and  on  the  optimal  investment  decision。  This  net  surplus     is

H E(V˜ | r H ) I F

and

L F , depending on the report filed by the auditor。 The informational value of an audit is the

difference  between  the  expected  value  of r

without an audit, V I :

with  an  audit  and  the  surplus  from continuation

(q) Pr(r H )H Pr(r L)L (V I ) q(1p)(I VL ) F 。 (4)

This expression is increasing in the quality of auditing q, decreasing in the firms’ quality p (the worse the pool, the more valuable is information), and increasing in the losses that would arise from

investing in bad firms。 The  term

I VL

is a measure of the potential misallocation of   investment

that can be prevented by auditors’ information。

3。2。The unregulated outcome

If the audit fee F just equals the auditors’ cost C(q), i。e。 if auditors make zero profits, then expression (5) becomes the net social surplus (on a per-firm basis):

W (q) q(1p)(I VL ) C(q),

(5)

Indeed, since auditors earn zero profits, the entire net social surplus accrues to the shareholders。

The first-best outcome is obtained by maximizing the net social surplus W(q)。 Given our assumptions about the auditor’s cost function, W(q) is concave and has an internal maximum where the marginal value of audit quality equals its marginal cost。 This identifies the first-best quality value  q fb (0,1) :

(1p)(I VL ) C '(q fb )。

(6)

Since the cost function C(q) is convex, q fb is decreasing in the quality of the pool and increasing in the potential misallocation of investment, just as the informational value of auditing。

If the audit quality is contractible, the first-best outcome emerges as the competitive market equilibrium。 Firms’  managers  choose  their  “demand  for  audit  quality”  by  maximizing      the

informational value of auditing, maximizing their profit per audit,

(q) 。  Auditors  choose  their  “supply  of  audit  quality”     by

F (q) C(q) , and make zero profits。 The market-clearing price of

an audit will then be the fee corresponding to the first-best level of audit quality, F (q fb ) 。

It is easy to show that if quality is observable, the first-best allocation coincides  with the Bertrand equilibrium of the model, that is, the Nash equilibrium of an extensive-form game where auditors choose the quality q of the audit and a fee function F(q)。 The strategy of auditor j is a choice of quality and fee, which is the best response to the qualities and fees chosen by competing auditors。 The situation in which all firms choose the first-best quality and price is a Nash equilibrium, since no firm can profitably deviate。

If instead the audit quality is privately unobservable, then for any positive audit quality expected by investors, auditors have an incentive to choose a lower level and save the corresponding cost。 As a  result,  the  equilibrium  audit  quality  is  zero,  the  market  price  will  equal  the   unconditional

expectation V , and an unprofitable firm will be more likely to continue operating。10 So in this case there is a rationale for public intervention。 To this we turn in the next subsection。