Consider the 2-period environment from class.The economy is populated by two types of agents A and B. There is an equalnumber (N) of each type. The agents have preferences which incorporate impatience. The agents put less emphasis on future consumption than on consumption in period 1.Specifically, the preferences are
MU(c1) = 1/c1 andMU(c2) = β/c2
Where β is positive but less than1
Type A's endowment pattern is(y1A,y2A) = (x,0) wherex > 0. Type B's endowment pattern is(y1B,y2B) = (0,1). Let1 + r1 be the real rate of return
(a) Write down the tangency conditionfor a type A and B agents.
(b) Find the equilibrium real rate of return.How does 1+ r1 depend on β? How does 1 + r1 depend on x? What is the intuition forthese effects?