Consider the special case solved in the lecture where 8 = 1 and utility takes the log form. Suppose the real interest rate is 5%. A middle-aged college professor contemplating retirement: his current income is Y1 = $150,000 and his future income is Y2 = $10, 000. (a) What is the college professor's present value of income? (b) According to the neoclassical model, how much does the college professor consume to- day and in the future? How much does the college professor save today? (c) If Y rises by $20, 000, by how much will saving change? (d) By how much does consumptionltoday rise if Ya rises by $10, 000? (e) If the interest rate rises to 10%, by how much do present value of income and today's consumption change? By how much does saving change? (f) Would this matter if the professor could not borrow