Uncertainty and Risk - DARP
Uncertainty and Risk - DARP
Uncertainty and Risk - DARP
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Microeconomics<br />
where the last term vanishes because of the …rst order condition. So<br />
@Eu <br />
@<br />
has the sign of E(u [p p]): But this must be positive if u is<br />
decreasing with <strong>and</strong> will be zero if u is constant. Hence the …rm strictly<br />
prefers certainty if it is risk averse <strong>and</strong> is indi¤erent between certainty <strong>and</strong><br />
uncertainty if it is risk neutral.<br />
2. For any known realization p we may write q = S(p) where S is the competitive<br />
…rm supply curve. Pro…ts as a function of P may thus be written:<br />
(p) = pS(p)<br />
C(S(p))<br />
which implies<br />
d(p)<br />
dp<br />
= [p C q ]S p (p) + S(p) = S(p) (8.20)<br />
where S p (p) is the slope of the supply curve at p, a positive number.<br />
Therefore, di¤erentiating (8.20) we have<br />
d 2 (p)<br />
dp 2 = S p (p) > 0:<br />
Hence () is increasing <strong>and</strong> convex. So it is immediate that E(p) > (p):<br />
cFrank Cowell 2006 133
Change language