below rovides a artial summary of costs of roduction for this firm. (Assume throughout that the firm is restricted to choosing from only the uantities of outut corresonding to each of the rows in the table below; in this context, Marginal Costs are eual to the change in Total Costs divided by the change in Quantity of Outut roduced that is, MC TC Q ). Quantity of Outut Variable Costs Fixed Costs Total Costs Marginal Costs Average Variable Costs Average Fixed Costs Average Total Costs 2, 2, 2 79,2 6, 6,64 4 2, 4, ,6 2,4,4 2, 4,67 A. Comlete the table above by correctly filling in all of the missing numerical values. B. If this firm is able to sell its outut for $3, er unit, how much outut would it sell, how much revenue would it earn, and is it able to earn a ositive rofit? C. If this firm is able to sell its outut for $, er unit, how much outut would it sell, how much revenue would it earn, and is it able to earn a ositive rofit? 6. Dan is the President and CEO of Owl Softdrinks, the roducer of Scray Cola. The consumer research division of Owl Softdrinks recently told Dan that under current market conditions (i.e., for the demand that the firm currently faces and at the rice that the firm is currently charging) the Price Elasticity of Demand for Scray Cola is aroximately (.79). Assuming that this value has been estimated correctly, what can you infer about the current ricing and outut decision of this firm? 2 7. Consider a firm with roduction costs of C ( 4 7, facing demand given by the inverse function P D ( A. Determine exressions for MC ( and MR ( for this firm. 7B. Determine the er unit rice that this firm would set and the uantity of outut that this firm would sell in order to maximize rofit. 7C. Determine the uantity of outut that would maximize Total Social Surlus in this market. 7D. Determine numerical values for Total Consumers Surlus, Total Producer s Surlus, Profit, and Deadweight-Loss in this market. 7E. Determine an exression for Price Elasticity of Demand as a function of uantity sold for the inverse demand function given above. 7F. Verify that when maximizing rofit, the firm is choosing a rice and uantity for which the Inverse Elasticity Pricing Rule is satisfied.

21 Answers to Multile Choice Questions:. A 2. C 3. A 4. B. C 6. D 7. C 8. C 9. D. C. D 2. A 3. D 4. D. B 6. D 7. C 8. D 9. B 2. B 2. B 22. A 23. C 24. D 2. D 26. D 27. C 28. C 29. A Answers to Problem Solving or Short Answer Questions: A. Inelastic. Note that the given demand function of D( ) 6, 2, describes a linear demand relationshi. The corresonding linear demand curve has a vertical intercet of 8 and a horizontal intercet of 6,. Thus, the oint along the demand curve at a rice of 2 lies on the bottom half of the demand curve. Recall that for any linear demand curve, demand is Inelastic along the bottom half of the curve. B. Increase. A decrease in rice from to. 89 is a movement down this linear demand curve along the to half of the demand curve. Recall that for any linear demand curve, demand is Elastic along the to half of the curve. Further, when demand is Elastic, a decrease in rice will (in general) lead to an increase in Total

22 Consumer Exenditures on the good. Thus, this decrease in rice leads to an increase in Total Consumer Exenditures. C. No, given this demand function it is not ossible for Total Consumer Exenditures to eual $3,. Recall that in general Total Consumer Exenditures can be increased: if demand is Elastic by decreasing rice, and if demand is inelastic by increasing rice. It follows that along any linear demand curve, Total Consumer Exenditures are maximized at the one oint where demand is unit elastic (the halfway oint of the curve ). For the demand function D( ) 6, 2, this halfway oint corresonds to a rice of 4 and uantity of 8,. Thus, Total Consumer Exenditures are maximized when 8, units are urchased each at a rice of $4. This leads to Total Consumer Exenditures of ( )( ($4)(8,) $32, $3,. 2A. Given the cost function ( ) 2 2 C, : MC C( 2, 8 ( 4 VC( C(, AVC ( 8 2, and ATC( B. The firm will choose to sell a ositive uantity of outut in the Short Run if and only if rice is greater than the minimum value of Average Variable Costs of roduction. From VC( the function AVC ( 8 2, it is straightforward to see that the minimum value of Average Variable Costs over all ossible is realized at : AVC min AVC() 2. 2C. So long as rice is greater than or eual to $2, the firm maximizes rofit by roducing the ositive uantity for which MC(. Given MC 2, this condition is ( Solving for as a function of, we obtain S ( ) 4 8,. 2D. A firm in a erfectly cometitive market will be able to earn a ositive rofit in the Short Run so long as rice is greater than the minimum value of Average Total Costs of roduction. Recall that at the oint where ATC ( achieves its minimum value, we must have MC( ATC(. Thus, we can determine the uantity of outut that minimizes ATC ( by setting MC( ATC( and solving for. Doing this:, ATC( MC( ) 2 4,, 2,. From here it follows that ATC min ATC (2,) 2. Therefore, the firm is able to earn a ositive rofit in the Short Run if and only if er unit rice is above $2. 3A. For ( ) C 22, we have MC ( C( B. For ( ) 3 2 VC( 2 C 22, we have AVC ( 22. 3C. For ( ) 3 2 C( 2, C 22, we have ATC( 22. 3D. In the Short Run the firm maximizes rofit by shutting-down and selling zero units of outut if and only if rice is below the minimum value of Average Variable Costs of

23 Production. Recall that at the oint where AVC ( achieves its minimum value, we must have MC( AVC(. Thus, we can determine the uantity of outut that minimizes AVC ( by setting MC( AVC( and solving for. Doing this: ) ( AVC MC ) 22.. ( From here it follows that AVC AVC 2. 7 min Therefore, the firm will choose to sell a ositive uantity of outut in the Short Run if and only if er unit rice is above $2.7. 4A. Recognize that: (i) for C 6 6 ( ) F it follows that MC ( C( and (ii) 648,8 D( ) is a demand function of the constant elasticity form with Recall that the Inverse Elasticity Pricing Rule states that when MC maximizing rofit a firm must be oerating where:. Thus, alying this 6 4 rule we obtain that the firm must be setting a rice for which:. Solving for 648,8 we obtain * 6. This rice results in sales of * D( *) 2, (6) 4B. When charging * 6 and selling * 2, 27, this firm earns revenue of ( *)( *) (6)(2,27) 324,4. Further, roducing * 2, 27 results in costs of 6 C( *) (2,27) F 64, 88 F. From here, the rofit of the firm is: ( *) 324,4 [64,88 F] 29, 2 F. Clearly the firm is able to earn a ositive rofit if and only if F 29, 2. A. (cells with values initially given are highlighted in yellow) Quantity of Outut Variable Costs Fixed Costs Total Costs 39,2 39,2 Marginal Costs Average Variable Costs Average Fixed Costs Average Total Costs 2, 39,2 9,2 2, 2, 3,92,92 2 4, 39,2 79,2 2, 2, 6,96 8,96 3 6, 39,2 99,2 2, 2, 4,64 6,64 4 8, 39,2 29,2 2, 2, 3,48,48 2, 39,2 24,2 2,2 2,4 2,784 4, ,6 39,2 266,8 3,2 2,2 2,4 4,6 64 6, 39,2 299,2,4 2, 2,7 4,67 B. If the firm is able to sell its outut at a rice of $3, er unit, then its Marginal Revenue is eual to $3, for each unit sold. From the values reorted for Marginal

24 Costs in the table above, it follows that the otimal uantity to sell in this case would be units. This would give the firm Total Revenue of $,. But, since the firm would be incurring Total Costs of $24,2, the rofit of the firm is eual to $( 9,2). C. If the firm is able to sell its outut at a rice of $, er unit, then its Marginal Revenue is eual to $, for each unit sold. From the values reorted for Marginal Costs in the table above, it follows that the otimal uantity to sell in this case would be 8 units. This would give the firm Total Revenue of $29,. Since the firm would be incurring Total Costs of $266,8, the rofit of the firm is eual to $(23,2). 6. Recognize that the estimated value of rice elasticity is within the range of inelastic demand. As a result, the firm could actually increase revenue by increasing the rice they charge and selling fewer units of outut. Further, since Marginal Costs of Production should always be greater than or eual to zero (i.e., it should never cost less to roduce more outut), decreasing uantity sold will also decrease costs of roduction. Since Profit is generally eual to (Total Revenues) (Total Costs), it follows that this change must result in greater rofit (again, since it increased Total Revenues and decreased Total Costs). Thus, in general, if we observe a firm that is oerating along an inelastic ortion of their demand curve, we know that the firm is not maximizing rofit. 7A. For ( ) 2 4 C 7 we have MC ( C( 4. When facing demand 2 of P D ( 3 2, Total Revenue can be exressed as R( PD ( 3 2. From here it follows that MR( R( 3. 7B. To maximize rofit, the firm must oerate where MR( MC(. From the functional forms derived above, this reuires: * 3. The otimal rice of the firm is: * P ( *) 3 2 (3) 3. D.. 7C. In order to maximize Total Social Surlus, trade would have to occur exactly u to the oint where MC( PD ( E 36. 7D. Note that grahically we have: $ 3. MC( 4 P D ( *). f b e c d MC ( *) a P D ( * 3 E,3 36 2,6 MR( 3 uantity

25 Total Consumers Surlus is reresented by Areas (e)+(f) in the grah above. Collectively these areas are a triangle with base of 3 and height of.. Thus, Total Consumers Surlus is eual to $22. Total Producer s Surlus is reresented by the sum of Areas (b)+(c) and Area (a) in the grah above. Areas (b)+(c) are collectively a rectangle with base of 3 and height of., and therefore an area of 4. Area (a) is a triangle with base of 3 and height of 6, and therefore an area of 9. Thus, Total Producer s Surlus is eual to $,3. Recall that Profit is eual to Producer s Surlus minus Fixed Costs of Production. Thus, rofit of the firm is eual to ($,3) ($7) = $6. Finally, Deadweight-Loss is reresented by Area (d) in the grah above. This area is a triangle with base of 6 and height of., and therefore has an area of 4. Thus, Deadweight-Loss is eual to $4. % Q PD ( 7E. Price Elasticity of Demand is. For P D ( 3 2 it follows that % P P ( P D ( 2. Thus, P D ( 3 2 2, 6. P D ( 2 7F. To satisfy the IEPR, the firm must be oerating where thus far we have: IEPR is being satisfied. and MC D 2,6 MC 3 2, From the answers. Thus, we see that the