solution2 - Solution HW2 1. To calculate the steady-state...

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Solution HW2 1. To calculate the steady-state level ratio of income per capita, we first find the steady-state level for each country and then divide. The steady-state level ratio for Country X to Y is given by: 1 1 1 , , X Xs s XX X Y Ys s Y YY y An yA n α γ δ ⎡⎤ ⎢⎥ ⎛⎞ + = ⎜⎟ ⎝⎠ + ⎣⎦ We now substitute in the values 20%, 0, n = = and 5% X = for Country X, and for Country Y, we use the values 5%, 4%, n == and 5%. Y = Also, set 1/3 = and . X Y AA = This yields, 1 1 (1/ 3) 1 2 3 1 2 , , 0.2 43 6 00 . 0 5 2.68. 0.05 5 5 0.04 0.05 9 s s y y ⎧⎫ ⎨⎬ ⎩⎭ + = ⎢⎥⎝⎠ + Therefore, we conclude the ratio of Country X to Y in their steady-state levels of income per capita to be near 2.68. 2. TFR = 4. NRR = (1/2) × [(1 child) × (Probability of reaching age 25) + (1 child) × (Probability of reaching age 28) + (1 child) × (Probability of reaching age 32) + (1 child) × (Probability of reaching age 35)] Substituting in the given information, we get NRR = (1/2) × [(2/3) + (2/3) + (1/3) + (1/3)] = 1 b. NRR = (1/2) × [(1) + (1) + (1/2) + (1/2)] = 1.5 c. TFR = 2 NRR = (1/2) × [(1/2) + (1/2) + (1/2) × (1/2) + (1/2) × (1/2)] = .75 3. The payment to human capital is the difference between the total wage and the wage for raw labor. Given the
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solution2 - Solution HW2 1. To calculate the steady-state...

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