Most economies have a goal of maximizing the average consumption per period. Assume that during each year, an economy saves the same (to be determined) percentage S of its production. During a year in which the beginning capital level is K, a quantity K1y2 of capital is produced. If the economy saves a percentage S of its capital, then during the current year it consumes (1 2 S)K units of capital and, through savings, adds (SK) 1y2 units of capital. Also, during any year, 10% of all capital present at the beginning of the year depreciates or wears out. a. What annual savings percentage S maximizes the long-run average
Most economies have a goal of maximizing the average consumption per period. Assume that during each year, an economy saves the same (to be determined) percentage S of its production. During a year in which the beginning capital level is K, a quantity K1y2 of capital is produced. If the economy saves a percentage S of its capital, then during the current year it consumes (1 2 S)K units of capital and, through savings, adds (SK) 1y2 units of capital. Also, during any year, 10% of all capital present at the beginning of the year depreciates or wears out. a. What annual savings percentage S maximizes the long-run average consumption level? Assume that year 50 represents the long run, so that the objective is the consumption level in year 50. You can assume the initial capital is 1 (for some appropriate measurement unit). b. Use SolverTable to see how the optimal value of S depends on the annual
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