Assume that the denominator is positive (due to uniqueness and slope, see Var-
ian (1992) p 288-289).
The sign of the denominator is determined by
∂2NB1 ∂2NB2
∂q1 ∂a ∂q22
The second term is negative (NB is concave in q), hence, we have that
∂q1 ∂2NB1
sign = sign ɔ ɔ .
∂a ∂q1 ∂a
We are, however, more interested in
∂q2
Sign 2 .
∂a
∂2NB1 ∂2NB1
|
d q 2 = |
∂q1 ∂a |
∂ q12 ∂2 NB 2 |
|
∂q1q2 | ||
|
∂a |
∂2NB1 |
∂2NB1 |
|
∂ q 1 |
∂q1 ∂q2 | |
|
∂2 NB 2 |
∂2NB2 | |
|
∂q1 q2 |
∂q22 |
Assume that the denominator is positive (due to uniqueness and slope, see Var-
ian (1992) p 288-289).
The sign of the denominator is determined by
41