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The Production Function II
1. Costs - short run measures relationship - production & costs 2. Costs - long run scale expansion path long run costs 3. Returns to scale & economies of scale
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1. Costs - short run Fixed & variable costs
fixed = unavoidable variable = avoidable Costs rise as output increases e.g. As L, TPP TC given PK and PL inverse relationship MP & MC, AC & AP Measures of cost - Table 1
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Measures of cost Total costs: TC = TFC + TVC
Average costs: ATC = TC \ TPP or TC \ Q ATC = AFC + AVC Marginal costs: MC =TC \ TPP ‘…the extra cost of producing one more unit.’ Shape - Figures 1 to 3
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Total costs for firm X Output (Q) 1 2 3 4 5 6 7 TFC (£) 12 TVC (£) 10
1 2 3 4 5 6 7 TFC (£) 12 TVC (£) 10 16 21 28 40 60 91 TC (£) 12 22 28 33 40 52 72 103 TC TVC TFC fig
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Average and marginal physical product
b c Output APP MPP Quantity of the variable factor fig
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Average and marginal costs
MC Costs (£) x fig Output (Q)
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2. Costs - long run K & L are variable
Profit maximisation requires cost minimisation Choice of technique: if MPK \ PK > MPL \ PL 20 \ 2 > 32 \ 8 10 > 4
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Cost minimisation i.e. last pound spent on K adds 10 units Therefore
spend 1 extra pound on K, TPP rises by 10 spend 2.50 less on L, TPP falls by 10 output is unchanged, but costs fall 1.50 Cost minimisation MPK \ PK = MPL \ PL tangency of isocost & isoquant
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Scale expansion path & long run costs
Vary K & L TPP rises (no. of factories) See Figure - scale expansion path Long run average costs Returns to scale Scale economies
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Deriving an LRAC curve from an isoquant map
At an output of 100 LRAC = TC1 / 100 Units of capital (K) 100 O TC1 fig Units of labour (L)
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Deriving an LRAC curve from an isoquant map
Expansion path Units of capital (K) 700 600 500 400 300 200 100 O TC1 TC2 TC3 TC4 TC5 TC6 TC7 fig Units of labour (L)
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A typical long-run average cost curve
LRAC Costs O Output fig
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Returns to scale (i) Increasing returns (ii) Constant returns LRAC
a % increase in inputs leads to a larger % increase in output economies of scale (ii) Constant returns LRAC constant a given % increase in inputs leads to the same % increase in output
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Returns to scale (iii) Decreasing returns Economies of scale
LRAC a % increase in inputs leads to a smaller % increase in output diseconomies of scale Economies of scale plant level economies multi-plant economies Diseconomies of scale
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Conclusion Cost minimisation - long run Profit = Revenue - Cost
Profit maximisation - level? Market structure: Perfect competition Monopolistic competition Oligopoly Monopoly
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