Question 1 (7 Marks) Joan has a utility function given by U(C'1, Cg) = C?

Question 1 and 2 talk about the utility function,MRIS,optimal consumption bundle

• Attachment 1
• Attachment 2

Question 1 (7 Marks) Joan has a utility function given by U(C'1, Cg) = C? + 60;, where C; and 02 representher consumption in the current period (i.e. Period 1) and future period (i.e. Period2), respectively. Her utility function meets the four strict axioms of preferences (Com-pleteness, Transitivity, Strict Non-satiation, and Strict Convexity). Joan earns Y1 in thecurrent period and does not earn any income in the future period. Her savings earn aneffective interest rate of r from the current period to future period, where r > 0. (a) 1.5 Mark. Write down the range of value for 7 so that Joan’s utility function meetsthe strict axioms. Explain your answer. (b) 2 Marks. Derive Joan’s Marginal Rate of Intel-temporal Substitution and pure rateof time preference. (c) 2 Marks. Find Joan’s optimal consumption bundle (C; and CE). (d) 1.5 Marks. Explain the impact of 6, r and 7 on the optimal consumption in thecurrent period.