哈佛大学宏观经济学习题答案.pdf

Key equation (production function): (3.1) Y = A·F(K, L). Y: real GDP A: technology level (ideas or designs) K: capital stock (or capital services)—could be physical capital (machines and buildings) or human capital (education and health). K is accumulated over time through investment. L: labor input. Relates to effort, labor-force participation, population size (involves fertility, mortality, retirement, migration). Growth-Accounting Results (3.3) ∆Y/Y = ∆A/A + α·(∆K/K) + β·(∆L/L) share of capital income + share of labor income = 1, α + β = 1. Key equation (growth-accounting formula): (3.4) ∆Y/Y = ∆A/A + α·(∆K/K) + (1-α)·(∆L/L) 2 Assumptions for Solow growth model: • With respect to labor input, L. No unemployment (or, at least, constant rate). Labor-force participation rate constant (=1 just to simplify). No labor-leisure choice (labor supply later). Exogenous population growth (unlike Malthus). Population growth rate = 0 in first model, positive later. • No government spending, taxes, money (later). • Closed economy, no international trade in goods services or assets (later). • Technological progress = 0 in first model. Exogenous in later model. Endogenous in still later model. 3 Basic Solow Growth Model With ∆A/A = ∆L/L = 0, growth-accounting formula becomes (3.5) ∆Y/Y = α·(∆K/K) . Focus on ∆K in basic Solow model. Y is output and income. Investment relates to saving, which depends on income. Solow assumes saving is S = sY, 0 s 1, exogenous saving rate. Y = C + sY (inco