Correct answers only.

Question 5 {EH points] This proble1n analyzes the eEe-ct of Future nancial constraints on current invest- ment decisions. Consider an economy with two datesJ denoted by t = 112. There are two goods: consumption and capital. There is a continuum of entrepreneurs and a continuum of consumers. All individuals have linear utility and consume only in period 2, so U = E[cg]. There is a xed supplyr of capital E1 initially owned by the oonsurners. Consumers are endowed with a large amount of consumption good in each period and they can store this good between dates1 such that if they store one unit of the consumption good in it = 1 they get one unit of the good in t = '2. The entrepreneurs have access to a linear technology that produces A units of consumption good in period 2 _per unit o_'f capital they own. The consumers have access to a concave technologyr Gr}, where F; denotes the capital owned by oonsurners in period 2. Assume IiWTk} = on and GTE] = D. The entrepreneurs enter period 1 1with a given net worth N1 in terms of consumption goods. Assume agents can trade a riskfree bond b; that pays an interest rate r. a} Argue that the gross rate of return on the risk-Free bond is equal to 1 (Le, the net return, I", is zero]. In} Suppose that entrepreneurs face no borrowing constraints. State the optimiza- tion problems of an entrepreneur and a consumer. Show that the equilibrium capital price is :31 = A and the entrepreneurs buy H, where GTE H] = A. c] Suppose that the entrepreneurs cannot borrow at all1 so 4:15;; E N1. Find the equilibrium price and allocation, show that :11 E A in equilibrium and that the expected utility of the entrepreneur is it :18} '31 irrespective of whether the constraint 4315;; 5 N1 binds or not. Show that qi is increasing in N1 for N1