Kindly solve the questions as attached.below.

Greg Softie just came up with a new protein powder. He has a very loyal fanbase composed of 100 typeAconsumers, and 50 type B consumers, so he behaves like a monopolist with them. The individual inverse demands of each type is 1 133(9) = 50 if: and 1 P301} = 50 3'1 where q denotes the quantity of protein boxes. Softie's total cost function is given by c(q) 2 2g. (a) Greg Softie, pretty new in the business, plans to apply a uniform per unit price to his customers, given that he wants both types to consume. What pricefquantity should he set? Call them Qm and Pm. What will his prots 1r,\" be? (5 points} One of his fans teaches him about 2'\"1 degree price discrimination. He cannot tell consumers apart, so he plans on implementing it by proposing two bundles: (qA, TA) and ((13, TB) where q is the quantity and T is the price of the bundle. (b) What quantity q will Softie propose in bundle B? (5 points) (c) Greg now needs to make sure type A consumers will purchase their bundle as opposed to no purchasing anything at all. Compute the consumer surplus ofa type A consumer if he buys bundle A: (qA, TA) and nd TA as a function of qA such that type A consumers are indifferent between buying that bundle and not buying at all. ('1 0 points) (d) Greg now needs to make sure type B consumers will purchase their bundle as opposed to purchasing bundle A. Compute the consumer surplus of a type B consumer when buying bundle B (using your answer (13 from (a)) and the consumer surplus of a type B consumer when buying bundle A. We assume that if a type B consumer is indifferent between the two bundles, he buys bundle B. Find TB as a function of (La. (use the expression of TA as a function of (Li found in {b} as well) (10 points) (e) Write down the prot as a function of (1,; only given that each type will consume the bundle made for him. Find the prot maximizing quantity (1:1. Conclude what the two optimal bundles (qg, T5) and (9:1 , T3) will be and compute prots ar". ('1 0 points) ]. Compme a two-year bond wii two successive one-year bonds in a situation in which an investor buys a one year bond today and then another oneyear bond when the rst matures. Suppose that the twoyear bond has an interest rate of 3 percent each year. a. Now consider the pattern of interest rates on the oneyear bonds listed below and explain whether an investor should buy the twoyear bond or the one-year bond today, assuming that the only thing that matters to the investor is the amount of money he has at the end of the two years. In each case. how much would an investor have at the end of two years if be invested $1.0m] today? i. The oneyear interest rate today is 7 percent; the oneyear interest rate will he 9 percent one year from now. ii. The oneyear interest rate today is 5 percent: the oneyear interest rate will he I 1 percent one year from now. iii. The oneyear interest rate today is 3 percent: the oneyear interest rate will he [3 percent one year from now. iv. The oneyear interest rate today is 0 percent: the oneyear interest rate will he [6 percent one year from now. h. From these results. is it reasonable to compare the average interest rates on aJternative nancial investments? [In other words. how reasonable is the assumption that we can compare average interest rates on short-term bonds with the interest rate on long-term bonds instead of using the exact method?) 4. Find an equation of the tangent line to the curve y = secr - 2 cour at (#, 1). 5. Use the formula lime-to 20 = 1 and trigonometric identities to evaluate the following limits. (a) lim - sin ST (b) lim sin 2r (c) lim tan 4r tan 63 (d) lim (e) lim x-0 tan 25 6. (a) Show that the curve y = r + 3x - 2 has no tangent line with slope 2. (b) Where does the normal line to the parabola y = r - 2' at the point (1, 0) intersect the parabola a second time? Illustrate with a sketch. (c) For what values of a and b is the line de + y = b tangent to the parabola y = or when a = 17 (d) Find the cubic function y = r* + ar' + be + e whoedgraph has a horizontal tangent at (-2, 10) and passes through the point (1, 1).1. You have recently started working in the Research and Economic Programming Division of the Bank of Jamaica (BOJ). The Director of the Division. Wynona Robson. is interested in forecasting the interest rate on 3-month Government of Jamaica Treasury bills for the year 2020. The forecasts would be used to inform the BOJ's monetary policies for the year. After examining your academic record, Ms. Robson realized that you had taken a class- and obtained a high grade-in Forecasting Time Series as a part of your Actuarial Science studies at the University of Technology, Jamaica. She, thus, assigned you the task of preparing the forecasts of Treasury bill interest rates for the four quarters of 2020. You began by gathering quarterly Treasury bill interest rate data from 1995 to 2019, The data are shown in Table I on page 5, where the interest rates are given as percentages. After generating a plot of the time series data, you determined that an autoregressive moving average (ARMA) model would be adequate for making the forecasts. You are now required to produce and submit a report addressed to Ms. Robson detailing the results of your analysis. Your report should include the following. 1. A time series plot of the data. 2. A discussion of how you determined the order of the autoregressive component of the ARMA model. 3. A discussion of how you determined the order of the moving average component of the ARMA model. 4. The estimated ARMA model. 5. The forecasts of the 3-month Treasury bill interest rates for the four quarters of 2020, Note: The forecasts should be picked up directly from the MINITAB output. There should be no hand calculations. 6. 95% prediction intervals for the forecasts. Give a concise verbal interpretation of each interval. 7. An assumption of the ARMA model is that (m, ) is white noise. A diagnostic check of the adequacy of the estimated ARMA model is provided by determining whether this assumption is satisfied. By examining the autocorrelation function of the residuals, is the white noise assumption of {u, } justified? Explain. Note: To obtain the autocorrelation function of the residuals using MINITAB, proceed as follows. In the ARIMA dialog box, select Graphs, Residual Plots, ACF of residuals