ANY TUTOR PLEASE FOR THIS MACRO-ECON QUESTION

OWN WORK NEEDED!

*TYPED WORK.

1.

Problem 1 Consider the Ramsey-Cass-Koopmans (RCK) model seen in class. The household seeks to maximize its lifetime utility, defined as follows: U = / e-ptu [C(t)] L (t) dt H 0 Assume that the household's instantaneous utility takes the following form: u [C (t)] = In C (t) Moreover, assume that there is no population growth (that is, L (t) = L for every t). Without loss of generality, use the following normalization: L = H = 1. Answer to the followings questions. 1. Set-up the current value Hamiltonian for this dynamic optimization problem, derive its necessary condi- tions, and find the Euler equation for consumption (MEDIUM). 2. Redo the same analysis but assume that utility is u [C (t)] = -ze (t). Hint: relative risk aversion is still defined as _ u COC (t) . However, in this specific case, - 4 C()] u"CO (t) is not equal to 0.Macroeconomics Indicators of the Kingdom of Bahrain You are a consultant at the Economic Development Board. Given the following macro data for Bahrain's economy over the period 2014 -2018, answer the below questions. Variable 2014 2015 2016 2017 2018 Net foreign direct investment ( millions of current BHD 2,962.69 3,328.87 3,541.35 3,849.29 4.276.99 Household final consumption expenditure (millions of current BHD) 5.083.84 5,312.25 5.448.56 5,596.35 5,605.00 Exports of goods and services (millions of current BHD) 12,058.00 9,702.80 10,107.60 11,264.60 General government final expenditure (millions of current BHD) 2,024.33 2,064.76 2,073.93 2,217.66 2,310.75 Statistical discrepancy (millions of current BHD) 257.23 282.96 GDP (millions of constant 2010 BHD) 11,567.97 10,589.49 Inflation, consumer prices (annual %) 2.6 1.8 2.8 2.1 Gross Fixed Capital Investments (millions of current BHD) 3.370.01 3,009.01 3.539.26 4,375.18 5.147.29 Imports of goods and services (millions of 9.982.40 Current BHD) 8,385.50 7,929.10 8.977.50 10.170.30 Consumer price index (2010 = 100) 108.5 110.5 115.2 117.6 GDP per capita (constant 2010 BHD) 8,421 8,436 8,399 8,320 8.076 Labor force, total 758,359 777.895 817,831 869,405 926.959 Population ages 0-15, total 276,233 286,027 290.718 296.447 302,185 Population ages 15-64, total 1,029,181 1,053,939 1,101,674 1,162,183 1,229,175 Population ages over 64, total 30.661 31,885 33.399 35.444 38.079 Population, total 1,336,075 1,371,851 1,425,791 1,494.074 1,569,439 GDP (millions of current BHD) 12,126.05 Unemployment (% of total labor force) 3.9 3.6 3.3 3.02 Employment (% of total labor force) 97.1 GDP growth (annual %) RGDP growth (annual %)Macroeconomics Indicators of the Kingdom of Bahrain You are a consultant at the Economic Development Board. Given the following macro data for Bahrain's economy over the period 2014 -2018, answer the below questions. Variable 2014 2015 2016 2017 2018 Net foreign direct investment ( millions of current BHD 2,962.69 3,328.87 3,541.35 3,849.29 4.276.99 Household final consumption expenditure (millions of current BHD) 5.083.84 5,312.25 5.448.56 5,596.35 5,605.00 Exports of goods and services (millions of current BHD) 12,058.00 9,702.80 10,107.60 11,264.60 General government final expenditure (millions of current BHD) 2,024.33 2,064.76 2,073.93 2,217.66 2,310.75 Statistical discrepancy (millions of current BHD) 257.23 282.96 GDP (millions of constant 2010 BHD) 11,567.97 10,589.49 Inflation, consumer prices (annual %) 2.6 1.8 2.8 2.1 Gross Fixed Capital Investments (millions of current BHD) 3.370.01 3,009.01 3.539.26 4,375.18 5.147.29 Imports of goods and services (millions of 9.982.40 Current BHD) 8,385.50 7,929.10 8.977.50 10.170.30 Consumer price index (2010 = 100) 108.5 110.5 115.2 117.6 GDP per capita (constant 2010 BHD) 8,421 8,436 8,399 8,320 8.076 Labor force, total 758,359 777.895 817,831 869,405 926.959 Population ages 0-15, total 276,233 286,027 290.718 296.447 302,185 Population ages 15-64, total 1,029,181 1,053,939 1,101,674 1,162,183 1,229,175 Population ages over 64, total 30.661 31,885 33.399 35.444 38.079 Population, total 1,336,075 1,371,851 1,425,791 1,494.074 1,569,439 GDP (millions of current BHD) 12,126.05 Unemployment (% of total labor force) 3.9 3.6 3.3 3.02 Employment (% of total labor force) 97.1 GDP growth (annual %) RGDP growth (annual %)Part I Problems solving (11 marks) 1. Given the above data, determine the gross domestic product of Bahrain at each year. Explain the method used. (3 marks) 2. As a consultant, do you think it is possible to find out the value of Bahrain's net exports at the year 2016 given the above information? If yes, what is the value of net exports and what does it reflect? (2 marks) 3. What is the value of Bahrain's real production (Real GDP) in the years 2017 and 2018? (1 mark) 4. Calculate the growth rates of Bahrain's nominal GDP and real GDP? (2 marks) 5. What is the level of unemployment in Bahrain during 2018? (1 mark) 6. In 2017, what is the level of inflation in Bahrain? What does it indicate? (2 marks)Part I Problems solving (11 marks) 1. Given the above data, determine the gross domestic product of Bahrain at each year. Explain the method used. (3 marks) 2. As a consultant, do you think it is possible to find out the value of Bahrain's net exports at the year 2016 given the above information? If yes, what is the value of net exports and what does it reflect? (2 marks) 3. What is the value of Bahrain's real production (Real GDP) in the years 2017 and 2018? (1 mark) 4. Calculate the growth rates of Bahrain's nominal GDP and real GDP? (2 marks) 5. What is the level of unemployment in Bahrain during 2018? (1 mark) 6. In 2017, what is the level of inflation in Bahrain? What does it indicate? (2 marks)Part II Essay question (9 marks) Write a short report (max 500 words) analysing the above data of Bahrain's economy over the period 2014 - 2018. The report must include the following (9 marks) . The differences between the nominal and real gross domestic product of Bahrain. . What does the growth in both nominal and real GDP reflect? . Between 2016 and 2018, which phase of business cycle best describes Bahrain's economy? What happens to the level of output, income, employment and unemployment? . Explain the possible events that have resulted in lower output and negative growth in Bahrain's GDP during specific years. . Interpretation of GDP per capita values. . The main effect of inflation rates over the citizens of Bahrain.Part II Essay question (9 marks) Write a short report (max 500 words) analysing the above data of Bahrain's economy over the period 2014 - 2018. The report must include the following (9 marks) . The differences between the nominal and real gross domestic product of Bahrain. . What does the growth in both nominal and real GDP reflect? . Between 2016 and 2018, which phase of business cycle best describes Bahrain's economy? What happens to the level of output, income, employment and unemployment? . Explain the possible events that have resulted in lower output and negative growth in Bahrain's GDP during specific years. . Interpretation of GDP per capita values. . The main effect of inflation rates over the citizens of Bahrain.Section 3. Present value and recursive asset pricing formula (i) Annuity pricing a) An annuity is a financial instrument that pays out a constant amount of income per period for as long as the annuitant (i.e. annuity purchaser) is alive. Let P be the expected present value of annuity payments. Let a denote annuity income payment per period, m denote the probability of dying by next period (a.k.a mortality rate) and r denote the interest rate. Use the recursive asset pricing formula a + EP' P = - 1+r to show that a P = r +m b) Suppose that an elderly annuitant has 500,000 in wealth and uses this wealth to purchase an annuity. Calculate the annual payment that the annuitant should expect if r = 0.05 and m = 0.03 per year. Explain how your answer is related to equilibrium economic profit of a financial institution that issued the annuity. (ii) Life insurance premium A life insurance policy is a financial contract that collects a premium of p per period from the insured and pays out a lump sum benefit B upon the death of the insured. Let m denote the mortality rate, r denote the interest rate and V denote the expected present value of economic profits of the insurance company on this policy. Use the recursive asset pricing formula VP+ EV' 1+r to express equilibrium life insurance premium, p, through exogenous variables. Explain your answer and show all work. (iii) Loan calculators Suppose that loan of size S is repaid over T periods with equal per-period payments p and interest rate on the loan r. Initial loan size has to be equal to the present value of the payments: P S = = P P 1 +r (1+r)2 (1 + r) I a) Calculate a monthly payment on the following mortgage. Annual interest rate is r = 0.06, mortgage term is 30 years, loan size S = 200,000. (Hint: since you are asked about the monthly payment, present value should be discounted at a monthly frequency. Start with figuring out the monthly interest rate and the mortgage term expressed in months, then apply the formula). b) Jill would like to buy a car that costs S = 20,000. The dealer offers her a 60-month loan with 0 down and a monthly payment p = 421. Calculate the annual interest rate on this loan using Excel. Take the following steps: 1. Generate a column of 40 monthly interest rates, with r = {0.001,0.002, ...,0.040], say column A, starting with Al. 2. Use the geometric series formula to express the present value of payments through p, T and I'm, where I'm is the monthly interest rate. Plug in the numeric value for p, T and put this formula into cell BI. Have the formula refer to the interest rate from cell Al. Select B1:B100 and press CTRL+D. This will copy the formula and generate a column of present values that correspond to different monthly interest rate. Pick an interest rate from a row whose cell B value corresponds most closely to S. 3. Convert the monthly interest rate I'm that you found on step 2 into annual using the compounding formula 1 +ra = (1 + rm)12.Section 3. Present value and recursive asset pricing formula (i) Annuity pricing a) An annuity is a financial instrument that pays out a constant amount of income per period for as long as the annuitant (i.e. annuity purchaser) is alive. Let P be the expected present value of annuity payments. Let a denote annuity income payment per period, m denote the probability of dying by next period (a.k.a mortality rate) and r denote the interest rate. Use the recursive asset pricing formula a + EP' P = - 1+r to show that a P = r +m b) Suppose that an elderly annuitant has 500,000 in wealth and uses this wealth to purchase an annuity. Calculate the annual payment that the annuitant should expect if r = 0.05 and m = 0.03 per year. Explain how your answer is related to equilibrium economic profit of a financial institution that issued the annuity. (ii) Life insurance premium A life insurance policy is a financial contract that collects a premium of p per period from the insured and pays out a lump sum benefit B upon the death of the insured. Let m denote the mortality rate, r denote the interest rate and V denote the expected present value of economic profits of the insurance company on this policy. Use the recursive asset pricing formula VP+ EV' 1+r to express equilibrium life insurance premium, p, through exogenous variables. Explain your answer and show all work. (iii) Loan calculators Suppose that loan of size S is repaid over T periods with equal per-period payments p and interest rate on the loan r. Initial loan size has to be equal to the present value of the payments: P S = = P P 1 +r (1+r)2 (1 + r) I a) Calculate a monthly payment on the following mortgage. Annual interest rate is r = 0.06, mortgage term is 30 years, loan size S = 200,000. (Hint: since you are asked about the monthly payment, present value should be discounted at a monthly frequency. Start with figuring out the monthly interest rate and the mortgage term expressed in months, then apply the formula). b) Jill would like to buy a car that costs S = 20,000. The dealer offers her a 60-month loan with 0 down and a monthly payment p = 421. Calculate the annual interest rate on this loan using Excel. Take the following steps: 1. Generate a column of 40 monthly interest rates, with r = {0.001,0.002, ...,0.040], say column A, starting with Al. 2. Use the geometric series formula to express the present value of payments through p, T and I'm, where I'm is the monthly interest rate. Plug in the numeric value for p, T and put this formula into cell BI. Have the formula refer to the interest rate from cell Al. Select B1:B100 and press CTRL+D. This will copy the formula and generate a column of present values that correspond to different monthly interest rate. Pick an interest rate from a row whose cell B value corresponds most closely to S. 3. Convert the monthly interest rate I'm that you found on step 2 into annual using the compounding formula 1 +ra = (1 + rm)12