# Number of employed workers is 475 iv the

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number of employed workers is 47.5 million (50-2.5). (iv) The employment/population ratio is 47.5% (47.5/100). 3. 6 points The average annual growth rates for each of the 6 decades. Using the exact method
Econ303 Homework 2 Answer 2 Average annual growth rate in 50 s = ( 15773 13244 ) 1 / 10 - 1 = 1 . 76% Average annual growth rate in 60 s = ( 20994 15773 ) 1 / 10 - 1 = 2 . 90% Average annual growth rate in 70 s = ( 25752 20994 ) 1 / 10 - 1 = 2 . 06% Average annual growth rate in 80 s = ( 32275 25752 ) 1 / 10 - 1 = 2 . 28% Average annual growth rate in 90 s = ( 39744 32275 ) 1 / 10 - 1 = 2 . 10% Average annual growth rate in 00 s = ( 42311 39744 ) 1 / 10 - 1 = 0 . 63% Using the approximating method Average annual growth rate in 50 s = ln(15773) - ln(13244) 10 = 1 . 75% Average annual growth rate in 60 s = ln(20994) - ln(15773) 10 = 2 . 86% Average annual growth rate in 70 s = ln(25752) - ln(20994) 10 = 2 . 04% Average annual growth rate in 80 s = ln(32275) - ln(25752) 10 = 2 . 26% Average annual growth rate in 90 s = ln(39744) - ln(32275) 10 = 2 . 08% Average annual growth rate in 00 s = ln(42311) - ln(39744) 10 = 0 . 63% 4. 8 points The production function takes the following form Y = F ( K, L ) = AK 0 . 4 L 0 . 6 The expressions for marginal product of labor and marginal product of capital are as follows. MP L = 0 . 6 · AK 0 . 4 L - 0 . 4 MP K = 0 . 4 · AK - 0 . 6 L 0 . 4 Table below are the values of the marginal product of labor L=1 L=2 L=3 L=4 L=5 A = 50 & K = 1000 475.4680 360.3373 306.3887 273.0846 249.7660 A = 60 & K = 1000 570.5615 432.4048 367.6664 327.7016 299.7192 A = 50 & K = 2000 627.3837 475.4680 404.2823 360.3373 329.5682
Econ303 Homework 2 Answer 3 When the total factor productivity increases, the marginal product of labor increases. The marginal product of labor curve shifts up. When the capital input increases, the marginal product of labor also increases. There is complementarity between labor and capital.