ECON191 (Spring 2011)
23 & 25.3.2011 (Tutorial 6)
Chapter 6 Production
Chapter 7 The Cost of Production
From short run to long run: long run cost functions
 In the long run, both labor and capital are variable.
LRTC




LRAC
For every quantity of output, there is an optimal SRTC curve and SRAC curve.
Use 5K when output < a
Use 10K when a < output < b
Use 15K when output > b
LRMC and SRMC
 LRMC intersects LRAC at its lowest point.
 At a quantity a, where
 SRAC = LRAC  SRMC = LRMC
 Quantity < a  SRMC < LRMC
 Quantity > a  SRMC > LRMC
Relationship between LR cost functions and SR cost functions

SRTC  LRTC since point a, b, d (SR) lies on an isocost line farther away from
the origin than point a’, b’ and d’ (LR). For c, SRTC = LRTC
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
SRAC  LRAC since point a, b, d (SR) lies on an isocost line farther away from
the origin than point a’, b’ and d’ (LR). For c, SRAC = LRAC

MC 
TC
, For
Q
Q < 300, SRMC < LRMC
Q > 300, SRMC > LRMC
 Increasing output from 200 to 300 (b to c), since ∆ (↑) SRTC < ∆ (↑) LRTC, and
∆Q = 100 in both LR and SR, therefore, LRMC > SRMC. (Why?)
o In the LR, we have increase L and K.
o In the SR, we only need to increase L
o SRMC < LRMC
 Increasing output from 300 to 400 (c to d), since ∆ (↑) SRTC > ∆ (↑) LRTC, and
∆Q = 100 in both LR and SR, therefore, LRMC < SRMC. (Why?)
o In the LR, we have increase L and K.
o In the SR, we have to increase L by a larger amount relative to LR,
since K cannot be adjusted in SR.
o SRMC > LRMC
Economies and Diseconomies of Scale
 Economies of scale: output can be doubled for less than a doubling of cost
(Decreasing AC)

Diseconomies of scale: a doubling of output requires more than a doubling of cost
(Increasing AC)
 What are the possible reasons for economies and diseconomies of scales?

Measure of economies of scale:

Cost-output elasticity (EC): percentage change in the cost of production resulting
from 1 percentage change in output
(1) Cost-output Elasticity
(2) Scale Economies Index

 EC < 1 implies Economies of scale, and EC > 1 implies Diseconomies of scale
(Why?)




Scale economies index (SCI): SCI = 1 – EC
SCI > 0  Economies of scale (EC < 1)
SCI = 0  neither Economies of scale nor Diseconomies of scale (EC = 1)
SCI < 0  Diseconomies of scale (EC > 1)
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 Algebraically, Economies of Scales is defined as





 Similarly, Diseconomies of Scales is defined as





Relationship between Economies of Scale and Increasing Return to Scale
 Increasing returns to scale: Output more than doubles when the quantities of all
inputs are doubled
 The proportion of K and L is fixed (linear expansion path)
 Economies of scale: a doubling of output requires less than a doubling of cost
 The proportion of K and L do change (non-linear expansion path)
 Increasing Returns to Scale  Economies of Scale
 Decreasing Returns to Scale  Diseconomies of Scale
 (The reverse is not necessarily true, why? What are the possible reasons for
economies and diseconomies of scales?)

Algebraically, given the production function:
IRTS:


[If we increase input by t times, output increases by more than t times. Total cost
increases with output level.]
ES:


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 IRTS  ES
 It could be shown that
 Since
(when we have IRTS)
 Therefore,


(ES)


K
tCF(K, L) = wtL + rtK
Q = F(tL, tK) > tQ
IEP
Q = F(L, K)
tK
K
L
L
tL
C (F(tK,tL))
wL + rK
Notes:
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