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Homework Assignment 1 Economics 514 Macroeconomic Analysis Due: October 18th, 2013 1. European Leisure We hope to explain the level of household leisure adopted in Italy vs. Hong Kong by differences in tax rates. First, get data on labor hours and productivity in the two countries from the Groningen Growth Development Center Total Economy database. Go to Link. Download the Excel file Total Economy Database™ - Output, Labor, and Labor Productivity, 1950 - 2012 Fill in the following table. Calculate the number of hours worked, L2012, as the hours per person aged between 15-64 in Hong Kong. Assume each person has time equal to TIME = 8,760 per year. What is the leisure time per person in Hong Kong if leisure is ls = TIME - L. Productivity – LP Total Hours (Thousands) Population (Thousands) % Pop. 15-64 L2012 Italy Hong Kong 65% 75% Calculate the number of hours worked, L2012, as the hours per person aged between 15-64 in Hong Kong. Assume each person has time equal to TIME = 8,760 per year. What is the leisure time per person in Hong Kong if leisure is ls = TIME - L. Households have a general utility function dsd Ut Ct 1 lst 1 1 They will earn labor income, wtLt, and private non-labor income, Πt. They pay a proportional tax rate, τ, on all private income and receive a subsidy S from the government regardless of how much they work. The budget constraint is C (1 ) wt TIME lst t St on all private income. The first order condition showing the ratio of leisure to consumption as a function of the real wage and the tax rate. MUls (1 )wt MUC a. Assume = 0 so the elasticity of substitution between consumption and leisure is 1. Assume that all taxes are paid back to the average household as a flat subsidy, so there are two equations. C wt TIME lst t and w(1 ) . Use the data from GGDC to solve for ls for Hong Kong. In Hong C ls Kong, we could say the tax rate is 15%, τ=.15. Assume that w is ⅔ of labor productivity. Assume that t is ¼ of wtLt. Solve for the parameter Γ that would generate the level of leisure in HK. b. Now assume that Italy has the same level, Γ, as solved for in Hong Kong. What would the tax rate need to be in Italy, to lead to a level of labor. 2. Growth Accounting Researchers at the University of Pennsylvania have assembled a database on comparable levels of output and investment for a large number of countries. Use the data from Penn-World Tables. Data can be obtained here: Link, Get data on Real GDP at constant 2005 national prices (in mil. 2005US$) (Yt) Capital stock at constant 2005 national prices (in mil. 2005US$) (Kt) Number of persons engaged (in millions) (Lt) Under Regions select China and India. Under Periods select 1960, 1970, 1980, 1990, 2000, and 2010. a. Calculate the average compound growth rate γ for GDP, Capital, and Number of Employees for each country for each decade. b. Assume a Cobb-Douglas utility function with α = ⅓. Calculate the growth of TFP in each country in each decade. c. Calculate the share of growth due to each factor and TFP for each country. 3. Development Accounting Compare the level of technology in Hong Kong with that in the USA. Assume a production function in each country of the form: Yt Kt ( At Ht Lt )1 H t e1 yearst yt kt ( At )1 e yearst where Ht is human capital which is a function of the number of years of schooling. A. Data on output, labor and capital can be obtained here: Link Expenditure-side real GDP at chained PPPs (in mil. 2005US$) , (Yt) Capital stock at current PPPs (in mil. 2005US$) (Kt) Labor can be calculated as the product of Number of persons engaged (in millions) Average annual hours worked by persons engaged Under Regions select Hong Kong and United States. Under Periods select B. Data on Human Capital can be obtained here Link Select China, Hong Kong Special Administrative Region and USA for Gender select Total; under Age group select 25+. Press Average years of schooling for both economies. 2010. 2010; under . Report Under the assumption that α = ⅓ and = .08, calculate the level of technology for both economies in 2010. Computational Problems Macroeconomics often uses computer simulations to study theoretical models. Do a couple of simulation exercises for an economy with a Cobb-Douglas production function 1 2 1 2 Yt Kt 3 ( At Lt ) 3 yt kt 3 ( At ) 3 a depreciation rate of 8% (δ=.08), a population growth rate of 1% (n = .01),and an annual technology growth rate of 2% (gA = .02). 1. Golden Rule Assume that the economy was on its balanced growth path. Normalize technology at L time t to At = 1. Assume a constant labor hours per population of t = 500. POPt Output is used for consumption and investment, Ct + It = Yt and investment is a constant share of output. Calculate consumption per capita at different levels of invest rates s = 1100 , 1 4 , 13 , and 1 2 . Which investment rate generates the highest steady state labor productivity. 2. Convergence Assume that the investment rate for the economy is at the level which generates the highest level of consumption per capita. Examine the dynamics of the neoclassical model. Start in period 0. In that period, technology is A0 = 1 and k0 = 1.5. Calculate labor productivity in period 0 and the labor productivity if the economy were on its balanced growth path. What is the percentage gap between the actual level of the economy and the balanced growth path (y0 and yBGP). Calculate the capital productivity in period 0. Use this to calculate the growth rate of the capital labor ratio, k g k kt 1 kt between period 0 and period 1. Use the growth rate of the capital t 1 k kt A At labor ratio and the growth rate of technology A gtA1 t 1 to calculate k1 and A At A1. Use these numbers to calculate actual and balanced growth path labor productivity and capital productivity in period 1. Use capital productivity to calculate the growth rate of the capital-labor ratio in period 1. Calculate technology and the capital labor ratio in period. 2. Repeat. Calculate the path of actual labor productivity as well as the balanced growth path for periods 0 through 30. How large is the percentage gap at period 30.