Economics of the Firm
Term paper 2005
Question I
Part (i).
Private information about project value, rather than assets in place.
Assets in place: A
Project revenue: R ∈ { H , L }, H > L
Prob( R = H ) = p ∈ (0, 1)
ER = R = pH + (1 – p ) L
Project costs: I < L q = outsiders’ subjective probability that R = H , given a decision by the firm to invest. q ∈ [0, 1].
Outsiders’ assessment of the firm’s value given a decision to invest: q ( A + H ) + (1 – q )( A + L ) = A + qH + (1 – q ) L f f = fraction of the firm owned by new shareholders
Competition among risk-neutral investors ⇒
Expected income = expected costs f [ A + qH + (1 – q ) L ] = I
=
A + qH
I
+ (
1 − q
)
L
Economics of the Firm - Tore Nilssen – Term paper 2005 – 1

Current owners left with:
(1 – f )( A + R ), R ∈ { H , L }
The investment is profitable for current owners if:
(1 ) > A ⇔ f <
A
R
+ R
Consider first the L -type: If it is of type L , then the firm invests if:
A + qH
I
+ (
1 − q
)
L
<
A
L
+ L
Thus, the firm invests, even if q = 0, since H > L > I and 0 ≤ q ≤ 1.
Consider next the H -type: The firm, if of type H , invests if:
A + qH
I
+ (
1 − q
)
L
<
A
H
+ H
If also the H invests, the investors’ beliefs must be such that q = p , in order for beliefs to be consistent with strategies.
Inserting, we find that an equilibrium exists in which also H -type invests, if
A
I
+ R
<
A
H
+ H
⇔
H
I
>
A
A
+
+
H
R
.
This condition always holds, because
H
I
>
H
L
>
A H
+
>
+
+
.
Economics of the Firm - Tore Nilssen – Term paper 2005 – 2

The H type does not invest if
A + qH
I
+ (
1 − q
)
L
>
A
H
+ H
H type not investing is consistent with investors’ beliefs if q = 0. Thus, an equilibrium exists in which the firm invests only if it is of type L , if:
A
I
+ L
>
A
H
+ H
⇔
H
I
<
A
A
+
+
H
L
This condition can never hold here, as we just saw . Thus, this equilibrium does not exist in this case.
There is thus only one equilibrium, in which the firm always invests, whether its project has a high or a low value .
Extra question:
Would this equilibrium be possible also in a case where L < I ?
Yes. What is needed is:
L
I
>
A
A
+
+
L
R
, which may hold even when L < I .
When this condition holds and q = p , both types prefer investing to not investing.
→ Overinvestment in equilibrium
Economics of the Firm - Tore Nilssen – Term paper 2005 – 3

Part B.
Money burning
Let’s keep the above model.
We need to specify outside investors’ beliefs: If no money burning is observed, then q = 0.
Three conditions need to be satisfied:
(i) low-type firm must prefer no money-burning (revealing being low-type) to money-burning (believed to be high type).
1 −
I
(
A L
)
1
I
(
A + L C
) ⇔
C ≥ C * =
1
2
⎡
⎣
A H − ( ) 2 − 4
( ) ⎤
⎦
(ii) Money-burning must be better for the high type than not investing:
1 −
I
(
A H C
) > A ⇔ C < H – I
(iii) Money-burning must be better for the high type than investing without money-burning and being believed to be low type:
1 −
I
(
A H C
)
1
I
(
A H
)
Economics of the Firm - Tore Nilssen – Term paper 2005 – 4

Compare (ii) and (iii). (ii) is redundant, since (iii) is always stricter:
A
⎝
I
⎠
(
(iii) can be rewritten as:
C < I
H − L
A + L
A H
) ⇔
H
I
>
A H
A L
(i) and (iii) are compatible if:
C * < I
H − L
⇔ A + L > I , which always holds.
General issues:
• Term paper versus exam
• Answering without addressing the specific problem
• Formal analysis versus verbal discussion
• Formal analysis: Explain expressions – give intuition.
Specific issues:
• Distinguish ex-ante beliefs and revised beliefs ( p vs. q )
• Equilibrium analysis: beliefs and strategies mutually consistent. Start out with strategies and find beliefs that fit.
Economics of the Firm - Tore Nilssen – Term paper 2005 – 5

Question II.
• Again: Address the specific problem
• The whole model: not asked for
• The examples:
contract incompleteness
relationship-specific investments
outcome: hold-up
ƒ details: ex-post and ex-ante costs of renegotiation
outcome: ownership and control
Economics of the Firm - Tore Nilssen – Term paper 2005 – 6