PROBLEM 2.2. Consider an economy with two individuals, one (consumption) good and two possible states of the world. The quantities of the good available to the individuals in each state are reported in Table 1 (on page 4). Both states have probability 21 and both individuals have the same utility function u(w)=logw, where w is the amount of the good consumed in each state. Table 1. The quantities of the good available to Individuals A and B in States 1 and 2. 2.2.1. What is the expected quantity of the good available (a) to Individual A, (b) to Individual B ? 2.2.2. What would be the expected utilities of Individual A and Individual B, if each individual consumed the quantity of the good available to him or her in each state of the world? 2.2.3. Suppose that before the "true" state of the world becomes known, individuals A and B can write a contract that entails the following obligations: (1) In State 1, Individual A transfers 15 units of the good to Individual B. (2) In State 2, Individual B transfers x units of the good to Individual A. What are the smallest and the largest value of x such that both A and B would in principle be willing to sign the contract? PROBLEM 2.2. Consider an economy with two individuals, one (consumption) good and two possible states of the world. The quantities of the good available to the individuals in each state are reported in Table 1 (on page 4). Both states have probability 21 and both individuals have the same utility function u(w)=logw, where w is the amount of the good consumed in each state. Table 1. The quantities of the good available to Individuals A and B in States 1 and 2. 2.2.1. What is the expected quantity of the good available (a) to Individual A, (b) to Individual B ? 2.2.2. What would be the expected utilities of Individual A and Individual B, if each individual consumed the quantity of the good available to him or her in each state of the world? 2.2.3. Suppose that before the "true" state of the world becomes known, individuals A and B can write a contract that entails the following obligations: (1) In State 1, Individual A transfers 15 units of the good to Individual B. (2) In State 2, Individual B transfers x units of the good to Individual A. What are the smallest and the largest value of x such that both A and B would in principle be willing to sign the contract