Agenda. Long-Run Economic Growth, Part 1. The Sources of Economic Growth. Long-Run Economic Growth. The Sources of Economic Growth

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1 Agenda The Sources of Economic Growth Long-Run Economic Growth, Part 1 Growth Dynamics: Long-Run Economic Growth Countries have grown at very different rates over long spans of time. The Sources of Economic Growth The economy s production function is: Y = AF(K, N) The growth accounting formula: Y/Y = A/A + a K K/K + a N N/N The a terms are the output elasticities with respect to the K and N inputs

2 The Sources of Economic Growth According to the growth accounting formula: Y/Y = A/A + a K K/K + a N N/N A rise of 10% in A raises output by 10%. A rise of 10% in K raises output by a K times 10%. The Sources of Economic Growth Accounting for Growth: Collect data on Y/Y, K/K, and N/N. Adjust for quality changes. Estimate a K and a N from historical data. A rise of 10% in N raises output by a N times 10% The Sources of Economic Growth Table 6.3 Sources of Economic Growth Accounting for Growth: Calculate the contribution of K as a K K/K. Calculate the contribution of N as a N N/N. Calculate productivity growth as the residual: A/A = Y/Y a K K/K a N N/N

3 The Sources of Economic Growth Accounting for Growth: Why the post-1973 productivity slowdown? Measurement inadequate accounting for quality improvements. The legal and human environment regulations for pollution control and worker safety, crime, and declines in educational quality. The Sources of Economic Growth Accounting for Growth: Why the post-1973 productivity slowdown? Oil prices huge increase in oil prices reduced productivity of capital and labor, especially in basic industries. New industrial revolution learning process for information technology from 1973 to 1990 meant slower growth Growth Dynamics: Three basic questions about growth: What is the relationship between the long-run standard of living and the saving rate, population growth rate, and rate of technical progress? How does economic growth change over time? Will it speed up, slow down, or stabilize? Basic assumptions: Population and work force grow at same rate n. Economy is closed (i.e., NX = 0) and G = 0. C = Y I Are there economic forces that will allow poorer countries to catch up to richer countries?

4 The Per-Worker Production Function The per-worker production function is: The Per-Worker Production Function = A 0 f() or y = A 0 f(k) or k is called the capital-labor ratio. Assume no productivity growth, i.e., A is fixed The Per-Worker Production Function What happens if: N changes? K changes? A changes? Changes in N or K = A 0 *f()

5 Changes in A = A 0 *f() The Per-Worker Saving Function The per-worker saving function: Assume that saving is proportional to income: S = sy where s is the saving rate and is between 0 and 1. In per-worker terms, this would be: S/N = s The Per-Worker Production, Saving Functions The Per-Worker Production, Saving Functions What happens if: s changes? A changes?

6 Changes is s = A 0 *f() Changes in A = A 0 *f() S/N = s * = s *A 0 *f() S/N = s * = s *A 0 *f() Gross Investment Gross investment, I, must: Replace worn out capital, dk, and Expand the capital stock, kk I = dk + kk = (k + d)k Or, in per-worker terms: Balanced Investment Function Balanced Investment, I b, is defined as: The gross investment that is required to keep steady at its current level. If is constant, then ΔK/K = ΔN/N, or k = n I/N = (k + d)

7 Balanced Investment Function The Per-Worker Balanced Investment Function If and I/N = (k + d) k = n Then balanced investment is given by: I b /N = (n + d) The Per-Worker Balanced Investment Function What happens if: Changes in n n changes? d changes? I b /N = (n + d)

8 Changes in d combines: I b /N = (n + d) The per-worker production function, The per-worker saving function, and The per-worker balanced investment function. Initially assumes that A is constant. So there is no productivity growth Determining the Steady State How fast is the economy growing at A? At the steady state, is constant. Therefore, ΔY/Y = ΔN/N The economy grows at the same rate as the labor force

9 How fast is the capital stock growing at A? At the steady state, is constant. Therefore, in a steady state: ΔY/Y = ΔN/N = ΔK/K Therefore, ΔK/K = ΔN/N so and are constant over time, assuming no productivity growth. The capital stock grows at the same rate as the labor force Disequilibrium dynamics Disequilibrium dynamics: What if the economy is not at its steady-state? Suppose () 1 < () A. () A (S/N) A = (I b /N) A A = A*f() I b /N = (n + d) S/N = s*a*f() () A

10 Disequilibrium dynamics: What adjustment mechanism moves the economy? If() 1 < () A, then at () 1, S/N > I b /N. Disequilibrium dynamics: What if the economy is not at its steady-state? Suppose () 1 > () A. If S/N > I b /N, then will increase. This process will continue until = () A Disequilibrium dynamics () A = A*f() Disequilibrium dynamics: I b /N = (n + d) What adjustment mechanism moves the economy? If() 1 > () A, then at () 1, S/N < I b /N. (S/N) A = (I b /N) A A S/N = s*a*f() If S/N < I b /N, then will decrease. This process will continue until = () A. () A

11 Disequilibrium dynamics: The growth process is stable. The economy will always converge over time to the SAME steady state. However, growth rates during the transition period will be different. With no productivity growth: The economy reaches a steady state, with a constant capital-to-labor ratio,, and with constant output-per-worker,. When < () A, ΔY/Y > ΔN/N. When > () A, ΔK/K < ΔN/N Key Diagram #4: Key Diagram #4: () A = A*f() Factors that Shift the: (S/N) A = (I b /N) A A I b /N = (n + d) S/N = s*a*f() Production Function: A Saving Function: s and A Balanced Investment Function: n and d () A

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