economcs

This problem analyzes the effect of future financial constraints on current investment decisions. Consider an economy with two dates, denoted by t = 1, 2. 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[c2]. There is a fixed supply of capital k, initially owned by the consumers. Consumers are endowed with a large amount of consumption good in each period and they can store this good between dates, such that if they store one unit of the consumption good in t = 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 of capital they own. The consumers have access to a concave technology G( ?k), where ?k denotes the capital owned by consumers in period 2. Assume limk?0G0 (k) = ? and G0 (k) = 0. The entrepreneurs enter period 1 with a given net worth N1 in terms of consumption goods. Assume agents can trade a risk-free bond b2 that pays an interest rate r. a) Argue that the gross rate of return on the risk-free bond is equal to 1 (i.e., the net return, r, is zero). b) Suppose that entrepreneurs face no borrowing constraints. State the optimization problems of an entrepreneur and a consumer. Show that the equilibrium capital price is q1 = A and the entrepreneurs buy k ? , where G0 (k ? k ? ) = A. c) Suppose that the entrepreneurs cannot borrow at all, so q1k2 ? N1. Find the equilibrium price and allocation, show that q1 ? A in equilibrium and that the expected utility of the entrepreneur is A q1 N1 (18) irrespective of whether the constraint q1k2 ? N1 binds or not. Show that q1 is increasing in N1 for N1

4. This question deals with Ellison (Rand '84) and Borenstein and Shepard (Rand '90). Both of these papers empirically test the validity of certain theoretical models of collusion. Set up a, Briefly describe the Rotemberg-Saloner and Green and Porter models of tacit collusion. Pay particular attention to what is known by the firms and the behavior of demand. Also, characterize the movements of price in the market. b. Discuss the main differences between the RS/I IH and GP models. Is the nature of "price wars" the same in the two classes of models?' If not, how do price wars differ and what within the theoretical models generates this difference? C. Closely related to the Rotemberg and Saloner model is the Haltiwanger and Harrington model. Briefly discuss how the Haltiwanger and Harrington model differs from the Rotemberg and Saloner model. Borenstein and Shepard d. What empirical prediction of the RS/HH models do Borenstein and Shepard test? Explain why this prediction is inconsistent with a model of pricing with switching costs. e. Describe the context of the paper: What is the industry? What are the data?' Is this a good setting to test the RS HH model? f. How do the authors propose to test the theory? Describe the empirical model. Is the model structural or reduced form? What is the dependent variable? What is are the main independent variables of interest? g. What econometric difficulties are implied by the prediction that current margins should be correlated with expected future prices and quantities! How do the authors deal with these problems? Be as detailed as possible. Ellison h. What empirical predictions of the RS/1 1H and the GP models does Ellison test? i. Describe the context of the paper: What is the industry? What are the data? What characterizes equilibrium prices in this industry? A priori, which theory seems to be most consistent with the industry and the dain (and why? j. How does the author propose to test the two theories? Is the model structural or reduced form? What istare) the dependent variable(s). Are all of the dependent variables observed? k. What alternative explanation does Ellison have to deal with? Can he completely rule this out?