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Let each consumer have preferences described by the utility function
and let the production function be given by
y = kα
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 = αkα-1, show that the steady-state interest rate is