ABE • Formulas + Meanings

Formulas

Yit = φ Kit

Output equals capital productivity times capital (firm i at time t)

πit = (uit φ - g rit) Kit

Firm profit equals revenue minus financing and variable costs

Ait = Ait-1 + π_it

Net worth update: previous equity plus current profit

K^dit = (φ / g rit) * (Ait / (1 - (g rit c / 2)))

Optimal desired capital stock based on profit, cost, and bankruptcy risk

Iit = K^dit - K_it-1

Investment equals desired capital minus existing capital

Lit = Iit - π_it-1

Credit demand equals investment minus retained profits

Lt = (1 / ν) Et

Total credit supply equals bank equity divided by risk coefficient

Lit = λ (Ait / At^s) Lt + (1 - λ)(Kit / Kt^s) L_t

Bank allocates credit based on firm’s share of equity and capital

πt^B = Σi (rit Lit - r^At Et - r^Dt Dt)

Bank profit equals loan income minus costs on equity and deposits

Bit = Lit - Kit = -Ait

Bad debt when firm i goes bankrupt (loan minus recoverable capital)

Nt^entry = N * [1 / (1 + exp(d - e rt))]

Number of new entrants depends inversely on average interest rates