In a certain economy that produces only one good, corn, people live two periods and value consumption in period 1 at C2/C1 units of consumption in period 2-that is, they would be willing to give up as much as C2/C1 units of consumption in period 2 to get one more unit of consumption in period 1, where C1 is consumption in period 1 and C2 is consum. in period 2. There are 100 people. Each has after tax real income of 100 bushels in period 1 and 84 in period 2. Business investment is 1000 bushels of corn no matter what the real interest rate is. a. Find period 1 saving per person as a function of real interest rate in the economy. Show work. Then pick values for r, find resulting value of savings for each r, and graph the savings function. b. Given that investment demand is 1000 or 10 bushels per person, find the equilibrium real rate for this economy-value of r that makes desired savings per person equal to investment per person.