7. There are two types of agents in an endowment economy: Half are Type Early and half are type Late. Eariys earn all their income in time 1: they earn S1 when young and 50 when old. Lates earn all their income in time 2: they earn 50 when young and 51.5 when old. Fortunately for us, both Eariys and Lates have the same utility function: this is a story about productivity diversity, not about taste diversity. Here's their utility function: U = in c: + In C; Since it's a 100% conventional endowment economy, net saying is zero, but financial markets work well enough that, if desired, Earlys and Lates can borrow or lend to each other with 100% confidence that lenders will be repaid. Of course, everyone faces interternporal budget constraints (IBCs), which will all hold exactlypeople consume all their wealth before death. a. What's the equilibrium interest rate in this economy? Report in correct units b. What will c; be for the Earlys? Report in correct units: c. What will c; be for the Lates? Report in correct units