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In a two-period model, suppose that a particular consumer's utility function is: U(cl, Cg) = 10g(c1) + log(cz) where c1, c2 are the consumption of a good (orange) in the two periods. The real interest rate is 20% (given). In is normalized to 1. The endowments in the two periods are 1 and 2.4 oranges respectively. ** Part a (5 marks) State the period budget constraints for the two periods. ** Part b (5 marks) Derive the lifetime budget constraint (in real terms). ** Part c (5 marks) Solve for the optimal consumption path (c1, C2). ** Part d (5 marks) Now suppose that there is an inflation of 10%. Using the Fisher equation, find the nominal interest rate