Macroeconomics: Growth and Ideas PDF

Chapter 6 Growth and Ideas 6.1 Introduction This chapter investigates: The development of new methods for using existing resources is key to sustained long-run growth. What is “nonrivalry” and how that makes ideas much different from other economic goods. The economics of ideas and...

Chapter 6 Growth and Ideas 6.1 Introduction This chapter investigates: The development of new methods for using existing resources is key to sustained long-run growth. What is “nonrivalry” and how that makes ideas much different from other economic goods. The economics of ideas and how this relates to increasing returns. problems with Adam Smith’s invisible hand. Romer’s model of endogenous economic growth. How Romer and Solow models work together. The Romer Model The Romer model divides the world into Objects Capital and labor from the Solow model These are finite. Ideas Items used in making objects These are virtually infinite. - This distinction between objects and ideas forms the basis for modern theories of economic growth. - Sustained economic growth occurs because of new ideas.  Objects: land, cell phones, oil, jet planes, computers, pencils, paper, capital, labor , … Ideas: instructions, or recipes. Ideas include designs for making objects. Ideas are not just created by engineering. Management techniques, just-in-time inventory methods, and algebra are also included. New ideas are new ways of arranging raw materials in ways that are economically useful. The amount of raw materials in the world is finite, but the number of ways of arranging these raw materials is so large as to be virtually infinite. Also, combining different ideas in new ways can lead to new types of products A new type of product would itself be a new idea This theory of economic growth has policy implications for many areas including intellectual property, antitrust policies, international trade, and economic development. 6.2 The Economics of Ideas Adam Smith’s invisible hand theorem: Perfectly competitive markets lead to the best of all possible worlds. Idea diagram: Problems Increasing Ideas Nonrivalry with pure returns competition Ideas If objects are the raw materials of the universe, ideas are the instructions for using these raw materials in different ways. How many ideas are possible? If we limit our ideas to 100 words, and use the English language, there are over 20,000 100 ideas. To give you an idea about how big that number is, there are thought to be 4 ∗ 1077 particles in the entire universe. Nonrivalry Nonrivalry Excludability Objects are rivalrous. Legal restrictions on use of a One person’s use reduces good or idea the usefulness to someone Ideas are nonrivalrous but else. may be excludable. Ideas are nonrivalrous. One person’s use does not reduce the usefulness to someone else. Returns to Scale Increasing returns to scale Average production per dollar spent is rising as the scale of production increases. Doubling inputs will more than double outputs. High fixed initial development costs Constant returns to scale Average production per dollar spent is constant. Doubling inputs exactly doubles output. The standard replication argument implies constant returns to scale. The Antibiotic Example: Suppose there are large fixed costs Returns to Scale—2 Proof of increasing returns Begin with the production function: Multiply all inputs by a constant (𝛾𝛾): Output is multiplied by more than 𝛾𝛾 Problems with Pure Competition—1 Pareto optimal allocation in economic theory Perfectly competitive markets Cannot make someone better off without making someone else worse off Perfect competition results in Pareto optimality because P = MC. Under increasing returns to scale, a firm faces initial fixed costs and marginal costs. If P = MC, no firm will do research to invent ideas. The fixed research costs will never be recovered. Problems with Pure Competition—2 Patents: Grant monopoly power over a good for a period Generate positive profits Provide incentive for innovation However, P > MC results in welfare loss. Other incentives may avoid welfare loss: Government funding (e.g. the National Science Foundation) Prizes to innovators Case Study: Open Source Software and Altruism Profits are not the only way to encourage innovation. Other motives: Altruistic generosity Desire to signal skills “Purpose motives” Examples: Linux Apache R (a statistics software package popular with economists) 6.3 The Romer Model The Romer model Distinction between ideas and objects Output requires knowledge and labor The production function of the Romer model Constant returns to scale in objects alone Increasing returns to scale in objects and ideas 𝑌𝑌𝑡𝑡 = 𝐴𝐴𝑡𝑡 𝐿𝐿𝑦𝑦𝑦𝑦 The Romer Model—2 New ideas depend on The existence of ideas in the previous period The number of workers producing ideas Worker productivity: Δ𝐴𝐴𝑡𝑡+1 = 𝑧𝑧𝐴𝐴 ̅ 𝑡𝑡 𝐿𝐿𝑎𝑎𝑎𝑎 Unregulated markets underprovide ideas The population (L) consists of: Workers producing ideas Workers producing output Solving the Romer Model—1 Express the endogenous variables in terms of the parameters, where 𝓵𝓵 = share of workers developing new ideas : where are parameters 𝐿𝐿𝑎𝑎𝑡𝑡 and 𝐿𝐿𝑦𝑦𝑡𝑡 are endogenous variables Solving the Romer Model—2 Solving the Romer Model—3 Romer model: Output per person depends on the stock of knowledge. The growth rate of knowledge is constant. Solow model: Output per person depends on capital per person. Solving the Romer Model—4 The growth rate of technology: The stock of knowledge depends on its initial value and its growth rate. Initial amount Growth rate of Stock of of knowledge knowledge knowledge Solving the Romer Model—5 Combining: and yields: Output per person is a function of the parameters of the model. Output per Person—1 Why Is There Growth in the Romer Model? The Romer model produces long-run growth. Does not have diminishing returns to ideas because they are nonrivalrous Labor and ideas have increasing returns together. Returns to ideas are unrestricted. In the Solow model, capital has diminishing returns. Eventually, capital and income stop growing. Balanced Growth The Solow model Transition dynamics The Romer model Does not exhibit transition dynamics Instead, has balanced growth path Constant growth rates of all endogenous variables Case Study: A Model of World Knowledge The United States has more researchers than Luxembourg has people. Growth rates 1960–2017 United States: 2.0 percent per year increase in per capita GDP Luxembourg: 2.7 percent per year increase in per capita GDP All countries can benefit from all ideas, no matter where the ideas were discovered. Experiment #1: Changing the Population Changes in the population → Changes in the growth rate of knowledge An increase in population → Immediately and permanently raises the growth rate of per capita output An Increase in 𝐿𝐿 —1 Experiment #2: Changing the Research Share An increase in 𝑙𝑙 ̅, the fraction of labor creating ideas. 1.The growth rate of knowledge will increase. There are more researchers producing more new ideas each year. 2.However, holding the population constant, if more people work to produce ideas, less people produce output. The level of output per capita decreases initially, but, the growth rate has increased for all future years, so, in the long run, output per person will increase. Increasing the research share thus involves a tradeoff in the short run  ̅ An Increase in 𝑙𝑙—2 Growth Effects versus Level Effects Growth effects: Changes to the rate of growth of per capita output Level effects: Changes in the level of per capita GDP The degree of increasing returns matters for growth effects. If the exponent on ideas is not equal to 1, there will still be sustained growth. growth effects are eliminated. Case Study: On the Possibility of Progress Can economic growth be sustained given that we live on a planet with finite resources? Prices of industrial commodities have been falling. We can see that the industrialization of China and India has made an impact around the year 2000. 6.4 Combining Solow and Romer: Overview The combined Solow–Romer model Nonrivalry of ideas results in long-run growth along a balanced growth path. The model exhibits transition dynamics if economy is not on its balanced growth path. For short periods of time, countries can grow at different rates. In the long run, countries grow at the same rate. 6.5 Growth Accounting Growth accounting determines The sources of growth in an economy and how they may change over time Consider the following production function Total factor productivity (TFP): stock of ideas 𝐴𝐴𝑡𝑡 Growth Accounting—1 Apply growth rate rules to the production function. The growth rate of each input weighted by its exponent Growth Growth rate Growth rate of of knowledge contribution output from Growth workers contribution from capital Growth Accounting—2 Adjust growth rates by labor hours: TFP growth is often called “the residual.” Productivity in the United States From 1973–1995: Output in the United States grew half as fast as 1948–1973. Known as the productivity slowdown From 1995–2007: Output grew nearly as rapidly as before 1973–1995. Known as the new economy Growth Accounting in the United States 6.6 Concluding Our Study of Long-Run Growth Institutions (property rights, laws) play an important role in economic growth. The Solow and Romer models provide a basis for analyzing differences in growth across countries. do not answer why investment rates and TFP differ across countries. Case Study: Institutions and Ideas Institutions Nonrivalrous Many of the poorest countries have to worst institutions 6.7 A Postscript on Solow and Romer The Solow and Romer models have made many additional valuable contributions: The modern theory of monopolistic competition New understanding of exogenous technological progress 6.9 Appendix: Combining Solow and Romer (Algebraically) The combined model is set up by adding capital into the Romer model production function. The combined model features five equations and five unknowns. The five unknowns: The five equations: Output Yt Capital Kt Knowledge At Workers Lyt Researchers Lat Setting Up the Combined Model The combined model will result in: A balanced growth path Since 𝐴𝐴𝑡𝑡 increases continually over time Transition dynamics The adjustment of capital, just as in Solow’s model without endogenous productivity growth Long-run growth: To be on a balanced growth path, output, capital, and stock of ideas all must grow at constant rates Setting Up the Combined Model For example, an increase Changes in any parameter in Solow Model results in in the investment rate transition dynamics …. affects only the level not the growth rate of y Long-run growth is from growth in ideas Differences in growth rates across countries are explained by the factors in Romer Model