John and Peter are two representative consumers/investors who maximize the util- ity of consumption. John's utility of consumption is characterized as In(a) + 2 ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2 ln(x) + In(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans for John and Peter, respectively, if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other? John and Peter are two representative consumers/investors who maximize the util- ity of consumption. John's utility of consumption is characterized as In(a) + 2 ln(y) while Peter puts more weight on the current consumption level and has a utility function of 2 ln(x) + In(y). John has a wealth of ($10, $20) thousand, while Peter has a wealth of ($20, $15) thousand now and next year, respectively. (a) What are the optimal consumption plans for John and Peter, respectively, if the interest rate is 5% per annum? (b) If John and Peter are the only investors/consumers, what is the equilibrium interest rate? (c) Further to part (b), how much do they borrow or lend to each other