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### Key Concepts

- Whereas Solow divides the world into capital and labor, Romer divides the world into ideas and objects. This distinction proves to be essential for understanding the engine of growth.
- Ideas are instructions for using objects in different ways. They are nonrivalrous; they are not scarce in the same way that objects are, but can be used by any number of people simultaneously without anyone’s use being degraded.
- This nonrivalry implies that the economy is characterized by increasing returns to ideas and objects taken together. There are fixed costs associated with research (finding new ideas), and these are a reflection of the increasing returns.
- Increasing returns imply that Adam Smith’s invisible hand may not lead to the best of all possible worlds. Prices must be above marginal cost in some places in order for firms to recoup the cost of research. If a pharmaceutical company were to charge marginal cost for its drugs, it would never be able to cover the large costs of inventing drugs in the first place.
- Growth eventually ceases in the Solow model because capital runs into diminishing returns. Because of nonrivalry, ideas need not run into diminishing returns, and this allows growth to be sustained.
- Combining the insights from Solow and Romer leads to a rich theory of economic growth. The growth of world knowledge explains the underlying upward trend in incomes. Countries may grow faster or slower than this world trend because of the principle of transition dynamics.

### 1. Introduction

- Recall that the Solow model, which is based on capital and labor, fails to provide a theory of sustained growth.
- The Romer model divides the world into
*objects*and*ideas*. - Objects include capital and labor from the Solow model.
- Ideas are items used in making objects.
- The distinction between ideas and objects forms the basis for modern theories of economic growth.

### 2. The Economics of Ideas

- Adam Smith’s invisible hand theorem states that perfectly competitive markets lead to the best of all possible worlds.
- An
*idea diagram*shows that ideas imply nonrivalry, which in turn implies increasing returns that result in problems with pure competition.

a. Ideas

- The number of ideas in the world is virtually infinite.
- The number of objects in the world is finite.
- Sustained economic growth occurs because of new ideas.

b. Nonrivalry

- An object is
*rivalrous*if one person’s use of a particular object reduces its inherent usefulness to someone else. - Ideas are
*nonrivalrous*if one person’s use of a particular object does not reduce its inherent usefulness to someone else.- Nonrivalry implies we do not need to reinvent the idea for additional use.

- Nonrivalry is different from excludability.
*Excludability*refers to the ability of someone to legally restrict use of a good.- Ideas may be excludable.

c. Increasing Returns

- Firms pay initial fixed costs to creating new ideas, but once the new idea is created, firms do not need to reinvent the idea to use it again.
- When firms have initial costs to create new ideas, in addition to traditional production costs, the firm’s production function will result in
*increasing returns to scale.*- Increasing returns to scale means that a doubling of inputs will result in a doubling of outputs.

*Constant returns to scale*means that the average production per dollar spent is constant (doubling inputs exactly doubles output).- The standard replication argument (see Chapter 4) implies constant returns to scale.

- Increasing returns to scale implies that the average production per dollar spent is rising as the scale of production increases.
- We can test for increasing returns by multiplying all inputs by two; increasing returns is present if output is then multiplied by more than two.

d. Problems with Pure Competition

- An allocation of goods is
*Pareto optimal*if there is no way to change an allocation to make someone better off.- Perfect competition results in Pareto optimality because price equals marginal cost.

- Under increasing returns to scale, a firm faces initial fixed costs and marginal costs (the cost of producing an additional good).
- If price equals marginal costs under increasing returns, no firm will undertake costly research to invent new ideas because the costs will never be recovered.

- Patents grant firms monopoly power over a good for a period in order to generate positive profits for the firm, which provide incentives for innovation.
- Allowing price to exceed marginal cost may result in welfare loss because some individuals can no longer afford the higher price.

- Other incentives for creating ideas, such as government funding or prizes, may avoid welfare loss.

e. Case Study: Open Source Software and Altruism

- Profits are not the only way of encouraging innovation.
- For example, Open Source Software programmers may be motivated by altruistic generosity or by a desire to signal their skills to others.

f. Case Study: Intellectual Property Rights in Developing Countries

- When poor countries ignore intellectual property rights, they obtain items or ideas helpful for economic development more cheaply.
- Ignoring intellectual property rights in developing countries may encourage multinational firms to relocate to developing countries.

### 3. The Romer Model

- The Romer model focuses on the distinction between ideas and objects.
- The assumptions of the model, yields four equations:
- Producing output requires knowledge and labor.
- The production function has constant returns to scale in objects alone, but increasing returns to scale in objects and ideas.

- New ideas depend on the existence of ideas in the previous period, the number of workers producing ideas, and their productivity.
- The number of workers producing ideas and the number of workers producing output sums to the population.
- Some fraction of the population produces ideas.
- Unregulated markets traditionally do not provide enough resources to produce ideas – and hence they are underprovided.

a. Solving the Romer Model

- Recall that to solve a model we express all the endogenous variables in terms of the parameters and time.
- The results from solving the model are:
- Output per person depends on the total stock of knowledge.
- In contrast, the Solow Model implies output per person depends on capital per person.

- The growth rate of knowledge is constant.
- The stock of knowledge at a given time is dependent on its initial value and its growth rate.
- Output per person grows at a constant rate and is a straight line on a ratio scale.

- Output per person depends on the total stock of knowledge.

b. Why is There Growth in the Romer Model?

- Then the Romer model produces the desired long-run economic growth that Solow did not.
- In the Solow model, capital has diminishing returns, which is eventually only enough to offset depreciation on capital. Capital has diminishing returns alone because labor and capital have constant returns together.
- This implies that capital and income stop growing.

- The Romer model does not have diminishing returns to ideas because they are nonrival. This means that labor and ideas have increasing returns together and the returns to ideas are unrestricted.

c. Balanced Growth

- The Solow model exhibits transition dynamics because the growth rate declines the closer the economy moves to steady state, but the Romer model does not exhibit transition dynamics.
- The Romer model has a
*balanced growth path*– on which the growth rates of all endogenous variables are constant. - Unless parameters of the model change, the economy has constant growth.

d. Case Study: A Model of World Knowledge

- Practically all countries in the world benefit from new ideas, even if they are created in another country.
- The Romer model is best viewed as a model of the world.

e. Experiments in the Romer Model

- Parameters in the Romer model are population, the fraction of the population doing research, productivity, and the initial stock of ideas at date t = 0.
- Experiment #1: Changing the Population,
- All other parameters held constant, a change in population changes the growth rate of knowledge.
- An increase in population will immediately and permanently raise the growth rate of per capita output.
- Experiment #2: Changing the Research Share,
- An increase in the fraction of labor making ideas, holding all other parameters equal, will increase the growth rate of knowledge.
- If more people work to produce ideas, less people produce output. This implies that (the
*level*of) output per capita jumps down initially.- Although output per person is lower initially, because the growth rate has increased for all future years, output per person will be higher than it would have been in the long run.

f. Growth Effects versus Level Effects

- The exponent on ideas in the production function determines the degree of returns to ideas alone.
- If the exponent on ideas is not one:
- The Romer model will still generate sustained growth.
*Growth effects*are eliminated if the exponent on ideas is less than one due to diminishing returns to ideas.

- Growth effectsare changes to the rate of growth of per capita output.
- Level effects are changes in the level of per capita GDP.

g. Recapping Romer

- The total stock of ideas is the key to sustained growth of per capita output.

### 4. Combining Solow and Romer: Overview

- In the combined Solow-Romer model, nonrivalry of ideas results in long-run growth (along a balanced growth path).
- The combined model also exhibits transition dynamics if the economy is not on its balanced growth path.
- In the long run, countries grow at the same rate, but transition dynamics allow countries to grow at different rates for periods of time.

### 5. Growth Accounting

*Growth accounting*helps determine the sources of growth in a particular economy and how they may change over time.- The stock of ideas is referred to as
*total factor productivity (TFP).* - Applying growth rate rules to the production function yields a growth rate version of the production function, with the growth rate of each input weighted by its exponent.
- These growth rates can be adjusted by labor hours.
- Since everything other than the growth of TFP can be measured, we can use the labor adjusted growth rate version of the production function to determine the unobserved residual (TFP growth).
- From 1973-1995, output in the U.S. grew half as fast as from1948-1973. This slower era of growth is known as the
*productivity slowdown.* - From 1995-2002, output grew nearly as rapidly as before the productivity slowdown. This recent era is known as the
*new economy.*

### 6. Concluding Our Study of Long-Run Growth

- Institutions (property rights, government, laws) play an important role in economic growth.
- The Solow and Romer model provide a basis for analyzing differences in growth across countries.
- However, the models do not answer why factors such as investment rates and TFP differ across countries.

### 7. A Postscript on Solow and Romer

The Solow and Romer models have made many additional valuable contributions

### 8. Additional Resources

- Summary
- Key Concepts
- Review Questions
- Exercises
- Worked Exercises

### 9. Appendix: Combining Solow and Romer (Algebraically)

a. Setting Up the Combined Model

- The combined model is set up by adding capital into the Romer model production function.
- The production function will have constant returns to scale in objects, but increasing returns in ideas and objects together.
- The change in the capital stock is investment minus depreciation.
- It is assumed that capital is not used to produce new ideas.

b. Solving the Combined Model

- The combined model will result in a balanced growth path and in transition dynamics.

c. Long-Run Growth

- The growth rate of knowledge is the same as in the Romer model.
- To be on a balanced growth path, the growth rate of capital must equal the growth rate of output.
- The growth rate in the number of workers is zero.
- The growth rate of output is even larger in the combined model than in the Romer model.
- Output is higher in this model because ideas have a direct and indirect effect. Increasing productivity raises output because productivity has increased and because higher productivity results in a higher capital stock.

d. Output per Person

- The capital to output ratio is proportional to the investment rate along a balanced growth path.
- Output depends on the square root of the investment rate.
- A higher investment rate raises the level of output per person along the balanced growth path.

e. Transition Dynamics

- The Solow model has transition dynamics because capital has diminishing returns.
- The combined model also has diminishing returns to capital.

- The
*principle of transition dynamics*for the combined model is defined as the farther below (above) its balanced growth path an economy is, the faster (slower) the economy will grow. - A permanent increase in the investment rate in the combined model implies:
- The balanced growth path of income is higher (parallel shift).
- Current income is unchanged so the economy is below the new balanced growth path.
- The growth rate of income per capita is immediately higher (the slope of the output path is steeper than the balanced growth path).
- As the output path moves closer to the new balanced growth path, the growth rate is quicker at first and slower as it nears closer.
- Eventually, the growth rate converges to its level prior to the shock, but along the new permanently higher balanced growth path.

- Changes in any parameter result in transition dynamics.
- The resulting theory generates long-run growth through ideas and explains differences in growth rates across countries through transition dynamics.

f. More Exercises

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