Econ 4450- 2009 Assigned Problem Number One
1
Econ 4450-2009 First Exercise
Sat, Mar 28, 2009 --
Typo in Assignment 1
Pt. 4)
qj** = 1/2cN should have no N
Problem I (Chiang and Masson, 1988 IER).
Economy E has N firms supplying the world market with a particular type of product. Each firm
j is too small to influence the market. In principle, it should be able to ‘choose the unit price’ in
the sense of selecting q
j
, its product quality, and hence the associated unit price p(q
j
).along the
‘hedonistic frontier’ of Sherwin Rosen. But due to information externality, the unit price of its
product depends on the average quality perceived on the market:
Q (q
1
, q
2
, . . ., q
j
, . . ., q
N
) = (1/N) ∑
k
q
k.
so that,
p = p(Q),
dp/dQ > 0
instead.
For firm j to produce x
j
units of its product, the marginal cost is known to be:
a(q
j
) +
bx
j
a > 0,
da/dq
j
> 0.
Now, unlike distance, weight, and temperature, product quality is not an extensive measure.
Without losing generality, one may simply define:
p(Q) = Q.
Next, note that there is no natural unit for the output, so that again, without losing generality,
one can always choose a unit such that b =1.
Finally, for concreteness, we assume that.