Econ 4450- 2009 Assigned Problem Number One
Econ 4450-2009 First Exercise
Sat, Mar 28, 2009 --
Typo in Assignment 1
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
, its product quality, and hence the associated unit price p(q
‘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/N) ∑
p = p(Q),
dp/dQ > 0
For firm j to produce x
units of its product, the marginal cost is known to be:
a > 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.