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Exercise 2 A variation of the Allais paradox. Denote by LA the lottery that yields $3000 for sure, by LB the lottery that yields $4000 with probability 0.8, and $0 otherwise. Denote by Lo the lottery that yields $3000 with probability 0.25, and $0 otherwise, and by Lp the lottery that yields $4000 with probability 0.2, and $0 otherwise. Many studies have shown a systematic tendency for subjects to express a strict preference for LA over LB and for LD over Lo. Show that this choice pattern violates the expected utility hypothesis.Short Questions [28 pts.] Determine whether each of the following statements is True, False or Uncertain. Give a brief explanation for each answer. 1. In an attempt to keep unemployment rate below its natural rate, many Latin American countries used expansionary fiscal and monetary policies heavily. These policy choices were the main reason why these same countries entered difficult periods of high inflation, from which they struggled to get out. [7 pts.] 2. If the number of employed workers in a country decreases, the unemployment rate in the country will increase. [7 pts.] 3. An increase in the duration of unemployment should be linked to a decrease in flows in and out of unemployment, if one is to keep unemployment constant. [7 pts.] 4. Workers reluctance to take nominal pay cuts offers a feasible explanation of why the Phillips Curve relation breaks down when there is deflation. [7 pts.]Long Question 1: Animal Spirits [26 pts.] Consider the following quote on investment from The General Theory of Employment, Interest and Money, the seminal book written by John Maynard Keynes in 1936: "[.../ most [...] of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits - of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities. Enterprise only pretends to itself to be mainly actuated by the statements in its own prospectus, however candid and sincere [...) if the animal spirits are dimmed and the spontaneous optimism falters, leaving us to depend on nothing but a mathematical expectation, enterprise will fade and die [...)." For the purpose of this test, we assume that what Keynes meant by "animal spirits" was really "business confidence". This implies that investment I does not only depend on interest rate and income, but on "business confidence" as well. In light of this fact: 2 1. How does this affect the shape of aggregate demand? Starting from the investment curve and moving to the IS-LM model, graphically derive both an optimistic AD (i.e. an AD curve which embeds high business confidence) as well as a pessimistic AD (i.e. an AD curve which embeds low business confidence). [13 pts.] 2. If animal spirits (business confidence) do indeed play a role in the economy, what does their presence imply about the potential tools policymakers have at their disposal for affecting output in the short run? Apart from monetary and fiscal policy, suggest a new type of policy that could be used for increasing or decreasing output in the short run (be specific in how the policy would affect output). [13 pts.]Long Question 2: Fire at Will [46 pts.] 1. Starting from the wage setting relation and the price setting relation, derive an expression for aggregate supply. Make sure you clearly explain each steps in the derivation. [11 pts.] Italy's Prime Minister, Mr. Mario Monti, has presented to the Italian parliament a proposal to change labor laws. The Italian government claims that the new measures would "create a dynamic, flexible and inclusive labor market, one able to (...) create good working conditions /.../". We interpret these proposals as a decrease in firing and hiring costs, i.e. a decrease in the variable z, the parameter in the wage setting relation. 2. Using the wage setting relation and the price setting relation you derived in part 1, predict what will happen to the unemployment rate in the medium run u, if these labor proposals are approved by parliament. [6pts.] 3. How will the change predicted in part 2 affect the AS-AD equilibrium? Show using the AS/AD graph. Let E be the initial medium rum equilibrium. Let the first short-run equilibrium the economy transitions to be labeled as E' and the new medium run equilibrium as E". [6 pts.]3 Long Question 2: A Modification of the Diamond- Dybvig model (30 points) Consider the standard version of the Diamond-Dybvig model discussed in class. A bank has access to two investment technologies. There is a short term technology which yields 1 in period t = 1 for every unit invested in period f = 0. There is also a long term technology which yields R > 1 in period t = 2 for every unit invested. The bank can choose to liquidate its long term investment in t = 1, in which case it gets L 1. What is the maximum amount of that a bank could promise to patient consumers under the assumption that only impatient consumers will withdraw of at t = 1? (5 points) 2. How much should the bank invest in each technology to fulfill its promise of (ci, c;)? (5 points) Now we change our assumptions. We assume that instead of the bank there is a firm which has access to exactly the same two technologies as the bank. The only difference is that instead of the deposit contract, for each dollar invested in the firm, the firm offers a share. A "share" is the right to receive a payment Dj at t = 1 and Dy at t = 2 independent of whether who owns the share is patient or impatient. In t = 1, consumers can sell or buy the shares of the firm, only after receiving Di and finding out whether they are impatient or patient. The sequence of events is as follows: In t = 0 people give their one unit of endowment to the firm. In t = 1 the firm pays Di. After D, has been paid and consumers find out whether they are patient or impatient, consumers can sell or buy the shares of the firm. In t = 2 the firm pays D2 = R(1 - D,), since we are assuming that the firm makes zero profit. 3. Let us first assume the price of the shares is such that patient consumers can buy all of the shares of impatient consumers by giving them their Dy dividends. Show that if D1 = (1-#)c; then impatient consumers consume ci and patient consumers consume c;. (5 points)