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Question 1 Let an individual's utility function be given as u(x1, x2) = 2 p x1 x2 . a) Compute the Marginal Rate of Substitution. b) Initially, the individual consumes bundle (x1 =100, x2 =12.5). Then, the individual's consumption of the first good is cut to x0 1 = 50. What is the new level of consumption of good 2, x0 2, that the individual needs to consume in order to reach the same utility level as before? c) Given the prices p1 = 1 and p2 = 2 for the first and the second good, respectively, and a budget of m = 100, what is the best consumer choice? d) Find the individual's general demand function for good 2. e) If the price for the first good rises to p0 1 = 50, how much less of good 2 will the individual conusme? f) Assuming the demand function for good 1 is x1(p1) = 12 m p1 , what is the inverse demand funtion, and what is the own-price elasticity of demand for good 1! g) Assuming the demand function for good 1 is x1(p1) = 1 2 m p1 , show mathematically that the good is not inferior.

1. Determine which statement about zero-cost purchased collars is FALSE (A) A zero-width, zero-cost collar can be created by setting both the put and call strike prices at the forward price. (B) There are an infinite number of zero-cost collars. (C) The put option can be at-the-money. (D) The call option can be at-the-money. (E) The strike price on the put option must be at or below the forward price. 2. You are given the following: The current price to buy one share of XYZ stock is 500. The stock does not pay dividends. The continuously compounded risk-free interest rate is 6%. A European call option on one share of XYZ stock with a strike price of K that expires in one year costs 66.59. A European put option on one share of XYZ stock with a strike price of K that expires in one year costs 18.64.

3. Happy Jalapenos, LLC has an exclusive contract to supply jalapeno peppers to the organizers of the annual jalapeno eating contest. The contract states that the contest organizers will take delivery of 10,000 jalapenos in one year at the market price. It will cost Happy Jalapenos 1,000 to provide 10,000 jalapenos and today's market price is 0.12 for one jalapeno. The continuously compounded risk-free interest rate is 6%. Happy Jalapenos has decided to hedge as follows: Buy 10,000 0.12-strike put options for 84.30 and sell 10,000 0.14-stike call options for 74.80. Both options are one-year European. Happy Jalapenos believes the market price in one year will be somewhere between 0.10 and 0.15 per jalapeno. Determine which of the following intervals represents the range of possible profit one year from now for Happy Jalapenos. (A) -200 to 100 (B) -110 to 190 (C) -100 to 200 (D) 190 to 390 (E) 200 to 400

5. The PS index has the following characteristics: One share of the PS index currently sells for 1,000. The PS index does not pay dividends. Sam wants to lock in the ability to buy this index in one year for a price of 1,025. He can do this by buying or selling European put and call options with a strike price of 1,025. The annual effective risk-free interest rate is 5%. Determine which of the following gives the hedging strategy that will achieve Sam's objective and also gives the cost today of establishing this position. (A) Buy the put and sell the call, receive 23.81 (B) Buy the put and sell the call, spend 23.81 (C) Buy the put and sell the call, no cost (D) Buy the call and sell the put, receive 23.81 (E) Buy the call and sell the put, spend 23.81

Consider the following arbitrage-free market

S0 =(1,c),D= [ 1 1 1

140 110 80]

D is a matrix that I've tried to show.

(a) (5 points) How many are the primary assets of the market and how many are the states of the world?Is the market complete?

(b) (6 points) If C0 = 70/3 and P0 = 10/3 are arbitrage-free prices for a call and a put 33

option with exercise price K = 100 respectively. Find c.

(c) (6 points) If C0 = 50 is an arbitrage-free price for a call option with exercise price

K = 70. Find c.

(d) (8 points) If = 10 is an arbitrage-free price for a contingent claim with payoff X = (15,12,9) at time T. Find c.

X = (15,12,9) at time T. Find c.

An excavation contractor deposited 200000 quarterly into a fund paying a nominal interest rate Of 8% per year compounded semiannually For a period of 4 years assume there is no interpolation interest accured . At the end of the fourth year they want to purchase a fleet of trucks for 5000000.The contractor intents to make an immediate cash payment equal amount accumulated and to pay for the rest by equal month end payments. Their financing agreement with the truck dealer is payment should be completed in 18 months and the nominal interest rate should be 18% per year compounded monthly. What will these monthly payments be? Use 4 digits after the decimal point in your interest rate calculation With cash flow diagram