all of the following are my questions

4. The Mankiw-Romer- Weil (1992). A different way of formulating human capital is to assume that human capital is accumulated just like physical capital, so it is measured in units of outputs instead of years of time. Assume production is given by Y = KOH(AL)I-a-8, where a and B are constant between zero and one whose sum is also between zero and one. Human capital is just accumulated like physical capital: H = SHY - 6H Where ay is constant share of output invested in human capital. Assume that physical capital is accumulated as K= SKY - OK That the labour force grows at rate n, and the technological progress grows at rate g. Solve the model for the path of output per worker. y = 1/2, along the balanced growth path as a function of 54. 48 . n. 9.6. a and 3. Discuss how the solution differs from the setup where human capital is accunnilated in years of time,Consider the following standard Homer Model and a variation that includes human capital. Goods Production Flmction Ideas Production Function Human Capital Production Function Resource Constraint Allocation of Labour Human Capital Y. = as... 15AM] : EAthLGJ H: 2 L511; Lyt+La3g +LM = L La; : TE Assume parameters take the following values in each specication. Standard Human lCapital E 1000 1000 Ly; 750 700 LG; 250 200 La; r 100 :2 0.0005 0.0005 A5 10 1 l] 1. Explain what using labour to produce human capital implies for the economy? 2. Solve for the balanced growth path of output per capita in both models, showing all working. 3. Does the inclusion of human capital increase the rate of growth compared to the standard model? What is the impact on output in the short and long run? Endogenous Growth Model Consider the endogenous growth model, where the future period quantity of human capital is a function of current human capital, which drives production and thus growth. [a] Find the growth rate of human capital and consumption. Be sure to show your work. [to] Use your answer from part {a}, in addition to the fact that C = Y in equilibrium, to explain why' the economy' will grow indenitelyr when oil u] :r 1. [c] The Canadian government subsidizes education for its citizens in an effort to increase the country's stock of human capital. What is the economic rationale for this policy"?I (c) (3 points) The figure below is a plot of various countries' average growth rates from 1960 to 2011 against those same countries' GDP per capita in 1960. 10 8 BWA' GNAOR SGP 6 ...TWN EGROU HKG 4 CYP ITA :NOR GDP per capita growth 1960 to 2011 (%) AT MUS LEHL LUX TTOSR 2 FREEBIESIMEANIS NZL . . HE . . NAM VEN AGHA JAM NERIN -2 COD. - Average growth 4 5 10 15 20 GDP per capita in 1960 (thousands of 2005 $ PPP) Does the figure support the notion of unconditional convergence? Clearly explain why or why not.Question 2: Capital formation in growth models 10 points each sub-part equally weighted 1.Derive the growth equation for Harrod Domar model. 2. Derive the capital formation equation for Solow model with and without labor augmenting technological progress. 3.Derive the human capital formation equation for the following production function Y = HOK'(TL)1-a-B where Y is output, H is human capital in the production function, K is physical capital used in the production function and L is labor. The saving rate in human capital is given by s.(b) You can see that in equation 1, the divided yield appears with negative sign, i.e. a decrease in dividend yield will causes the price of a futures contract to increase. Hence, if you believe that the dividend yield in the next 9 months will be lower than 2.84%, it implied that you believe the future is priced too "cheaply", i.e. you think the replicating portfolio for the futures contract would cost more than the price this contract is traded for in the market. To take advantage of that, you must enter into a contract to be able to buy the S&P index in June 2008. As a general rule, you always try to buy the asset that appears to be under priced according to your model or you view in this case. You also need to take appropriate positions in the S&P index in the spot market to hedge your exposure to S&P index. Since you are long the future, the appropriate position you need to take is to sell S&P index (compare this with question one, the logic is the same). But since you don't own the S&P index you need to borrow this to sell it, i.e. you will take a short position in S&P. Let's assume that you borrow the S&P index from a mutual fund to sell in the market for $1453.55 today. You will deposite this money into a bank for 9 months which will grow to $1524.23. As time progresses, you need to pay the equivalent amount of divided paid by the stocks in the S&P index to the mutual fund that lent you the index. If your view is current, the total dividend you have to pay out is less than $1524.23-$1453.55=$30.53 and you will end up being positive - remember you need to buy back the S&P index in 9 months to return it to the mutual fund that lent you the index initially but you can do this at the price of $1453.55 which you agreed upon initially. In short, you have a positive exposure, i.e. you make money, if your view is correct about slow down in the rate of dividend yield. 7. Recall futures pricing formula: H = So(1 + 7 - yr)" Rearrange this to get: yr = 1+ rr - H 1/T So where ry is the annualized interest rate and yr is the annualized con- venience yield over the time horizon indicated by 7. Apply this to the market data: . October: you = 1 + 0.0405 - (67.50/67.50)12 = 0.04058. (a) You can go long 10,000,000/1,000=10,000 future contract with December maturity. You then get a lock in price of $69.60 per barrel. (b) You should buy oil in the spot market and store it until December. The total cost will be 67.50 x (1 + 5% + 5.34%)3/12 = $69.18. here we assumed the rent of 5% is compounded monthly and you should also include the time value of money. For simplicity, we have assumed the rent payment are paid upfront. (c) You should follow option b because the cost as calculated above is slightly less than the current market price of $69.60 for these contracts. In fact, you should do even more than hedging and try to eliminate this arbitrage. You can do this because you have access to cheaper storage facility than what is priced into the future prices through the convenience yield (5% vs. 7.69%) but the difference is small. 9. We already eluded to this answer above. Here is what you should to precisely. . Sell future contract as the price of $69.60. . Borrow $68.70 at the rate of 5.34% for 3-month. This will grow to exactly $69.60 in 3-months. . Use $67.50 of the above money to buy oil in the spot market . Pay $67.50 x (1 + 5%)1/4 - $67.50 = $0.83 of the storage cost up- front (again depending on how the rent is quouted, compounded, and paid this calculation may change) . Pocket the difference today, i.e. take the arbitrage profit of $68.70- $67.50-$0.83=$0.37. . In December, take deliver the oil, get $69.60 and pay back your debt. 10. (a) F = $13.50 ( 1+ 0.05 0.1 + (1+ 0.05 + " (1+ 205)"+ 94 (1+205 ) = $14.0931. Suppose that the actual rate of return on the S&P 500 index from December 17, 2001 (today) to December 17, 2002 (12 months hence) is 9.0%, including dividends paid by companies in the index. You are given the following information about the performance of mutual funds X, Y and Z. Each mutual fund invests only in common stocks. Fund (manager) Rate of return Alpha (SE) Beta (SE) R2 X (Gladys Friday) 9.8% +.48% (1.0%) 1.05 (.05) .92 Y (Gene Pool) 9.0% -.65% (3.0%) 1.10 (.07) .88 Z (Hugh Betcha) 13.4% +.50% (3.1%) 1.60 (.09) .65 Alphas and betas are estimated from 52 weekly returns from December 2001 to December 2002. Returns and alphas are given above as annual percentage returns. SE means standard error. The start-of-year risk- free rate is 2.5%. Based on these statistics, what can you say about the investment strat- egy and performance of each of the three managers? Explain. Consider risk as well as return before answering. 32. Your company offers three funds to its employees for their pensions: a money-market fund, an S&P 500 index fund and a new-economy equity fund. You need to form a portfolio from these funds for your own pension investments. The money-market fund is invested in 3-month Treasury bills, now with a risk-free return of 1.5% per annum. The index fund gives a premium of 8% and a standard deviation of 20% per annum. The new-economy fund's return can be described by the following equation: Tt - TF = a + 3(TMt - TF ) + et where re and ran are the fund and market returns, ry is the risk-free return, o is a constant, and e, is the part of the fund's returns not explained by the market. The performance of the fund over the last 60 months gives 39 2008, Andrew W. Lo and Jiang Wang 1.7 CAPM 1 QUESTIONS . ( = 0.0 . 3 = 1.2 . R2 = 0.75 (proportion of the variance of the fund's return ex- plained by the market return). (a) Compute the expected return of the new-economy fund using CAPM. Use reasonable estimates for the market return and the risk-free return. (b) If CAPM holds, what is the optimal portfolio to achieve an ex- pected return of 8% per annum. (c) If instead, the estimate of o is 0.0050 (0.5% per month) with a standard error of 0.0015. Without doing any calculations, discuss how this may affect your portfolio. 33. Two mutual fund managers are being evaluated for their performance in the last ten years. One of them, Mr. Hare, has achieved an eye-popping 34% annual average return; the other, Ms. Tortoise, has obtained a modest 12% annual average return. On closer examination of their portfolios, it is found that Mr. Hare always bet on risky Argentinian stocks (whose beta is 4), whereas Ms. Tortoise always invested in conservative technology firms like IBM (whose beta is (a) If the risk-free return was 3% every year and the expected mar- ket return was 11% every year, who should get the higher bonus? Why? (Credit only if reasoning is correct.) (b) If the risk-free return was 7% every year and the expected market return was 13% every year, who should get the higher bonus? Why? (Credit only if reasoning is correct)Exercises Exercise 11.1 (Easy) Suppose the aggregate production technology is Y = 34 . and that [ = 150. Both the labor force and productivity are constant. Assume that the depreciation rate is 10% and that Exercises 109 20% of output is saved and invested each year. What is the steady-state level of output? Exercise 11.2 (Moderate) Assume that the Solow model accurately describes the growth experience of Kuwait. As a result of the Gulf war, much of the capital in Kuwait (oil extracting equipment, vehi- cles, structures etc.) was destroyed. Answer the following questions, and provide brief explanations. . What will be the effect of this event on per capita income in Kuwait in the next five years? . What will be the effect of this event on per capita income in Kuwait in the long run? What will be the effect of this event on the annual growth rate of per capita income in Kuwait in the next five years? What will be the effect of this event on the growth rate of per capita income in Kuwait in the long run? . Will recovery in Kuwait occur faster if investment by foreigners is permitted, or if it is prohibited? . Would Kuwaiti workers gain or lose by a prohibition of foreign investment? Would Kuwaiti capitalists gain or lose? Exercise 11.3 (Moderate) In this and the following two exercises, you will apply growth accounting to measure the determinants of growth in output per worker in a country of your choice. To start, you need to pick a country and retrieve data on real GDP per worker and capital per worker. You can get the time series you need from the Penn World Tables. See Exercise 9.1 for information about how to access this data set. You should use data for all years that are available. In Section 11.3, we introduced growth accounting for output growth, while in this exercise we want to explain growth in output per worker. We therefore have to redo the analysis of Section 11.3 in terms of output per worker. The first step is to divide the production function in equation (11.11) by the number of workers Ly, which yields: (11.20) Equation (11.20) relates output per worker 1,/L, to capital per worker K-1/L. If we use lower case letters to denote per-worker values (1: = Y:/Lt, ke-1 = Ki-1/L:), we can write equation (11.20) as: (11.21) 1 = APRET