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Demystifying Efficiency in the Economics Classroom

Demystifying Efficiency in the Economics Classroom. David A. Anderson Centre College. Consumption Efficiency. Goods and services are purchased so as to maximize utility Condition: The Optimal Consumption Rule. The Model. Coffee. Q coffees. Indifference Curve. Budget Line. Q scones.

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Demystifying Efficiency in the Economics Classroom

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  1. Demystifying Efficiency in the Economics Classroom David A. Anderson Centre College

  2. Consumption Efficiency Goods and services are purchased so as to maximize utility Condition: The Optimal Consumption Rule

  3. The Model Coffee Qcoffees Indifference Curve Budget Line Qscones Scones

  4. Indifference Curve Coffee All the combinations of coffee and scones that give you the same level of happiness Utility = 342 Scones

  5. Indifference Curve Slope(Marginal Rate of Substitution) Suppose that at a particular point, MUs = 50 and MUc = 10 Coffee Slope = -MUs/MUc = -MRS = -50/10 = -5 Utility = 342 Scones

  6. Indifference Curve Coffee Utility = 1361 Utility = 933 Utility =618 Utility = 410 Utility = 342 Utility = 11 Scones

  7. Budget Line Coffee All the combinations of coffee and scones that you can afford with a given budget Scones

  8. Budget Line Coffee Pc = 4 Ps = 2 10 7 2 Budget = $40 6 20 16 Scones

  9. Budget Line Coffee Ps = 2 Pc = 4 10 7 Slope = -Ps/Pc = -2/4 = -1/2 2 6 20 16 Scones

  10. Money Spent, U not Maximized Coffee Utility = 1361 Utility = 933 Utility =618 Utility = 410 Utility = 342 Utility = 11 Scones

  11. The U Max Combination Coffee Utility = 1361 Utility = 933 Utility =618 Utility = 410 Utility = 342 Utility = 11 Scones

  12. The U Max Combination Coffee Qcoffees Utility = 342 Qscones Scones

  13. Slopes are Equal at Tangency Point Coffee -Ps/Pc = -MUs/MUc Qcoffees Indifference Curve Budget Line Qscones Scones

  14. Beginning with the tangency condition: -Ps/Pc = -MUs/MUc cancel negative signs,multiply both sides by MUc, divide both sides by Ps: MUc/Pc = MUs/Ps The Optimal Consumption Rule! Coffee Qcoffees Indifference Curve Budget Line Qscones Scones

  15. Production Efficiency The production of any mix of goods in the least costly way. Conditions: P = min ATC MPL/w = MPK/r RTSFirm A = RTSFirm B

  16. Production Efficiency Capital Qcapital Isoquant Isocost Qlabor Labor

  17. Isoquant = One Quantity Capital All the combinations of capital and labor that produce the same level of output Scones = 200 Labor

  18. Isoquant Slope(Marginal Rate of Technical Substitution) Suppose that at a particular point, MPL = 10 and MPK = 30 Capital Slope = -MPL/MPK = RTS = -10/30 = -1/3 Scones = 200 Labor

  19. Isocost = One Cost Capital All the combinations of capital and labor that cost a certain amount Cost = $300 Labor

  20. Isocost Slope Capital Wage (w) = 15 Rental rate (r) = 3 100 Slope = - w/r = -15/3 = -5 20 20 16 Labor

  21. The Cost Min. Combination Capital Qcapital Qlabor Labor

  22. Slopes are Equal at Tangency -w/r = -MPL/MPK cancel negative signs,multiply both sides by MPk, divide both sides by r: MPL/w = MPK/r Again, the goal is simply to maximize bang per buck. Capital Qcapital Labor Qlabor

  23. What we really want for productive efficiency is for each firm to have the same rate of technical substitution (MPL/MPK): RTSFirm A = RTSFirm B

  24. The Intuition The rate of technical substitution is the rate at which one input can be substituted for another while holding output constant. Suppose Firm A has RTS = MPL/MPK = 1/3. It can substitute 1 machine for 3 workers and make the same amount of output.

  25. The Intuition The rate of technical substitution is the rate at which one input can be substituted for another while holding output constant. Suppose Firm A has RTS = MPL/MPK = 1/3. It can substitute 1 machine for 3 workers and make the same amount of output. Suppose also that Firm B has RTS = 1. It can substitute 1 machine for 1 worker and make the same amount of output.

  26. The Intuition The rate of technical substitution is the rate at which one input can be substituted for another while holding output constant. Suppose Firm A has RTS = MPL/MPK = 1/3. It can substitute 1 machine for 3 workers and make the same amount of output. Suppose also that Firm B has RTS = 1. It can substitute 1 machine for 1 worker and make the same amount of output. An exchange of (for example) 2 workers from Firm A for 1 machine from Firm B will allow both firms to produce more output.

  27. Firm A Capital 1 Scones = 100 3 Labor

  28. Firm A Capital 2 Scones = 110 1 Scones = 100 3 Labor

  29. Firm B Capital 1 Scones = 115 Scones = 100 1 2 Labor

  30. Mission Accomplished If wages and rental rates are the same for each firm, w/r will be the same for each firm, and so by setting RTS = w/r to minimize costs, each firm will have the same RTS. Firm A’s MPL/MPK = w/r = Firm B’s MPL/MPK

  31. P = Min ATC Selecting inputs such that RTS = w/r is necessary in order to minimize ATC, so the P = Min ATC condition implies the tangency condition we have discussed.

  32. Allocative Efficiency The available inputs are allocated to produce the most desirable combination of goods and services Simple Condition: P = MC Alternative Conditions: MB = MC MRS = MRT

  33. Production Possibilities FrontierSlope = -Marginal Rate of Transformation (-MRT) Coffee Slope = -MRT = -MCS / MCC Scones

  34. Tangency Condition Coffee MRT = MRS Qcoffees Social Indifference Curve Qscones Scones

  35. How Perfect Competition Gets Us to MRS = MRT • We know that from consumption efficiency (utility maximization), MUS/MUC = PS/PC • We know that in perfect competition, PS = MCS and PC = MCC • Thus, PS/PC = MCS/MCC • Put this together and we have MUS/MUC = PS/PC = MCS/MCC or MRS = MRT

  36. So we’re here indeed! Coffee MRT = MRS Qcoffees Social Indifference Curve Qscones Scones

  37. Distributive Efficiency Goods and services are received by those with the greatest need. To make someone better off you must make someone else worse off. Condition: MRSChris = MRSPat

  38. The Intuition The marginal rate of substitution is the rate at which one good can be substituted for another while holding utility constant. Suppose Chris has MRS = MUS/MUC = 1/3. Chris can substitute 1 coffee for 3 scones and receive the same level of utility.

  39. The Intuition The marginal rate of substitution is the rate at which one good can be substituted for another while holding utility constant. Suppose Chris has MRS = MUS/MUC = 1/3. Chris can substitute 1 coffee for 3 scones and receive the same level of utility. Suppose that Pat has MRS = 1. Pat can substitute 1 coffee for 1 scone and receive the same level of utility.

  40. The Intuition The marginal rate of substitution is the rate at which one good can be substituted for another while holding utility constant. Suppose Chris has MRS = MUS/MUC = 1/3. Chris can substitute 1 coffee for 3 scones and receive the same level of utility. Suppose that Pat has MRS = 1. Pat can substitute 1 coffee for 1 scone and receive the same level of utility. An exchange of (for example) 2 scones from Chris for 1 coffee from Pat will allow both people to be happier.

  41. Chris Coffee 2 Utility = 437 1 Utility = 400 3 Scones

  42. Pat Coffee 1 Utility = 215 Utility = 200 1 2 Scones

  43. The Edgeworth Box Coffee Scones Chris

  44. The Edgeworth Box Pat Coffee Scones

  45. The Edgeworth Box Pat Coffee Scones Chris

  46. The Edgeworth Box Pat Coffee Scones Chris

  47. The Edgeworth Box Pat Coffee Scones Chris

  48. The Edgeworth Box Pat Coffee Scones Chris

  49. The Edgeworth Box Pat Coffee Scones Chris

  50. The Edgeworth Box Pat Coffee Scones Chris

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