Consider the Euler equation for consumption for log utility, equation (16.8), and answer the following questions:
(a) If the real interest rate is 5 percent and β = 1, what growth rate for consumption will households choose?
(b) What if β = 0.95?
(c) Alternatively, suppose the long-run growth model means GDP per person will grow at a constant rate of 2 percent per year. Suppose β = 0.95. In order for the Euler equation to hold in this case, what value must the real interest rate take?