1) Imagine an economy with the following set of assumption: 1) There is only one good in the economy that is consumed for two periods: X1 and X2 2) Two (groups of) individuals: Individual A and Individual B 3) Utility function of Individual A: UA(X1A,X2A)=logX1A+AlogX2A 4) Utility function of Individual B: UB(X1B,X2B)=logX1B+BlogX2B 5) Individuals have period 1 endowment (e1A,e1B)=(40,20) 6) Individuals do not have any endowments in period 2. Instead, in period 1, they own shares of the company that will produce the consumption good in period 2 . One share of the stock is a claim to 1 unit of consumption good to be produced in period 2. The company will produce 40 units of good in period 2 and the current ownership of the firm is as follows: (A,B)=(15,25) 7) Individuals can trade shares in period 1. The relative price of the share is . A. Interpret the coefficient in the utility functions of individuals. B. Set A=2/3 and B=1/2. Write down and explain market clearing conditions, budget constraints in terms of contemporary prices (two for each individual for each period) and optimization conditions for the two individuals. C. Solve for the equilibrium (you must rewrite the budget constraints). What is the real interest rate in the equilibrium? What is the consumption level for each individual in both periods? Who bought shares and who sold shares in period 1 ? In other words, who decided to save more and who to save less? D. Explain intuitively, what will happen to the real interest rate if: - the value of for the two agents decreases. - the second period endowments increase. E. Now assume that inflation is 100%. What is the price a bond that pays $1 in the second period? 1) Imagine an economy with the following set of assumption: 1) There is only one good in the economy that is consumed for two periods: X1 and X2 2) Two (groups of) individuals: Individual A and Individual B 3) Utility function of Individual A: UA(X1A,X2A)=logX1A+AlogX2A 4) Utility function of Individual B: UB(X1B,X2B)=logX1B+BlogX2B 5) Individuals have period 1 endowment (e1A,e1B)=(40,20) 6) Individuals do not have any endowments in period 2. Instead, in period 1, they own shares of the company that will produce the consumption good in period 2 . One share of the stock is a claim to 1 unit of consumption good to be produced in period 2. The company will produce 40 units of good in period 2 and the current ownership of the firm is as follows: (A,B)=(15,25) 7) Individuals can trade shares in period 1. The relative price of the share is . A. Interpret the coefficient in the utility functions of individuals. B. Set A=2/3 and B=1/2. Write down and explain market clearing conditions, budget constraints in terms of contemporary prices (two for each individual for each period) and optimization conditions for the two individuals. C. Solve for the equilibrium (you must rewrite the budget constraints). What is the real interest rate in the equilibrium? What is the consumption level for each individual in both periods? Who bought shares and who sold shares in period 1 ? In other words, who decided to save more and who to save less? D. Explain intuitively, what will happen to the real interest rate if: - the value of for the two agents decreases. - the second period endowments increase. E. Now assume that inflation is 100%. What is the price a bond that pays $1 in the second period
