Problem 1. The amount of total output produced by Buckeyeland every year is given as 1 2 where Y}, is the output, K; is the capital stock, and L: is the number of workers in year t. Suppose that Buckeyeland has 8 workers and 1000 units of capital stock in year 1. Workers save 20 percent of their income to invest into new capital stock. Every year, 10 percent of the existing capital stock becomes obsolete. (a) What is the change in the capital stock per worker from this year to the next year? Compute the changes in the capital stock from the next year to two years later, and from two years to three years later. (b) What is the steady-state level of capital stock per worker? What about the steady- state level of output per worker? (c) What is the Golden Rule level of capital in this economy in the steady state? What is the required saving rate achieve this level in the steady state? ((1) In general, suppose that a country's production function is Y = AKaLl'\