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Problem 2. The Golden Rule (1 point). Consider an economy that behaves according to the Solow model with constant population and no technological progress. The aggregate production function in this economy is given by F(K, L) = KaLl-a The depreciation rate is 0.1, and the capital share (a) is equal to 0.5. The initial population is L = 1. a. Using a spreadsheet, calculate steadystate consumption, 0*, and steadystate capital, K *, for different saving rates. For instance, you may vary the savings rate from 0 to 1, in intervals of 0.05. Plot 0.. and K} as a function of s b. What is the savings rate and the associated K, that maximizes 0,, in your plot? Provide intuition for this result. 0. Assume that initially the savings rate was s = 0.4. What is the effect on 02., and K,.,, of increasing the savings rate to s = 0.5? What if we increase the savings rate to s = 0.6? Explain the intuition for this result