Let each consumer have preferences described by the utility function and let the production…

Let each consumer have preferences described by the utility function

and let the production function be given by

y = k^α

a. Demonstrate that utility maximization results in demands that satisfy

b. Using the result in part a, the consumer’s budget constraint and the capital market equilibrium condition, show that the steady-state value of k satisfies

c. Employing the factor price condition r = αk^α-1, show that the steady-state interest rate is