1. Rita Dillard is the Admiral of the First Galactic Fleet, She plans to make some investment with her 15,000 energy credits (currency used in the Galactic Federation). Two choices are on the table: Galactic Exotic Gases, selling for 300 energy credits per share, and National Living Metal, selling for 150 energy credits. The future state of the Galactic Federation is uncertain. If there is a war with Galactic Empire (state 2), Rita expects Galactic Exotic Gases to be worth 540 energy credits since the Exotic Gases can boost the speed of military starships, which gives them an edge to win the war. However, if peace prevails (state 1), Galactic Exotic Gases will be worth only 60 energy credits per share. National Living Metal should sell at a future price of 90 energy credits per share in either state. a. Compute the determinant of the matrix with the two securities as columns to determine whether the market is complete or not. b. Compute the prices of pure securities. c. If Rita only buys Galactic Exotic Gases, how many shares can she buy? What would be her final wealth in each state? If she only buys National Living Metal, how many shares can she buy? What would be her final wealth in each state? d. Suppose Rita can buy as well as short-sell securities, but she must be able to meet all claims in the future. What is the maximum number of National Living Metal shares she can short-sell to buy Galactic Exotic Gases? How many shares of Galactic Exotic Gases could she short-sell to buy National Living Metal? What would be her final wealth in both cases and in each possible future state? 1 ECON 3413 Assignment 3 Fall 2022 e. Suppose a third security, Interplanetary Dark Matter, is available and should be worth 420 energy credits per share if peace continues and 540 energy credits per share if war breaks out. What would be the price of Interplanetary Dart Matter? f. Suppose Rita's utility function be written as U=W10.8W20.2, where W1 denotes her wealth level if state 1 (peace) realizes, and W2 denotes her wealth level if state 2 (war) occurs. What is her optimal portfolio? (i.e., how many shares of each security should she buy or sell) Hint: Rita needs to maximize her utility with the budget constraint of a1W1+a2W2=a3, where you can find a1,a2,a3 by summarizing wealth results from (c), (d) on a graph with axes W1,W2. 1. Rita Dillard is the Admiral of the First Galactic Fleet, She plans to make some investment with her 15,000 energy credits (currency used in the Galactic Federation). Two choices are on the table: Galactic Exotic Gases, selling for 300 energy credits per share, and National Living Metal, selling for 150 energy credits. The future state of the Galactic Federation is uncertain. If there is a war with Galactic Empire (state 2), Rita expects Galactic Exotic Gases to be worth 540 energy credits since the Exotic Gases can boost the speed of military starships, which gives them an edge to win the war. However, if peace prevails (state 1), Galactic Exotic Gases will be worth only 60 energy credits per share. National Living Metal should sell at a future price of 90 energy credits per share in either state. a. Compute the determinant of the matrix with the two securities as columns to determine whether the market is complete or not. b. Compute the prices of pure securities. c. If Rita only buys Galactic Exotic Gases, how many shares can she buy? What would be her final wealth in each state? If she only buys National Living Metal, how many shares can she buy? What would be her final wealth in each state? d. Suppose Rita can buy as well as short-sell securities, but she must be able to meet all claims in the future. What is the maximum number of National Living Metal shares she can short-sell to buy Galactic Exotic Gases? How many shares of Galactic Exotic Gases could she short-sell to buy National Living Metal? What would be her final wealth in both cases and in each possible future state? 1 ECON 3413 Assignment 3 Fall 2022 e. Suppose a third security, Interplanetary Dark Matter, is available and should be worth 420 energy credits per share if peace continues and 540 energy credits per share if war breaks out. What would be the price of Interplanetary Dart Matter? f. Suppose Rita's utility function be written as U=W10.8W20.2, where W1 denotes her wealth level if state 1 (peace) realizes, and W2 denotes her wealth level if state 2 (war) occurs. What is her optimal portfolio? (i.e., how many shares of each security should she buy or sell) Hint: Rita needs to maximize her utility with the budget constraint of a1W1+a2W2=a3, where you can find a1,a2,a3 by summarizing wealth results from (c), (d) on a graph with axes W1,W2
