# Eco 685 Graphs, Tables, and Definitions

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1 Eco 685 Graphs, Tables, and Definitions David L. Kelly 1 1 Department of Economics, University of Miami Fall, 2017

2 Introduction Introduction

3 Managerial Economics Definition Definition 1 Managerial Economics is the application of economic theory to decisions made by managers and firms. Definition 2 Economics is the study of the allocation of scarce resources.

4 Value of the Firm Definition 3 The value of a firm is the present value of the firm s expected future profits.

5 Economic Profits Definition 4 Economic Profits Revenues less opportunity costs. Definition 5 Accounting Profits Revenues less accounting costs Definition 6 Opportunity Cost Accounting costs plus the value of inputs in their next best use.

6 Production Theory Part I: Production Theory

7 Definition Definition 7 The Production Function is a graph, table, or equation showing the maximum output rate that can be achieved by any specified set of inputs.

8 Table Form Q = 30L+20L 2 L 3 (0.1) Full time laborers (L) Parts Produced (Q) Table 1 : Production data for Thompson Machine Co.

9 Table Form Q = 30L+20L 2 L 3 (0.2) Full time laborers (L) Parts Produced (Q) Table 1 : Production data for Thompson Machine Co.

10 Graph Form Output of Thompson Machine Co Q=Parts Produced Per Year Slope or derivative of objective is zero at the maximum. Adding Laborer increases production ( Positive Marginal Product ). Adding an 11th laborer increases production more than adding a 12th laborer (diminishing marginal product) L=Full Time Laborers Per Year Figure 1 : Typical production function using one input.

11 Marginal Product Definition 8 The Marginal Product is the additional output from an additional unit of an input.

12 Marginal Product Table Full time laborers (L) Parts Produced (Q) Marginal Product (MP) Table 2 : Production function and marginal product.

13 Marginal Product Table Full time laborers (L) Parts Produced (Q) Marginal Product (MP) Table 2 : Production function and marginal product.

14 Marginal Revenue Product and Marginal Expenditure Definition 9 Marginal Revenue Product is the amount of additional revenue from an additional unit of an input. Definition 10 The Marginal Expenditure is the amount of additional costs from an additional unit of input.

15 Marginal Revenue Product and Marginal Expenditure Table Full time laborers (L) Parts Produced (Q) Marginal Product (MP) Marginal revenue product (MRP = MR MP) Table 3 : Production function and marginal revenue product.

16 Marginal Revenue Product and Marginal Expenditure Table Full time laborers (L) Parts Produced (Q) Marginal Product (MP) Marginal revenue product (MRP = MR MP) \$24, \$41, \$55, \$73, \$79, \$58, \$21, \$-10,500 Table 3 : Production function and marginal revenue product.

17 Isoquant Definition Definition 11 An Isoquant is a curve which shows all possible input levels capable of producing a given output level.

18 Isoquant Graph K K 0 K 1 Q=30 Q=20 L 0 L 1 Slope= K or= dk L (negative) dl Q=10 Figure 2 : Isoquants for a typical production function corresponding to Q = 10,20,30. L

19 MRTS and Isocost Definition 12 The Marginal Rate of Technical Substitution (MRTS) is the rate at which one input is substituted for another while keeping production constant. It is the negative of the slope of the isoquant. Definition 13 The Isocost curve shows all input combinations that have the same total budget.

20 Isocost Graph K M P K Slope= P L P K M P L Figure 3 : Isocost for a budget of M. L

21 Optimal Inputs K MRT S> p L p K 2b 2a K L 1b 1a MRT S< p L p K Q<10 Q=10 Figure 4 : Efficient and inefficient input combinations. L

22 Returns to Scale Definition 14 The production function exhibits Increasing (decreasing, constant) returns to scale if increasing all inputs by a proportion increases output by more than (less than, exactly) the same proportion

23 Output Elasticity Definition 15 The output elasticity is the percentage increase in output from a one percent increase in inputs.

24 Production Theory Part II: Cost Theory

25 Accounting and Opportunity Costs Definition 16 Accounting Costs: Costs that would appear as costs in an accounting statement. Definition 17 Opportunity Costs: The value of all inputs to a firm s production in their most valuable alternative use.

26 Fixed, Variable, and Sunk Costs Definition 18 Total Variable Cost The total cost of all inputs that change with the amount produced (all variable inputs). Definition 19 Total fixed costs The total cost of all inputs that do not vary with the amount produced (all fixed inputs). Definition 20 Sunk costs Are costs that have been incurred and cannot be reversed.

27 Average and Marginal Costs Definition 21 Average Costs: Costs divided by output. Definition 22 Marginal Costs: The cost of one additional unit of an input.

28 Cost Formulas Type of Cost Total Cost equals Variable Costs Plus Fixed Costs Total TC = TVC +TFC Average ATC = TC Q = TVC AVC = Q +AFC = TFC Q Marginal MC = dtc dq = TC Q

29 Short Run Total Costs 500 Total Cost Functions 450 Total Costs Total Fixed Costs Total Variable Costs Cost (\$) Q Figure 5 : Typical short total cost curves.

30 Short Run Average and Marginal Costs 120 Short Run Cost Functions 100 Average Total Costs Average Fixed Costs Average Variable Costs Marginal Costs 80 Costs per unit (\$) Q Figure 6 : Typical short run average and marginal cost curves.

31 Average vs Marginal Costs Cruises (Q) Total variable costs Marginal costs (MC) (TVC) = (20 2 )/20 = 20 = (20 0)/(20 0)= 1 25 = (25 2 )/20 = = ( )/(25 20) = Table 4 : Variable costs on a cruise ship.

32 Average vs Marginal Costs Gas Production (Q) Typical Data Total costs (TC) Average Total costs (ATC) Marginal Costs (MC) Calculate this! Profits (π)

33 Average vs Marginal Gas Production (Q) Typical Data Total costs (TC) Average Total costs (ATC) Marginal Costs (MC) Calculate this! Profits (π)

34 Long Run Average Costs Average cost (\$/unit) Short Run Average Costs small plant medium size plant Long Run Average Costs Q Q d Cost of making Cost of making Q d with a Q d with a small plant medium plant Figure 7 : Long run average cost curve.

35 Plant Size Example Cost Type Plant Size AVC Small Medium Large Labor \$3.70 \$2.50 \$1.10 Materials \$1.80 \$1.40 \$0.90 Other \$2.00 \$2.60 \$3.00 TFC \$25,000 \$75,000 \$300,000 Capacity 50, , ,000 Table 7 : Plant size and LRAC.

36 Plant Size Example Long Run Average Cost Curve Small Factories Medium Factories Large Factories LRAC cost per unit units Figure 8 : Long run average cost curve.

37 Market Demand Table Price of beer Quantity Demanded \$ \$5 500 \$7 300 \$10 90 Table 8 : Market demand for beer.

38 Elasticity Meaning elasticity economics term pricing level of competition price sensitivity power e p = perfectly elastic none perfect competition very sensitive e p < 1 elastic little competitive sensitive e p = 1 unitary elastic moderate moderate competition moderate 1 < e p < 0 inelastic strong imperfect competition not very sensitive e p = 0 perfectly inelastic infinite no competition insensitive Table 9 : Terminology for price elasticity.

39 Calculate Price Elasticity Using the Table Price of beer Quantity Demanded e p \$ NA \$5 500 \$7 300 \$10 90 Table 10 : Price elasticity for beer.

40 Calculate Price Elasticity Using the Table Price of beer Quantity Demanded e p \$ NA \$ \$ \$ Table 11 : Price elasticity for beer.

41 Elasticity: Examples Industry Price Elasticity Interpretation Beer elastic/price sensitive Wine inelastic/insensitive Domestic Cars inelastic/insensitive Foreign Cars elastic/sensitive Cigarettes (everyone) inelastic/insensitive Cigarettes (young adults) -0.8 inelastic/insensitive Prescription Drugs inelastic/insensitive Emergency Room Visits inelastic/insensitive Legal Services -0.4 inelastic/insensitive Higher Education -1.1 elastic/sensitive Fresh Tomatoes -4.6 elastic/sensitive Economy airline tickets elastic/sensitive First class tickets inelastic/insensitive Table 12 : Price elasticities across industries.

42 Table 13 : Average and marginal costs in the gas industry. Table of Optimal Price Typical Data Calculate this! Q P TR TC ATC MC MR P ATC π

43 Table 14 : Average and marginal costs in the gas industry. Table of Optimal Price Typical Data Calculate this! Q P TR TC ATC MC MR P ATC π

44 Income Elasticity Income Elasticity Economics Term Sensitivity e I > 1 Luxury Good, Normal Good Sensitive to income 0 < e I < 1 Necessity, Normal Good Not sensitive 1 < e I < 0 Inferior Good Not sensitive e I < 1 Inferior Good Sensitive Table 15 : Meaning of income elasticity.

45 Payoff Matrix Definition 23 The payoff matrix lists all rewards that each player gets as a function of decisions made by all players.

46 Price War Game Firm B Hold prices Cut prices Firm A Hold prices 3,3 1,4 Cut prices 6,-1 0,0 Table 16 : Payoff matrix for the price war game.

47 Dominant Strategy Definition 24 A Dominant Strategy is an action that is at least as good as all other actions regardless what the opposing player chooses.

48 Nash Equilibrium Definition 25 A Nash Equilibrium is a set of strategies such that each player accurately believes that he/she is acting optimally given the strategy of the other players. Definition 26 A (non) credible threat is a threat that it is (not) optimal to carry out.

49 Nash Equilibrium Definition 25 A Nash Equilibrium is a set of strategies such that each player accurately believes that he/she is acting optimally given the strategy of the other players. Definition 26 A (non) credible threat is a threat that it is (not) optimal to carry out.

50 Price War Game II Firm B Hold prices Cut prices Firm A Hold prices 3,3 1,4 Cut prices 5,1 0,0 Table 17 : Price war game, version 2.

51 Price War Game II Firm B Hold prices Cut prices Firm A Hold prices 3,3 1, 4 Cut prices 5, 1 0,0 Table 18 : Price war game, version 2.

52 Price War Game II Firm B Hold prices Cut prices Firm A Hold prices 3,3 1, 4 Cut prices 5, 1 0,0 Table 19 : Price war game, version 2.

53 Coordination Game Car B B s Left Side B s Right Side Car A A s Left Side 10,10-5,-5 A s Right Side -5,-5 10,10 Table 20 : Typical coordination game.

54 Coordination Game Car B B s Left Side B s Right Side Car A A s Left Side 10, 10-5,-5 A s Right Side -5,-5 10, 10 Table 21 : Typical coordination game.

55 Anti-Coordination: Reduce Competition Buell Sport Bikes Cruisers Harley Sport Bikes 0,0 5,2 Cruisers 2,5 0,0 Table 22 : Anti-coordination game.

56 Anti-Coordination Game Buell Sport Bikes Cruisers Harley Sport Bikes 0,0 5, 2 Cruisers 2, 5 0,0 Table 23 : Anti-coordination game.

57 Store Location Game Target Uptown Center City East Side West Side Macy s Uptown 30,40 50,95 55,95 55,120 Center City 115,40 100, ,85 120,95 East Side 125,45 95,65 60,40 115,120 West Side 105,50 75,75 95,95 35,55 Table 24 : Location game. Coordinate or not?

58 Store Location Game Target Uptown Center City East Side West Side Macy s Uptown 30,40 50,95 55,95 55,120 Center City 115,40, ,85 120,95 East Side 125,45 95,65 60,40 115,120 West Side 105,50 75,75 95, 95 35,55 Table 25 : Location game. Coordinate or not?

59 Price War Firm B Hold prices Cut prices Firm A Hold prices 3,3 0,5 Cut prices 5,0 1,1 Table 26 : Prisoner s dilemma game.

60 Price War Firm B Hold prices Cut prices Firm A Hold prices SB = 6 SB = 5 Cut prices SB = 5 SB = 2 Table 27 : Social benefit of the prisoner s dilemma game.

61 Price Matching Firm B Hold and match prices Cut prices Firm A Hold and match prices 3,3 1,1 Cut prices 1,1 1,1 Table 28 : Price matching game.

62 3 Player Game Alec Sells April Sells Holds out Jack Sells 45,45,45 50,40,50 Holds Out 40,50,50 48,48,65 Alec Holds Out April Sells Holds Out Jack Sells 50,50,40 65,48,48 Holds Out 48,65,48 48,48,48 Table 29 : Takeover game.

63 3 Player Game Alec Sells April Sells Holds Out Jack Sells 45, 45, 45 50,40, 50 Holds Out 40, 50, 50 48,48, 65 Alec Holds Out April Sells Holds Out Jack Sells 50, 50,40 65,48,48 Holds Out 48, 65,48 48,48,48 Table 30 : Takeover game solution.

64 Blue Light Special Customer Shop today Shop tomorrow Firm Sale today 4,12 8,6 Sale Tomorrow 12,8 6,10 Table 31 : Blue light special game.

65 Anti-Coordination Customer B Shop TJ Maxx Shop Macy s Customer A Shop TJ Maxx 4,4 10,7 Shop Macy s 7,10 5,5 Table 32 : Anti-coordination game.

66 Sequential Anti-Coordination Expand Apple: \$50 Million Samsung: \$50 Million Samsung Expand Don t Expand Apple: \$150 Million Samsung: \$60 Million Apple Don t Expand Expand Apple: \$60 Million Samsung: \$120 Million Samsung Don t Expand Apple: \$80 Million Samsung: \$80 Million Figure 9 : Anti-coordination game in sequential form.

67 Sequential Anti-Coordination Expand Apple: \$50 Million Samsung: \$50 Million Apple earns \$150 here Samsung Expand Equilibrium Path Don t Expand Sub game perfect Nash eq. Apple: \$150 Million Samsung: \$60 Million Apple Don t Expand Expand Apple: \$60 Million Samsung: \$120 Million Samsung Apple earns \$60 here Don t Expand Apple: \$80 Million Samsung: \$80 Million Figure 10 : Anti-coordination game in sequential form.

68 Simultaneous First Mover Samsung Expand Don t Expand Apple Expand 50,50 150,60 Don t Expand 60,120 80,80 Table 33 : Simultaneous first mover game.

69 First Mover Advantage Definition 27 First Mover Advantage: Advantage to the first mover in sequential games when the simultaneous game has multiple Nash Equilibria.

70 Entry Game Cut Prices AMD: \$6 Million Intel: \$3 Million Intel Enter Don t Cut Prices AMD: \$12 Million Intel: \$4 Million AMD Don t Enter Cut Prices AMD: \$9 Million Intel: \$8 Million Intel Don t Cut Prices AMD: \$9 Million Intel: \$13 Million Figure 11 : Entry game.

71 Entry Game Cut Prices AMD: \$6 Million Intel: \$3 Million Intel Enter AMD; \$12 Don t Cut Prices AMD: \$12 Million Intel: \$4 Million AMD Don t Enter AMD \$9 Cut Prices AMD: \$9 Million Intel: \$8 Million Intel Don t Cut Prices AMD: \$9 Million Intel: \$13 Million Figure 12 : Entry game.

72 Entry Game II Intel Cut Prices AMD: \$6 Million Intel: \$3 Million AMD Enter Don t Cut Prices AMD: \$12 Million Intel: \$4 Million Don t Expand Don t Enter Cut Prices AMD: \$9 Million Intel: \$8 Million Intel Intel Don t Cut Prices AMD: \$9 Million Intel: \$13 Million Intel Cut Prices AMD: \$6 Million Intel: \$3 Million Expand Enter Don t Cut Prices AMD: \$12 Million Intel: \$2 Million AMD Don t Enter Cut Prices AMD: \$9 Million Intel: \$6 Million Intel Don t Cut Prices AMD: \$9 Million Intel: \$11 Million

73 Entry Game II AMD: \$12 Intel Cut Prices AMD: \$6 Million Intel: \$3 Million AMD Enter Don t Cut Prices AMD: \$12 Million Intel: \$4 Million Intel Intel \$4 Don t Expand Don t Enter AMD: \$9 Intel Cut Prices Don t Cut Prices AMD: \$9 Million Intel: \$8 Million AMD: \$9 Million Intel: \$13 Million Intel \$11 Expand AMD \$6 Enter Intel Cut Prices Don t Cut Prices AMD: \$6 Million Intel: \$3 Million AMD: \$12 Million Intel: \$2 Million AMD Don t Enter Cut Prices AMD: \$9 Million Intel: \$6 Million AMD \$9 Intel Don t Cut Prices AMD: \$9 Million Intel: \$11 Million

74 Preemption Definition 28 Preemption is an action taken to deter later actions by other players.

75 Summary and Takeaways 1 Be on the lookout for better opportunities. Avoid committing time and resources to low-profit endeavors. 2 Think marginally. Think: is this hire going to bring in more revenue that his/her salary? Think: is this client going to bring in more revenue than the cost of servicing the client? Avoid thinking in terms of averages. These tell you only what has happened in the past. 3 Ignore sunk costs. It is sometimes painful, but one has to sometimes ignore the sunk costs and move on. Hanging on too long because of past investments can cause more pain later.

76 Summary and Takeaways cont. 4 Think carefully about expansion. The graveyard is littered with firms that over-expanded. Conversely many firms get stuck at a size which is too small. Find a way (merge/expand/spin-off/fire clients) to get to an ideal size. 5 Use tiered pricing tricks. Profits are not easy to come by. Getting some extra profits by charging different prices to different groups is one of the few easy ways to increase profits. 6 Predict: how will competitors react to my plan? Try to anticipate the reaction of other firms and coworkers to your plans.

77 Summary and Takeaways cont. 7 Remember: other firms and consumers will eventually react to your decisions. Avoid decisions which are easy to react to, such as having a sale at the end of every month. Consumers will catch on quickly. 8 Segment markets. Avoid head-to-head competition. In general, it is better to segment a market by producing a version of a product which is of interest only to a subset of the consumers, than to compete head on with an established firm. 9 Preempt, do not react. Acting preemptively is always cheaper and more decisive than reacting to moves by other firms.

78 Repeated Prisoner s Dilemmas Firm B Hold prices Cut prices Firm A Hold prices 3,3 0,5 Cut prices 5,0 1,1 Table 34 : Prisoner s dilemma game.

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