j Let the measure of unemployed workers be denoted by u = uL + uH, be useful to define the market tightness as /u. Once a match has been formed, the wage is determined through Nash bargaining, with (0, 1) representing the worker's power. The output of all jobs is p > 0 per unit of time, i.e., p does not depend on the worker's type and p > zi , for all i. Also, while a firm is searching for a worker it has to pay a search (or recruiting) cost, pc > 0, per unit of time. All jobs are exogenously destroyed at rate >. a) Write down the value functions for a firm and a worker of each type in all possible states. b) Exploiting the free entry condition of firms, derive the analogue of the job creation (JC) curve for this economy. c) Using the same methodology as in the lectures (adjusted to accommodate the differences in the new environment), derive the wage curve (WC) for this economy. d) Combine the JC curve and the WC curve determined in the previous parts in order to provide an equation that (implicitly) determines the equilibrium . Compare with the analogous equilibrium condition from the lectures. For the remainder of this question, we will make an important change in the environment. We will assume that the total production of a filled job is given by px, where x is the match-specific (idiosyncratic) productivity. (But we will maintain the assumption that there are two types of workers and they enjoy a different unemployment benefit.) As in the theory of "endogenous job destruction" (Chapter 2 of Pissarides' book), we will assume that existing matches get hit by a productivity shock at rate ; when that happens the random variable x attains a new value drawn from the cdf G(x). This distribution is iid over time and has support in the interval [0, 1]. 2 New jobsworker decide whether it is worth keeping the match alive and, if yes, they renegotiate over the wage. To answer the following questions make a conjecture about the equilibrium form, similar to the one we made in class in the endogenous job destruction theory. e) In this new environment what is the unemployment rate of workers of type i = L and H? Is it the same? f) Write down the value functions for a firm in all possible states. g) Write down the value functions for a worker of each type in all possible states. h) Without characterizing equilibrium (just using the economic intuition you have developed by studying these types of models) answer the following question: In the model with exogenous job destruction L-type workers are worse off compared to H-type workers because they get paid a lower wage. How is the well being of L-types compared to that of H-types affected as we switch from the model of exogenous to the model of endogenous job destruction? (Hint: Compare the wage the two types receive but also the length of time for which they get to keep this wage, since now job destruction is endogenous.) 3

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A closed economy can be described by the long-run classical model:

Y = 5000

C = 950 + 0.5(Y - T) - 70r

I(r) = 3000 - 30r

Note: r is measured in percentage points (i.e., if r = 5, then r = 5%).

Initially, the government collects 14% of output as income taxes and it runs a budget surplus of 100.

Part (a) Find the equilibrium levels of real interest rate and investment.

Part (b) Suppose the business confidence index changes from 113 to 115. As a result, autonomous investment changes by 6%. Find the new equilibrium levels of real interest rate, and investment.

Note: you will need to decide whether autonomous investment increases or decreases.

Part (c) (continued from part b) Suppose the government wants to raise its budget surplus by 60 via a change in government spending. Find the level of government spending that could achieve this goal and the new level of investment.

Answers:

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Part (a)

Government spending = (keep your answer to 1 decimal place if needed)

Real interest rate = (keep your answer to 1 decimal place if needed)

Investment = (keep your answer to 1 decimal place if needed)

Part (b)

New investment function: I = - 30r (keep your answer to 1 decimal place if needed)

Real interest rate = (keep your answer to 1 decimal place if needed)

Investment = (keep your answer to 1 decimal place if needed)

Part (c)

Government spending = (keep your answer to 1 decimal place if needed)

Investment = (keep your answer to 1 decimal place if needed)

Describe the concept of zero lower bound as it relates to interest rates. In the prescribed textbook, Blanchard states that the federal funds rate cannot be zero (2017: 27).

Explain why you agree or disagree with this statement.

(5)

Q.1.2

Give two equations that can be used to represent the consumption function equation.

(Hint: Name each of its components.)

27. Parmacheenee Belle's entire common stock portfolio ($500,000) is allotted to an index fund tracking the Standard & Poors 500 index. The expected rate of return on the index is 9.5% and the standard deviation is 18% per year. The one-year risk-free rate is 2.0%. Now Ms. Belle receives a strongly favorable security analyst's report on Mycronics Corp. The analyst projects a return of 25%. Myroncis has a high volatility (40% annual standard deviation) but its correlation coefficient with the S&P 500 is only .3. Assume the return in the analyst's report is an unbiased forecast. Should Ms. Belle sell part of her index fund holdings and invest in Myronics? If so, how much? Note: Ms. Belle can also lend or borrow at the 2.0% risk-free rate. 28. Samantha Darling's entire common stock portfolio ($100,000) is allotted to an index fund tracking the Standard & Poors 500 index. The 27 c 2008, Andrew W. Lo and Jiang Wang 1.6 Risk & Portfolio Choice 1 QUESTIONS expected rate of return on the index is 12% and the standard deviation is 16% per year. The one-year risk-free rate is 5.5%. Now Samantha receives a strongly favorable security analyst's report on e.Coli Corp. The analyst projects a return for e.Coli of 25%. e.Coli has a high volatility (50% annual standard deviation) but its correlation coefficient with the S&P 500 is only .4. Assume the analyst's report is accurate. Should Samantha sell part of her index fund holdings and invest in e.Coli? If so, now much? Note: Samantha can also lend or borrow at the 5.5% risk-free rate. 29. You are a salesman/investment advisor working for a major investment bank. Whenever clients contact you with money to invest, your job is to help them find an appropriate mutual fund to invest in given their financial position. The available investments are: Fund E[R] (R) A 10% 15% B 20% 45% C 20% 55% Assume throughout this problem that you only recommend one of the three funds to your clients (possibly a different recommendation for different clients though). a) Would you recommend investment C to someone who comes to you with all his investment funds? Explain. b) Which investment would you recommend to Keith Richards, the really, really old rock star from the Rolling Stones? Assume he invests all his wealth in your particular recommendation. c) Might your answer to b) change if Keith invests only half his wealth in your particular recommendation? If so, under what circumstances? 30. Sarah runs an investment consulting business offering advice to clients on portfolio choices, using what she has learned in 15.401. Her analysis shows that the efficient frontier of risky assets can be obtained by mixing two portfolios, a portfolio of "large cap" stocks (L) and a portfolio of "small cap" stocks (S). In addition, she can also invest in riskless T-Bills (F). For a very risk-averse retiree, Sarah has recommended the following portfolio: 70% in F, 20% in L and 10% in S. For a young, less riskaverse executive, however, Sarah recommends only 10% in F and the 28 c 2008, Andrew W. Lo and Jiang Wang 1.6 Risk & Portfolio Choice 1 QUESTIONS rest in the two risky portfolios. Assume that Sarah has chosen the optimal portfolios for both the old retiree and the young executive. What are the weights for the young executive on the "large cap" and "small cap" portfolios, respectively? (Hint: The tangent portfolio should a combination of portfolios L and S.) 31. Which of the following common stock portfolios is best for a conservative, risk-averse investor? Explain briefly. Expected Expected Standard Deviation Return Risk Premium of Return Portfolio A 19% 13% 20% Portfolio B 16% 10% 16% Portfolio C 13% 7% 12.5% Note: the risk premium is calculated by subtracting a 6% Treasury bill rate from the expected rate of return. The investor can also buy Treasury bills. 32. Suppose the overall stock market is divided in four asset classes: largecap growth stocks (LGR, 40% of the market), large-cap income stocks (LINC, 35% of the market), small-cap growth stocks (SMGR, 15% of the market) and small-cap income stocks (SMINC, 10% of the market). Forecasted returns, standard deviations () and correlation coefficients for these asset classes are given on the table below. You can borrow or lend at the risk-free interest rate of 5%. You have $1 million to invest in some combination of the four asset classes. (You can buy index funds or exchange traded portfolios tracking the asset classes.) LGR LINC SMGR SMINC % of market 0.40 0.35 0.15 0.10 r 0.1438 0.1092 0.1329 0.0931 0.28 0.20 0.30 0.22 Correlations: LGR LINC SMGR SMINC LGR 1 0.65 0.70 0.30 LINC 0.65 1 0.40 0.55 SMGR 0.70 0.40 1 0.45 SMINC 0.30 0.55 0.45 1 29 c 2008, Andrew W. Lo and Jiang Wang 1.6 Risk & Portfolio Choice 1 QUESTIONS (a) What are the expected rate of return and standard deviation of the market portfolio? What is the market's Sharpe ratio (the ratio of expected risk premium to standard deviation)? (b) Can you improve the portfolio's Sharpe ratio by investing more in any of the asset classes? (Hint: Analyze a two-asset portfolio, with the market as one asset and a particular asset class as the other. If you sell some of the market portfolio and put the proceeds in that asset class, you end up over-weighting the asset class.) 30 c 2008, Andrew W. Lo and Jiang Wang 1.7 CAPM 1 QUESTIONS 1.7 CAPM 1. What is the beta of a portfolio with E(rp) = 18%, if rf = 6% and E(rM) = 14%? 2. You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars): Years from Now After-Tax Cash Flow 0 40 1 10 15 The project's beta is 1.8. Assuming that rf = 8% and E(rM) = 16%, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative? 3. Are the following true or false? (a) Stocks with a beta of zero offer an expected rate of return of zero. (b) The CAPM implies that investors require a higher return to hold highly volatile securities. (c) You can construct a portfolio with a beta of 0.75 by investing 0.75 of the investment budget in bills and the remainder in the market portfolio. 4. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%. A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year? 5. Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%. A stock has an expected rate of return of 4%. What is its beta? Why would anyone consider buying this risky asset which provides an expected return less than the risk-free rate? 6. In 1997 the rate of return on short-term government securities (pe

Distinguish between a floating (flexible) exchange rate system and a fixed exchange rate system in an open economy

ensure to answer all questions.