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

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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 Budget Line Scones Indifference Curve Q coffees Q scones

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

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

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

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

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

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

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

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

Coffee Scones Utility = 342 Q coffees Q scones

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

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!

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

Production Efficiency Capital Isocost Labor Isoquant Q capital Q labor

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

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

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

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

The Cost Min. Combination Capital Labor Q capital Q labor

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.

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

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.

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.

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.

Firm A Capital Labor Scones = 100 1 3

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

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

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

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.

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

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

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

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

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

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

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.

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.

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.

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

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

The Edgeworth Box Chris Coffee Scones

The Edgeworth Box Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

The Edgeworth Box Chris Pat Coffee Scones

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

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

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

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

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

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

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.

The burlap lens of Pareto Improvements Chris Pat Coffee Scones

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.

Exchange Efficiency No mutually beneficial trades are possible.

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

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