For a two-period binomial model, you are given: (i) Each period is one year. (ii) The current price for a nondividend-paying stock is 20. (iii) u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up. (iv) d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down. (v) The continuously compounded risk-free interest rate is 5%. Calculate the price of an American call option on the stock with a strike price of 22.

Determine which of the following statements about futures and forward contracts is false. (A) Frequent marking-to-market and settlement of a futures contract can lead to pricing differences between a futures contract and an otherwise identical forward contract. (B) Over-the-counter forward contracts can be customized to suit the buyer or seller, whereas futures contracts are standardized. (C) Users of forward contracts are more able to minimize credit risk than are users of futures contracts. (D) Forward contracts can be used to synthetically switch a portfolio invested in stocks into bonds. (E) The holder of a long futures contract must place a fraction of the cost with an intermediary and provide assurances on the remaining purchase price. 70. Investors in a certain stock demand to be compensated for risk. The current stock price is 100. The stock pays dividends at a rate proportional to its price. The dividend yield is 2%. The continuously compounded risk-free interest rate is 5%. Assume there are no transaction costs. Let X represent the expected value of the stock price 2 years from today. Assume it is known that X is a whole number. Determine which of the following statements is true about X. (A) The only possible value of X is 105. (B) The largest possible value of X is 106. (C) The smallest possible value of X is 107. (D) The largest possible value of X is 110. (E) The smallest possible value of X is 111.

Problem 1: Learning by Doing with Spillovers Consider the model of learning by doing with spillovers (Arrow & Romer) presented in class and assume that the production function is Cobb-Douglas, that is, Y m m m 1 t = (Kt ) (htLt ) However, assume there are diminishing returns to technological progress, ht = kt , for some constants > 0, 0 < < 1, where Km kt = t Lm . t i. We want to write the equilibrium dynamics are functions of c and k alone: (a) Express the return R that firms are willing to pay in equilibrium as a function of kt alone. (b) Express the resource constraint in terms of c and k. ii. Imagine the continuous time version of the dynamics in part (a) and draw the phase diagram. iii. Repeat parts (a) and (b) for the social planner's problem (Hint: this is similar to the Ramsey model). iv. How does the phase diagram of part (c) compare to that of part (b)? which line changes, the c = 0 locus or the k = 0 locus? What happens to the steady state levels of c and k? v. If the equilibrium allocations differ from the planner's allocations, describe a policy that would restore efficiency. 1 Problem 2: Tax smoothing Consider a two-period economy. Households preferences are given by U = u (c1, c2, n1, n2) = c1 n 2 1 + c 2 2 n2 , where ct 0 is consumption in period t {1, 2} and nt 0 is lab or supply. Labor is used to produce output with the technology yt = Ant (there is no capital). The wage is thus given by wt = A, for t {1, 2}. The government taxes labor income at rates t in period t, so households' intertemporal budget constraint is given by 1 1 c1 + c2 = (1 1)An1 + (1 2)An2 1 + r 1 + r The government has constant expenditues, gt = g for t {1, 2}. Its intertemporal budget constraint is thus given by 1 IBC (1An1 g1) + (2An2 g2) = 0 1 + r Finally, the resource constraints in the economy are y1 = An1 = c1 + g and y2 = An2 = c2 + g. 1) Consider the household's optimal consumption and labor-supply problem. Argue that the solution is interior only if the interest rate r is such that 1 = . 1+r Assume that this is the case for the rest of the exercise. 2) Solve for the household's optimal n1 and n2 as functions of 1 and 2. 3) Use the two resource constraints to replace ct = Antg into U. Next, use the previous result to replace nt with a function of t . You should now have expressed the household's utility U as a function of the two tax rates: U = U(1, 2) 4) Do the same for the government's intertemporal buget: replace nt with the function of t that you found in part 2 so as to express IBC in terms of 1 and 2 : IBC = IBC(1, 2) 5) It follows that the optimal policy is given by the combination of 1 and 2 that solves the following problem: maxU(1, 2) s.t. IBC(1, 2) = 0 Prove that the optimal policy satisfies 1 = 2 (tax smoothing). 6) Suppose that we increase g1 but reduce g2 so that g1 + g2 stays constant. What happens to the optimal taxes? Explain.

7. Which of the following is one way that businesses use marketing information: A. To predict change B. To analyze data C. To develop surveys D. To conduct research 48. Which of the following is a characteristic of the data collection step in marketing research: A. The least expensive step in marketing research B. The least tedious step in marketing research C. The step in which the most mistakes are made D. The step that is most interesting to researchers 49. Which of the following is an example of a durable good: A. House B. Haircut C. Gasoline D. Hamburger 50. Motives, perception, attitude, lifestyle, personality, and abilities are __________ factors influencing consumer behavior. A. political B. social C. psychological D. economic 51. Business goals are accomplished by means of marketing A. salespeople. B. budgets. C. profit. D. strategies. 52. Products that appeal to the majority of customers are often sold through __________ marketing efforts. A. segmented B. mass C. demographic D. psychographic

The current price of a non-dividend-paying stock is 100. The annual effective risk-free interest rate is 4%, and there are no transaction costs. The stock's two-year forward price is mispriced at 108, so to exploit this mispricing, an investor can short a share of the stock for 100 and simultaneously take a long position in a two-year forward contract. The investor can then invest the 100 at the risk-free rate, and finally buy back the share of stock at the forward price after two years. Determine which term best describes this strategy. (A) Hedging (B) Immunization (C) Arbitrage (D) Paylater (E) Diversification 74. Consider an airline company that faces risk concerning the price of jet fuel. Select the hedging strategy that best protects the company against an increase in the price of jet fuel. (A) Buying calls on jet fuel (B) Buying collars on jet fuel (C) Buying puts on jet fuel (D) Selling puts on jet fuel (E) Selling calls on jet fuel.

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