I(t)H(t) : [Aag(t)] (Investment Equation) where t) is the fraction of time spent investing, H (t) is the human capital the worker already has, and I (t)H (t) is the amount of additional human capital accumulated at time t. The parameters A, a govern how much additional investment I (t)H (t) increases human capital stock H (t) They represent ability. The equation g(t) is dened as 1 _ e(a+r)(t7T) t : y() 0 Ha where a is the depreciation rate of human capital, 1' is the impatience parameter, and T is the last year of work. What does the Investment Equation say about the relationship between optimal investment and the pa- rameters listed below? Is investment increasing, decreasing, or constant as each parameter below increases? Explain the economic intuition in each case. Hint: Note that the function 1 er\" is decreasing as m increases. a) r: the impatience parameter. Note that high r means the worker is impatient, and tow r means that the worker is patient. (3 pts) b) a: the depreciation rate of human capital (3 pts) (3) t: age (3 pts) d) T: the last year of work (3 pts)