Behind The Supply Curve: Production Function I

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Behind The Supply Curve Production Function I

• 1. Production - short run
• Productive efficiency
• The Law of diminishing marginal returns
• 2. Production - long run
• isoquants isocosts
• least cost method of production

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Background

• Firms seek to maximise profit (?)
• ? R - C
• How do firms produce output and minimise costs
  (C)?
• What is production?
• production is simply the process of
  transforming inputs and outputs.
• inputs capital (K) and labour (L)

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A production function

• Functional relationship
• Q f(K, L , T)
• T changes over time
• At a point in time T is fixed
• Productive efficiency
• A method of production is efficient if, for a
  given level of factor inputs, it is impossible to
  obtain a higher level of output, given the
  existing state of technology.

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The short run

• Period of time over which one factor is fixed
• Capital - machines, factory, etc.
• Total and Marginal Physical Product
• marginal product is the additional output
  produced by an additional unit of labour
• MPP ?TPP / ?L
• See Figure

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Wheat production per year from a particular farm
TPP
Tonnes of wheat produced per year
Number of farm workers
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Wheat production per year from a particular farm
TPP
Tonnes of wheat per year
Number of farm workers (L)
Tonnes of wheat per year
Number of farm workers (L)
MPP
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Law of Diminishing Returns

• Definition
• as units of one input are added (with all other
  inputs held constant), a point will be reached
  where the resulting additions to output will
  begin to decrease that is marginal product will
  decline.
• On figure - between 2 and 3 workers

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2. The Long Run

• All factors are variable
• Decisions
• Scale
• Location
• Technique
• Choice of technique
• Isoquants
• Isocosts

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Isoquants

• An isoquant
• is a contour line which joins together the
  different combinations of two factors of
  production that are just physically able to
  produce a given quantity of a good.
• Construction, slope and maps

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An isoquant
Units of K 40 20 10 6 4
Units of L 5 12 20 30 50
Units of capital (K)
Units of labour (L)
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Diminishing marginal rate of factor substitution
g
MRS 2
MRS DK / DL
DK 2
h
DL 1
Units of capital (K)
isoquant
Units of labour (L)
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An isoquant map
Units of capital (K)
I5
I4
I3
I2
I1
Units of labour (L)
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Isocosts

• Actual output also depends on costs
• isocosts
• join combinations of K L - same cost
• assuming constant factor prices
• Construction, slope map

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An isocost
Assumptions PK 20 000 W 10 000 TC 300
000
Units of capital (K)
TC 300 000
Units of labour (L)
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Finding the least-cost method of production
Assumptions
PK 20 000 W 10 000
TC 200 000
Units of capital (K)
TC 300 000
TC 400 000
TC 500 000
Units of labour (L)
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Finding the least-cost method of production
Units of capital (K)
TPP1
Units of labour (L)
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Least cost method of production

• Tangency between isoquant and isocost
• Where
• Slope of isoquant slope of isocost
• Successive points of tangency - scale expansion
  path