You are to price options on a futures contract. The movements of the futures price are modeled by a binomial tree. You are given: (i) Each period is 6 months. (ii) u/d = 4/3, where u is one plus the rate of gain on the futures price if it goes up, and d is one plus the rate of loss if it goes down. (iii) The risk-neutral probability of an up move is 1/3. (iv) The initial futures price is 80. (v) The continuously compounded risk-free interest rate is 5%. Let CI be the price of a 1-year 85-strike European call option on the futures contract, and CII be the price of an otherwise identical American call option. Determine CII CI. (A) 0 (B) 0.022 (C) 0.044 (D) 0.066 (E) 0.088 47. Several months ago, an investor sold 100 units of a one-year European call option on a nondividend-paying stock. She immediately delta-hedged the commitment with shares of the stock, but has not ever re-balanced her portfolio. She now decides to close out all positions. You are given the following information: (i) The risk-free interest rate is constant. (ii) Several months ago Now Stock price $40.00 $50.00 Call option price $ 8.88 $14.42 Put option price $ 1.63 $ 0.26 Call option delta 0.794 The put option in the table above is a European option on the same stock and with the same strike price and expiration date as the call option. calculate profit

for constant returns to scale in production. D. Use a graph to explain the relationship between the purchase of insurance and the concept of risk aversion. Why might someone who purchases fire insurance also play the lottery? E. Your uncle gives you a government bond for your Bar Mitzvah that can be given back to the government for 100 dollars in five years. You would rather have cash. How much could you sell the bond for today if the interest rate on FDIC insured savings accounts is fixed at 5 percent (compounded annually)? F. Suppose that the demand for MP3 downloads is a linear function of their price and the annual income of college students. Make up some notation for a demand equation that expresses this model of demand (assume downloads are not free). Use this equation to compute the price-elasticity of demand for MP3 downloads as a function of price and income. G. Do private schools do a better job of preparing students for MIT than public schools? Consider two regressions that address this question, one short and one long. The short regression looks like this: MITGPAi = 0+ 0PRIVATEi + 0i The long regression adds controls for a student's SAT score: MITGPAi = 1 + 1PRIVATEi + 1SATi + 1i (i) Why is the long regression likely to be a better measure of the effect of a private school education on MIT GPA? (ii) Use the omitted variables bias formula to give a precise description of the likely relationship between 0 and 1. MIT OpenCourseWare http://ocw.mit.edu 14.64 Labor Economics and Public Policy Fall 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms

BOP Transactions. Identify the correct BOP account for each of the following transactions.

a. A German-based pension fund buys U.S. government 30-year bonds for its investment porte Financial account portfolio investment liabilities

b. Scandinavian Airlines System (SAS) buys jet fuel at Newark Airport for its flight to Copenhagen. Current account: Goods: Exports FOB

C. Hong Kong students pay tuition to the University of California, Berkeley Current account Services credit

d. The US Air Force buys food in South Korea to supply its air crews. Current account Goods Imports

e. A Japanese auto company pays the salaries of its executives working for its US subsidiaries Current account Services credit AUS tounst pays for a restaurant meal in Bangkok.

Current account Services debat

g. A Colombian citizen smuggles cocaine into the United States receives cash and imeggles the dollars back into Colombia Unrecorded, but should be a current account item

h. AUK corporation purchases a euro denominated bond from an Italian MNE Does not enter the US balance of payments.

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Part I. (45 points) 1. Use the following algebraic model of an economy to answer parts a-d. You may use graphical versions of this model to answer parts e and f.

(1) Labor Demand: Ld = n0 - n1*(W/P) + n2*K (2) Labor Supply: Ls = s0 + s1*(W/P) - s2*to (3) Labor Market Position: U = (Ls - Ld)/Ls + U* (4) Production: Y = Tech*Ld.7 *K.3 (5) Consumption: C = co + c1*Yd (6) Investment: I = d - e*r + f*Y (7) Net Exports: X = go - g1*Yd - g2*r +g3*Yf (8) Disposable Income Yd = Y - T (9) Taxes: T = to + t1*Y (10) Aggregate Expenditure: AD = C + I + G + X (11) Goods Market Equilibrium: Y = AD (12) Money Demand: Md - P = h1*Y - h2*i (13) Money Supply: M = m0 + m1*i + m2*(Yp - Y) (14) Money Market Equilibrium: Md = M (15) Nominal Interest Rate: i = r + e

Endogenous Variables Exogenous Variables Ld,P,U,Ls,Y,C,Yd,T,r W,K,U*, Tech, Yf, Yp, e and I,X,AD,Md,M,i various autonomous terms (e.g., no, so, and to)

(8) a. Derive the IS Curve. (6) b. Derive the LM Curve. (6) c. Derive the Aggregate Demand Curve and indicate its slope. (5) d. Derive the Aggregate Supply Curve and determine the sign of its slope. (10) e. Determine the effect of an increase in expected inflation (e) on output, prices, real interest rates, and employment. Show graphics. (10) f. Show how an increase in the capital stock (K) affects output, prices, real interest rates, and employment. Show graphics.

2. (30 points) Consider the following version of model 5. McCallum's Rule has replaced Taylor's Rule. Except where indicated, variables are expressed in current year terms thus the "t" subscript has been suppressed.

IS Curve: Y = Yp - (r - ) + Fisher Equation: r = i - e Phillips Curve: = e + (Y - Yp) + v Inflation Expectations: e = -1 McCallum's Rule: M = M-1 + 1*(* - ) + 2*(Yp-Y) Money Demand: Md = k*Y - h*i Money Market Equilibrium: M = Md

Endogenous variables: Y, r, , e, M, Md, i Exogenous variables: Yp, , , v, *

(4) a. Derive the LM curve. (6) b. Derive the dynamic aggregate demand curve. Indicate its slope. (4) c. Determine the dynamic aggregate supply curve and indicate its slope. (8) d. Indicate the effects of a change in the potential GDP (Yp) on the paths of output and inflation. (8) e. Indicate the effects of a negative supply shock (v >0) on the paths of output and inflation.

Part II (15 points each) Answer four of the following questions. Indicate any noteworthy assumptions.

1. Evaluate the quotation at the beginning of the exam. If you believe that it is true, provide evidence to support your assertion. If you believe that it is false, how would you change the statement to make it true? Provide evidence to support your claim.

2. a. What is Okun's Law? b. How have macroeconomic policy makers used it to determine how much stimulation should be provided by monetary and fiscal policy? c. In what ways might Okun's Law be a misleading guide to appropriate policy?

3. Expectations and Credibility a. Distinguish between forward and backward looking formulations of expectations regarding the inflation rate. b. How does this distinction matter in terms of macroeconomic stabilization policy? c. Whose credibility matters in terms of part b? Why does it matter?

4. The effects of macroeconomic stabilization policy depend on a number of factors. a. Clearly illustrate and discuss how the specification of the Aggregate Supply curve matters for determining the effects of stabilization policy on output and prices. b. Clearly explain one set of circumstances under which money would be neutral; that is, changes in the stock of money would not affect real variables?

5. The Natural Rate of Unemployment and the Phillips Curve a. What is meant by the term "natural rate of unemployment"? b. What is the Phillips Curve and how do some policy makers use it? c. What's the relationship between the natural rate of unemployment and the Phillips Curve? d. What can the character and stability of the Phillips Curve tell us about the Sacrifice Ratio?

6. The Iron Triangle or Impossible Trilogy a. Is monetary or fiscal policy more potent under fixed exchange rates? Explain why. b. In terms of policy making regarding openness of the economy, what three policy options must be jointly considered by macroeconomic policy makers? Explain why the third policy depends upon the choice of the first two. c. In light of the Iron Triangle, why might large countries and small countries make different policy choices? "There are two and only two ways to grow an economy in real terms. You can grow your working population or you can increase your productivity. That's it. - John Mauldin

Part I. (40 points) 1. Use the following algebraic model of an economy to answer parts a-d. You may use graphical versions of this model to answer parts e and f.

(1) Labor Demand: Ld = n0 - n1*(W/P) + n2*K + n3*RM (2) Labor Supply: Ls = s0 + s1*(W/P) (3) Labor Market Position: U = (Ls - Ld)/Ls + U* (4) Production: Y = Tech*Ld.6 *K.3*RM.1 (5) Consumption: C = co + c1*Yd +c2*NW - c3*P (NW = net worth) (6) Investment: I = d - e*r (7) Governmental Expenditures G = G0 + f*(Yp - Y) (8) Net Exports: X = go - g1*Yd - g2*r (9) Disposable Income Yd = Y - T (10) Taxes: T = to + t1*Y (11) Aggregate Expenditure: AD = C + I + G + X (12) Goods Market Equilibrium: Y = AD (13) Money Demand: Md - P = h1*Y - h2*i (14) Money Supply: M = m0 + m1*i (15) Money Market Equilibrium: Md = M (16) Nominal Interest Rate: i = r + e

Endogenous Variables Exogenous Variables Ld,P,U,Ls,Y,C,G,Yd,T,r W,K,RM, U*, Tech, NW, Yp, e and I,X,AD,Md,M,i various autonomous terms (e.g., n0, s0, t0)

(6) a. Derive the IS Curve. (4) b. Derive the LM Curve. (6) c. Derive the Aggregate Demand Curve and indicate its slope. (6) d. Derive the Aggregate Supply Curve and determine the sign of its slope. (9) e. Determine the effect of an increase in potential GDP (Yp) on output, prices, real interest rates, and employment. Show graphics based on the above model. (9) f. Show how an increase in the raw materials (RM) affects output, prices, real interest rates, and employment. Show graphics based on the above model.

2. (24 points) Consider the following version of model 5. Except where indicated, variables are expressed in current year terms thus the "t" subscript has been suppressed. Be sure to show your work for all parts.

IS Curve: Y = Yp - (r - ) + NX+ Net Exports NX = x0 - x1*E Fisher Equation: r = i - e Phillips Curve: = e + (Y - Yp) + v Inflation Expectations: e = -1 Monetary Rule: i= + + *( - *) + (1- )*(Y-Yp) 0 < < 1

Endogenous variables: Y, r, NX, , e, i Exogenous variables: Yp, , , E, x0,v, *

(6) a. Derive the dynamic aggregate demand curve. Indicate its slope. (3) b. Determine the dynamic aggregate supply curve and indicate its slope.

Determine if the following statement is true or false: When developing an exit strategy entrepreneurial venture, the most important consideration is finding a suitable buyer. A. False, there are many factors to consider, such as company valuation and personal goals. B. True, if the buyer is inexperienced, the business risks monetary losses and long-term failure. C. False, the most important factor that an entrepreneur should consider is profitability. D. True, the valuation of a business is dependent on the buyer's financial resources. 32. Which of the following is an example of an intangible asset: A. Equipment B. Inventory C. Office building D. Accounts receivable 33. Which of the following is a characteristic of a profit-and-loss statement: A. Is the same as a balance sheet B. Summarizes expenses and revenue from sales C. Shows the owner's financial position D. Lists assets and liabilities 34. In managerial accounting, the number of hours that a business runs its machinery during the production process is classified as a(n) A. production output. B. cost driver. C. unexpected expense. D. inflexible transaction. 35. Businesses often obtain cash to produce and sell goods by borrowing against their A. current liabilities. B. accounts receivable. C. operating expenses. D. promissory notes. 36. When determining financing needs, what factor should businesses consider that will help decide whether they can repay the debt? A. Liquidity B. Depreciation C. Equity D. Inventory.