4. Consider an economy with a population of size 1 of consumers. Each consumer behaves exactly as in question 1 above. Assume that a fraction in of consumers are impatient. with b = I]. while a fraction 1 m of consumers are patient. with b = 1. Assume that patient and impatient types each have the same nonlabor income today and tomorrow. y and y'. There is no government, i.e. G = G' = T = T' = B = t}. {a} Find an expression for the equilibrium interest rate in this economy in terms of m,y.y'. You do not need to solve this expression. Hint: the tot-at supply of savings is equal to the fraction of impatient types times their saying, plus the fraction of patient types times their satiny. Eb} Suppose m = D so that everyone is patient. 1What is the real interest rate? How does it depend on endowments? Provide an economic interpretation. [c]: Suppose m = 1 so that everyone is impatient. "What is the real interest rate? How does it depend on endowments? Provide an economic interpretation. Ed} Suppose y = yr and m = 1f2. Find an expression for the equilibrium interest rate. [e]: Describe: in general. how the real interest rate varies with m