The Production Function II

1
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

2
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

3
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

4
Total costs for firm X
Output (Q) 0 1 2 3 4 5 6 7
TVC () 0 10 16 21 28 40 60 91
TC () 12 22 28 33 40 52 72 103
TFC () 12 12 12 12 12 12 12 12
TC
TVC
TFC
5
Average and marginal physical product
b
c
Output
APP
MPP
Quantity of the variable factor
6
Average and marginal costs
MC
Costs ()
x
Output (Q)
7
2. Costs - long run

• K L are variable
• Profit maximisation requires cost minimisation
• Choice of technique if
• MPK \ PK gt MPL \ PL
• 20 \ 2 gt 32 \ 8
• 10 gt 4

8
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

9
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

10
Deriving an LRAC curve from an isoquant map
At an output of 100 LRAC TC1 / 100
Units of capital (K)
100
O
TC1
Units of labour (L)
11
Deriving an LRAC curve from an isoquant map
Expansion path
Units of capital (K)
700
600
500
400
300
200
100
O
TC1
TC5
TC2
TC3
TC4
TC7
TC6
Units of labour (L)
12
A typical long-run average cost curve
LRAC
Costs
O
Output
13
Returns to scale

• (i) Increasing 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
• 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

15
Conclusion

• Cost minimisation - long run
• Profit Revenue - Cost
• Profit maximisation - level?
• Market structure
• Perfect competition
• Monopolistic competition
• Oligopoly
• Monopoly