# Bhuyan Slides ```Bhuyan, Sanjib, and Lopez
Oligopoly power in the food and tobacco industries
Method:
Theoretical Model
Specify a general profit function
Derive several parameters related to MARKET POWER
Empirical Model
Specify a specific profit function, demand function
Collect data
Estimation of parameters - statistical methods
Method: Theoretical Model -Profit function
j  (P(Y ) Y j  C j (W ,Y j )
P(Y )  price (output dem and function)
W  vector of input prices
Y j  firm j's output
C j  cost of producing Y j at prices W
Differentiate profit with respect to output
j
j
PY
 sYj 
 Revenue to cost ratio
j
Y
Cj
j
Y
s
  j 
 lnC j

 1  
j
 lnY
  
Method: Theoretical Model: Parameters
 ln C j
 outputelasticity of cost (linked to MC)  1 /  j 
j
 ln Y
Output elasticity of cost - reciprocal of “economies of size”
eg. for a 1% increase in output, is there more or less percent change in cost?
j
 ln Y
= conjectural elasticity
j
 ln Y
(changein industry outputY in responseto a changein the outputof firm j )

 ln P(Y )
elasticity of outputdem and for the industry
 ln P
How doesindustry outputreact to a changein the price level?
Method: Theoretical Model: Lerner Index (L)
Measures degree of the exercise of oligopoly power
L
P  MC 

P

MC  MC for the industry
  industry level conjectural variations elasticity
  elasticity of output dem and
Method: Empirical Model
Specify a Translog Cost function (Transcendental-logarithmic)
Ln(C) = f(W,Y,T)
C = industry total cost
Y = industry output
T = time trend
W = vector of input prices (wi)
Logarithmic differentiation (Shephard’s Lemma)
factor (input) share equations
 lnC
wi  x i

 Si
 ln w i
C
(input share equations ) = f (w i ,Y,T)
Method: Empirical Model
Specify a Cobb-Douglas output demand function
(derived demand facing industry)
lnY  D(lnP, lnq, ln Z, lnT)
P  price of output
Z  substitute price
q  incom e
T  tim e trend
Method: Estimation
Statistical methods - estimate the parameters of a system of equations
4 input share equations (KLEM) (derived from C=C (W,Y,T)
1 demand function (Cobb-Douglas)
1 equation representing profit max criterion
Annual data 1972 – 1987
40 food and tobacco processing industries: SIC 4 digit level
L



- Lerner index
- elasticity of returns to scale
- conjectural variation elasticity for the industry
( = 0 =&gt; no strategic activity e.g. price taking)
- output demand elasticity
Results:
1) Testing the Lerner index
H0: L = 0
Reject =&gt; evidence of oligopoly power (price distortion)
Rejected - 37 of 40 industries (average L = 0.33)
&quot;degree of oligopoly power is significant&quot;
Results:
2)
Other Parameters
 - conjectural variation elasticity
- mostly greater than zero and significant
- evidence of strategic behaviour
 - output demand elasticity – inelastic in all cases
 - elasticity of scale ..... mostly increasing returns e.g.  &gt; 1
Constant returns to scale - CRS rejected for 33 industries
Ho:  = 0
20 industries – increasing returns
13 industries – decreasing returns
&gt;1
&gt;1
Statistical Significance – high in most cases
Aggregate Industries SIC 2:
- Food Industries
- Tobacco Industries
- Food &amp; Tobacco
Comparisons with Previous Research
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