Behind The Supply Curve: Behind The Supply Curve: Production Function IProduction Function I

1. Production - short run1. Production - short run– Productive efficiencyProductive efficiency– The Law of diminishing marginal returnsThe Law of diminishing marginal returns

2. Production - long run2. Production - long run– isoquants & isocostsisoquants & isocosts– least cost method of productionleast cost method of production

BackgroundBackground

Firms seek to maximise profit (Firms seek to maximise profit () ) = R - C= R - C

How do firms produce output and How do firms produce output and minimise costs (C)?minimise costs (C)?

What is production?What is production?“…“…production is simply the process of production is simply the process of

transforming inputs and outputs.”transforming inputs and outputs.” inputs = capital (K) and labour (L)inputs = capital (K) and labour (L)

A production functionA production function

Functional relationshipFunctional relationshipQ = f(K, L , T) Q = f(K, L , T) T changes over time T changes over time At a point in time T is fixedAt a point in time T is fixed

Productive efficiencyProductive efficiency““A method of production is efficient if, for a A method of production is efficient if, for a

given level of factor inputs, it is impossible given level of factor inputs, it is impossible to obtain a higher level of output, given the to obtain a higher level of output, given the existing state of technology.”existing state of technology.”

The short runThe short run

Period of time over which one factor Period of time over which one factor is fixed is fixed

Capital - machines, factory, etc.Capital - machines, factory, etc.

Total and Marginal Physical ProductTotal and Marginal Physical Product“…“…marginal product is the additional output marginal product is the additional output

produced by an additional unit of labourproduced by an additional unit of labourMPP = MPP = TPP / TPP / LL

See FigureSee Figure

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Number of farm workers

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Wheat production per year from a particular farm

Wheat production per year from a particular farm

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Wheat production per year from a particular farm

Wheat production per year from a particular farm

Ton

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TPP

Ton

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Number offarm workers (L)

Number offarm workers (L)

Law of Diminishing ReturnsLaw of Diminishing Returns

Definition Definition “…“…as units of one input are added (with all as units of one input are added (with all

other inputs held constant), a point will be other inputs held constant), a point will be reached where the resulting additions to reached where the resulting additions to output will begin to decrease; that is output will begin to decrease; that is marginal productmarginal product will will declinedecline.”.”

On figure - between 2 and 3 workers On figure - between 2 and 3 workers

2. The Long Run2. The Long Run

All factors are variableAll factors are variable DecisionsDecisions

ScaleScaleLocationLocationTechniqueTechnique

Choice of techniqueChoice of technique IsoquantsIsoquants IsocostsIsocosts

Isoquants Isoquants

An isoquantAn isoquant“…“…is a contour line which joins together the is a contour line which joins together the

different combinations of two factors of different combinations of two factors of production that are just physically able to production that are just physically able to produce a given quantity of a good.”produce a given quantity of a good.”

Construction, slope and maps Construction, slope and maps

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An isoquantAn isoquant

Unitsof K

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Unitsof L 512203050

Units of labour (L)

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Units of labour (L)

K = 2

L = 1

isoquant

MRS = 2 MRS = K / L

Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution

g

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Units of labour (L)

An isoquant mapAn isoquant map

IsocostsIsocosts

Actual output also depends on costsActual output also depends on costs isocostsisocosts

join combinations of K & L - same costjoin combinations of K & L - same costassuming constant factor pricesassuming constant factor prices

Construction, slope & mapConstruction, slope & map

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An isocostAn isocost

Units of labour (L)

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Assumptions

PK = £20 000 W = £10 000

TC = £300 000

TC = £300 000

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Finding the least-cost method of productionFinding the least-cost method of production

Units of labour (L)

Un

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Assumptions

PK = £20 000W = £10 000

TC = £200 000

TC = £300 000

TC = £400 000

TC = £500 000

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TPP1

Finding the least-cost method of productionFinding the least-cost method of production

Least cost method of productionLeast cost method of production

Tangency between isoquant and Tangency between isoquant and isocostisocost

Where:Where:Slope of isoquant = slope of isocostSlope of isoquant = slope of isocost

Successive points of tangency - Successive points of tangency - scale scale expansion pathexpansion path