Instructions: This homework assignment is focused on the papers we reviewed in class: "Credit Traps and Credit Cycles" , by Matsuyama (AER 2007). There is one question with total worth of 100 points. Please try to provide a detailed explanation of each question you attempt to answer. I encourage you to use the Mathematica/Matlab or any other programming software to plot draw figures or to find solutions numerically. Homework assignment will not be accepted once the deadline has passed.

Questions from Matsuyama (2007): Consider the following modification of Matsuyama (AER 2007). Economy is represented by a continuum of two period lived agents with unit mass. Young agents supply one unit of labor endowment inelastically and earn labor income tut during the first period.

Young agents decide how much to save during first period, stwt (st is a savings propensity), and whether to become an entrepreneur or a depositor during second period. Entrepreneurs decide wether to produce a capital with a modern or a traditional technology.

Modern technology requires a minimum m₂ = 1 units of final goods for investment in period t and produces m₂R₂ = 1 units of capital good in period t + 1. Traditional technology, in contrast, requires a minimum m₁ = m units of final goods for investment in period t and produces m₁R₁ = m_R units of capital good in period t + 1. Produced capital can be rented to the consumption commodity producing firm which produces final commodity according to a Cobb-Douglas production function, f(k_t) = k_t^α with α ∈ (0, 1). While borrowing, entrepreneurs can pledge only up to a fraction 1 - λ ∈ (0, 1) of the project revenue for debt repayment independent wether they produce capital with a modern or a traditional technology. Young agents maximize the lifetime utility log c_1t + log c_2t+1 where c_1t and c_t+1 are first and second period consumptions.

Question Q1: Credit is allocated only to modern sector if and only if R < R^c (ω_t, m, λ). What is R^c(ω_t, m, λ)?