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///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 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

This question considers a distortionary labor income tax in the New Keynesian model. The representative household's utility function is: C 1?? t 1 ? ? ? N 1+? t 1 + ? (6) The household's budget contraint is: QtBt+1 + PtCt = Bt + (1 ? ?t)wtPtNt + ?t + PtTt (7) C is consumption, N is hours worked, w is the real wage, ? is the distortionary labor income tax rate, ? are firm profits distributed lump sum, T are lump-sum taxes. B are bonds that are in zero net supply. P is the aggregate price level. Qt is the bond price. In linearized form, the household's Euler equation and labor supply conditions are: Etc?t+1 ? c?t = 1 ? (?it ? Et??t+1) (8) w?t = ?c?t + ?n?t + ??t (9) The linearized equilibrium conditions for firms are: y?t = ?nt (10) w?t = ?mct (11) ??t = ?Et(??t+1) + ?mc? t (12) The resource constraint is: y?t = ?ct (13) Monetary policy follows a simple Taylor Rule: ?it = ????t (14) consumption, ?wt is the real wage, ?nt is hours worked, ?yt is output. In deviations from 7 steae t = 0, which implies ?xt = ?yt = ?ct .) c) Using the method of undetermined coefficients, find the response of the welfare relevant output gap and inflation to an exogenous cut in income taxes when prices are sticky and monetary policy follows the Taylor Rule above. To do this, guess that the solution for each variable is a linear function of the shock ???t . (Hint: you will need to rewrite the consumption Euler equation in terms of the welfare relevant output gap noting that ?xt = ?yt = ?ct). d) Discuss how, and why, labor income tax cuts affect the natural rate of output, the output gap and inflation. Are these results surprising?

Section C 5. This question deals with Haile and Tamer. "Inference with an Incomplete Model of English Auctions". (/PE. 2003) and Haile. Hong, and Shum, "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions". (2005). (a) Consider a single-object "button" auction (a la Milgrom and Weber) with independent private values. There are N potential bidders, Assume N is exogenous and known. Bidders are symmetric and risk-neutral, Each bidder draws his or her private value v from a common distribution Av) with a support [0. ). The seller's value for the object is wa and she wants to maximize her revenue from the auction by setting a reserve price r. Write down the seller's maximization problem and derive a condition for the optimal reserve price /* from the F.O.C. of the max problems. (b) Write down the two axioms (or behavioral assumptions regarding bidding strategies) of Haile and Tamer (2003). (c) Construct, as fully as you can, the nonparametric (partial) identification result (i.e. the bounds) of Haile and Tamer (2003) from the two axioms. (d) Discuss. as fully as you can, the advantages of the incomplete approach taken by Haile and Tamer (2003) in the identification and estimation of ascending auctions. (e) In Haile. Hong. and Shum (2005), their nonparametric test of common values depends on the following theorem. Prove the theorem. Theorem Under standard assumptions of symmetry, affiliation. nondegencracy and an participation. v(y, x. o) is invariant to a for all x in a4. 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