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

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

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The Model Coffee Budget Line Scones Indifference Curve Q coffees Q scones

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

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

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

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

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Budget Line Coffee Budget = $40 Scones P c = 4 P s = 2 10 20 7 16 2 6

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Budget Line Coffee Scones P s = 2 P c = 4 10 20 7 16 2 6 Slope = -P s /P c = -2/4 = -1/2

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

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

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Coffee Scones Utility = 342 Q coffees Q scones

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Slopes are Equal at Tangency Point Coffee Scones Indifference Curve Q coffees Q scones Budget Line -P s /P c = -MU s /MU c

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Coffee Scones Indifference Curve Q coffees Q scones Budget Line Beginning with the tangency condition: -P s /P c = -MU s /MU c cancel negative signs, multiply both sides by MU c, divide both sides by P s : MU c /P c = MU s /P s The Optimal Consumption Rule!

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Production Efficiency The production of any mix of goods in the least costly way. Conditions: P = min ATC MP L /w = MP K /r RTS Firm A = RTS Firm B

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Production Efficiency Capital Isocost Labor Isoquant Q capital Q labor

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

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

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

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

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The Cost Min. Combination Capital Labor Q capital Q labor

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Slopes are Equal at Tangency Capital Labor Q capital Q labor -w/r = -MP L /MP K cancel negative signs, multiply both sides by MP k, divide both sides by r: MP L /w = MP K /r Again, the goal is simply to maximize bang per buck.

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What we really want for productive efficiency is for each firm to have the same rate of technical substitution (MP L /MP K ): RTS Firm A = RTS Firm B

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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 = MP L /MP K = 1/3. It can substitute 1 machine for 3 workers and make the same amount of output.

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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 = MP L /MP K = 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.

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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 = MP L /MP K = 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.

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Firm A Capital Labor Scones = 100 1 3

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

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

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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 MP L /MP K = w/r = Firm B’s MP L /MP K

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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.

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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

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Production Possibilities Frontier Slope = -Marginal Rate of Transformation (-MRT) Coffee Slope = -MRT = -MC S / MC C Scones

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Tangency Condition Coffee Scones Social Indifference Curve MRT = MRS Q coffees Q scones

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How Perfect Competition Gets Us to MRS = MRT We know that from consumption efficiency (utility maximization), MU S /MU C = P S /P C We know that in perfect competition, P S = MC S and P C = MC C Thus, P S /P C = MC S /MC C Put this together and we have MU S /MU C = P S /P C = MC S /MC C or MRS = MRT

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So we’re here indeed! Coffee Scones Social Indifference Curve MRT = MRS Q coffees Q scones

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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: MRS Chris = MRS Pat

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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 = MU S /MU C = 1/3. Chris can substitute 1 coffee for 3 scones and receive the same level of utility.

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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 = MU S /MU C = 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.

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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 = MU S /MU C = 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.

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

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

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The Edgeworth Box Chris Coffee Scones

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The Edgeworth Box Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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The Edgeworth Box Chris Pat Coffee Scones

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To make someone better off you must make someone else worse off. MRS Chris = MRS Pat Chris Pat Coffee Scones

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Production Efficiency (RTS Firm A =RTS Firm B ) helps get us on the PPF Coffee Scones

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Allocative Efficiency puts us at the right point on the PPF Coffee Scones Social Indifference Curve MRT = MRS Q coffees Q scones

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Distributive Efficiency Gets goods to the right people Coffee Scones Q coffees Q scones MRS Chris =MRS Pat

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Social Efficiency Usually synonymous with allocative efficiency, but more often in the context of externalities Condition: MSC = MSB

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Economic Efficiency Various interpretations, including a combination of allocative and productive efficiency

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Pareto Efficiency Essentially, this means there is no waste. The Pareto criterion depends on the context: Allocative: No one can be made better off without making someone worse off. Productive: An increase in the production of one good necessitates a decrease in the production of another good. Distributive: No one can receive more of a good without someone else receiving less.

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The burlap lens of Pareto Improvements Chris Pat Coffee Scones

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Kaldor-Hicks Efficiency Similar to Pareto efficiency except that the mutual improvement need only be possible. With Kaldor-Hicks efficiency, no changes that would create a net gain are possible, whether or not everyone would actually be at least as well off as before. If you gain more than I lose, this is Kaldor-Hicks efficient because you could compensate me. It is not Pareto efficient if you don’t make me at least as well off as before.

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Exchange Efficiency No mutually beneficial trades are possible.

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X-efficiency Efficiency motivated by competition. With X-inefficiency, the lack of competition leads to laziness, overinvestment, etc.

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