Kindly solve the following
Economics 333 HR #3 Use the following information on the supply and demand for oil in the hypothetical country Economica to answer the questions below. Assume that the demand and supply curves are linear. Questions 2a is worth 10 points. Each part of every other question is worth 5 points. Domestic Domestic Price {SI Demand Supply 20 330 6D 40 3GB 120 60 2TH 130 30 240 240 100 210 300 120 180 36D 1. Assume that the world price of oil is $4 per barrel. a. What is the quantity of oil imports? Now assume that Economica is a small country and that Economica imposes a $20 per barrel tariff on imported oil. Calculate the effect of the tariff on The price of oil in Economica The change in producer surplus The change in consumer surplus . Government tariff revenue Consumption distortion loss Production distortion loss Total deadweight loss oil imports . The change in domestic oil production to U-F'S' r-nm on o- Suppose that Economica is a large country. Use the domestic supply and cbmestic demand curves from the top of the page to calculate the import demand curve. The export supply curve is as follows Price Quantity 0 D 20 90 4B 180 60 210 ED 360 a. Graph the import demand and export supply curves b. Now assume that Economica imposes a 52D per barrel tariff on oil imports. Graph the effect of the tariff on export supply curve . Use your graph to calculate the following {provide numerical answers- You will need to graph accurately} b. the price of oil in Economica c. the price of oil in the Rest of the World d. The change in producer surplus 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)12.1 of 2 Econ 202: Intermediate Macroeconomics Problem Set 1: Goods markets Spring 2019 This assignment is due in hard copy at the beginning of class on Thursday February 7. Remember that the process of how you arrive at an answer is as important as the answer itself. For full credit you are required to show all steps and work, clearly label all graphs, and fully explain any answers that ask for an explanation. Question 1: Calculating GDP Consider an economy with three firms: . Firm | sells $50 of steel to Firm 3. From its earnings, it pays $20 in wages and keeps $30 in profits. Firm 2 sells $30 of rubber to Firm 3. Finn 2 pays $10 in wages and keeps 520 in profits. Firm 3 sells $260 of cars to households. It pays for its inputs (from Firm | and Firm 2): keeps one third of its remaining earnings as profits, and pays two thirds in wages. Let's calculate GDP various ways. Show your work (i.c. do not just write a final answer for parts (b) and (c): instead, show me how you got there). (a) What is the final value of goods and services? (b) Calculate GDP as the sum of value added. (c) Calculate GDP as the sum of all incomes earned in the economy. [Note that, in order to do this, you first need to calculate wages and profits for Firm 3]. Question 2: Working with the Keynesian cross model Consider the following hypothetical economy: C = 140+ 0.6(Y - T) T = 200 G = 150 T = 150 All variables are in units of constant dollars per year ($). (a) What is the equilibrium level of GDP (Y)? [ Make sure that you start from the equilibrium condition, and show your work]. (b) Using your answer to (a). solve for the following variables in equilibrium: Disposable income (Y, ). ii. Consumption spending (C). Aggregate demand (2). Show that the level of aggregate demand is equal to the equilibrium level of GDP. (c) Let's analyze fiscal policy: i. What is the government spending multiplier in this coonomy? ii. Say that the government increases government spending by 100. How much does GDP increase? (d) Now assume that investment is described by / = 100 + 0.3Y. (Return government spending to the original level of 1 50)
