Industrial Economics Notes (First-Best )
To compute for the social optimum, or the rst-best, there are two ways that
we can proceed.
1. The rst would be to maximize welfare (the sum of consumer and producer
surplus) with respect to the variable of interest.
(a) Example: circular city (product dierentiation)
i. max CS + P S , where
ˆ
ˆ
1
2n
(v − tx − p)dx = 2n
CS = 2n
0
ˆ
1
2n
(v − p)dx − 2n
0
P S = n[
1
2n
txdx
0
1
(p − c) − F ]
2n
ii. This problem is equivalent to minimizing transportation cost and
xed costs. To see this, note that the maximization problem
´ 1
above reduces to max v − p − 2n 02n txdx + (p − c) − nF . This,
n
´
1
in turn, is equivalent to max v − c − 2n 02n txdx − nF , and since
n
v and c do not depend on n, and since maximizing an objective
function is equivalent to minimizing its negative, we get the same
problem as the one on the slides.
(b) The take-away from this is that price does not come into the computation of welfare because it is only a transfer of wealth from consumers
to producers. It only changes quantity sold.
2. The second would be to use the First Welfare Theorem : without distortions, the competitive situation gives you the optimal outcome.
1