Chapter 7 Economic Growth I: Capital Accumulation and Population Growth Notes N differences in income must come from differences in capital, labour, and technology N Solow growth model a theory of economic growth in per-capita income; a model showing how saving, population growth, and technological progress determine the level of and growth in the standard of living 7.1 The Accumulation of Capital N the Solow growth model is designed to show how growth in the capital stock, growth in the labour force, and advances in technology interact in an economy, and how they affect a nations total output of goods and services The Supply and Demand for Goods N the supply and demand for goods play a central role in the Solow model N the supply of goods in the Solow model is based on the production function, which states that output depends on the capital stock and the labour force: Y = F(K, L) N the Solow growth model assumes that the production function has constant returns to scale (CRTS), which is considered realistic N production functions with CRTS allow the analysis of all quantities in the economy relative to the size of the labour force N by letting z = 1L: Y L = F(K L, 1) N this equation shows that the amount of output per worker Y L is a function of the amount of capital per worker K L N the assumption of CRTS implies that the size of the economyas measured by the number of workersdoes not affect the relationship between output per worker and capital per worker N because size of economy doesnt matter, y = Y L, k = K L, and f(k) = F(k, 1) and production function is written as: y = f(k) N the slope of the production function shows how much extra output a worker produce when given an extra unit of capital N this amount is the marginal product of capital, MPK, shown as: MPK = f(k + 1) f(k) N as amount of k increases, production function becomes flatter, indicating that production function exhibits diminishing MPK N when k is low, average worker has only little k to work with, so extra unit of k is very useful and produces lot of additional output; on other hand, when k is high, average worker already has lot of k, so extra unit increases production only slightly N the demand for goods in the Solow model comes from consumption and investment N in other words, output per worker y is divided between consumption per worker c and investment per worker i: y = c + i N this equation is the per-worker version of the national accounts identity for the economy N the Solow model assumes that each year people save a fraction s of their income and consume a fraction (1 s) N this idea can be expressed with the following consumption function: c = (1 s)y, where s is saving rate between 0 and 1 N this implies for investment: y = (1 s)y + i : i = sy Growth in the Capital Stock and the Steady State N

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