Problem 3 Irving Fisher Determination of Interest Rate Consumption can take place in two periods only: today (Cl) and tomorrow (02). Jane's income is $0 today (she is a student now). Tomorrow she is going to be a CEO with income $1000 (hence her endowment is off : (0, 1000)). William is a sportsman with $1000 income today, and tomorrow he will get $0 (03W : (1000, 0)). They both have an identical utility function: Ui(Cl,Cg) =ln01 +ll'102f01'i: J,W where )8 is a discount factor. (The higher the )3, the more patient the consumer is since the value of utility tomorrow relative to utility today is higher). a) Plot an Edgeworth box and mark the allocation corresponding to the initial endowments. Is the allocation of initial endowments Pareto efcient? b) Assume : 1/ 2. Find the equilibrium interest rate and depict the equilibrium on the Edgeworth box. (Hint: Instead of working with a harder \"intertemporal\" model, you can rst nd equilibrium prices 131 and p2 similar to the apple and orange model and then use: pl/p2 = 1 + r. c) Is the equilibrium allocation Pareto efcient? d) Assume now that consumers are more patient and )5 = 1. Repeat the question in part (b). How does your new equilibrium interest rate compare to the one in part (b)? Can you give some economic intuition about your result? e) Now assume )3 = 1/2, and Jane's income tomorrow changes to $2000 (MI 2 (O, 2000)). Is the interest rate higher or lower than the one in part (b)? Explain