Equity Markets and Economic Development: What Do We Know

Turning to debt contracts, the bank’s expected outcome is r[zpD+ (1 - z)npk₂]. Using the
lender’s participation constraint, this is equivalent to:

D = [pa (α )- r (1^- z )npk 2 ]

rzp

With probability p , the firm is successful, repays the loan and retain control over output
production Φ . With probability (1 - p), the firm fails, goes bankrupt and produces a
subsistence amount of home production φ. The firm’s expected net income can thus be
defined as VD = rp(k₁ -D)+ pΦ + (1 - p)φ. By substitution, we have:

VD = [r (^em )^{- p}a {g )] + p φ + (₁ - p φ

z_t

The optimal choice of contract for a type-1 firm can then be characterized by the function

V* = VE - VD ; that is, from (5) and (7):

(1 _{- p})(1 _-φ)_- ^{[r (emv} - pa(α))](1^{- z})npk2 = 0

^V ʌ ⁷          z (EMV )

An equity contract is chosen if VE- VD > 0, while a debt contract is chosen if VE- VD < 0 .
For each level of efficiency α ∈ (0,1) , it can be shown that V * is a concave function in
z ∈ (0,1) , with lim_z→0 V* = +∞ and lim_z→1 V* = (1 - p)(Φ -φ) > 0 .

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