Apologies to regular readers for posting something rather drier and more technical than the usual fare on this blog, but I wanted to post a sketch of the model that I hope will become my dissertation. It's a model of economic growth and technological change.

**Increasing Returns**

The first chapters of Adam Smith’s *The Wealth of Nations* contain two powerful and intuitive ideas, which however have proven proven challenging to model formally: (a) specialization and gains from trade, which is closely related to the ideas of *increasing returns* and *economies of scale*, most vividly illustrated in Smith’s account of a Pin Factory, (b) “the division of labor is limited by the extent of the market,” which in Smith is explicitly a *geographical* concept: large cities allow more division of labor than small towns, which in turn allow more than villages, etc. By contrast, contemporary economic models generally assume constant returns to scale.

**Technological Progress**

Division of labor and increasing returns are linked in several ways to another old-new idea in economics: the importance of *knowledge* and *the introduction of new goods* to economic progress. Knowledge itself is characterized by increasing returns—ideas are “non-rival” and, once developed, can be spread at low cost—and developments at the technological frontier often open new possibilities for division of labor (a concept akin to *introduction of new goods* since newly subdivided tasks can be thought of as new goods) and economies of scale. Paul Romer has played the leading role in mainstreaming the economics of “endogenous growth,” so called because it seeks to endogenize the (in)famous “Solow residual,” the portion of growth which, according to the Solow model, is not explained by capital and labor, and so is attributed to “technology.”

In Romer’s model of endogenous growth, entrepreneurs invest in research to develop designs for new goods. Oddly, in Romer’s model, there is nothing exogenous in the invention/discovery of new goods at all: given a certain investment in research, new varieties will always be invented, and these varieties enter symmetrically into production functions: every design is as useful as every other, and none ever becomes obsolete. One of the goals of the model I am developing is to capture the notion that the possibilities for technological advance are exogenous, *out there,* not knowable in advance. We discover them, we do not make them.

**New Goods and Backwards-Compatibility of Utility/Production Functions**

There is no room for new goods the traditional Cobb-Douglas production function, q=Ak^{α}l** ^{β}**, or utility function,

^{α}y

^{β}, because the Cobb-Douglas function requires firms/agents to have access to

__all__inputs/goods to get

__any__output/utility.

The Cobb-Douglas function __can__ be extended to include many goods. We can have a Cobb-Douglas production function, q=k_{1}^{α1}k_{2}^{α2}…k_{n}^{αn}l_{1}^{β1} l_{2}^{β2}… l_{n}^{βn}, where k_{1}...k_{n} are *n* types of capital and l_{1}…l_{m} are *m* types of labor. Likewise, we can have a utility function of the form _{1}…x_{n})=k_{1}^{α1}k_{2}^{α2}…k_{n}^{αn}_{1}…x_{n} are *n* types of goods. But if the producer hires zero of __any__ type of labor or capital, or if the consumer consumes zero of __any__ type of good, the resulting production/utility will be zero. But what if k_{n}, or l_{m}, or x_{n}, was recently invented and didn’t exist in previous periods? In that case, until its invention, there could have been no production/utility.

If we want to model new goods, then, we need to make utility and production functions *backwards-compatible* by making it possible to have some utility/production in the absence of goods/inputs that were invented at some point in time. The other standard utility function, the “constant elasticity of substitution” function…

(Equation 1)

… does allow for positive utility/production if the use of some goods/inputs is zero, and it is the basis for the Dixit-Stiglitz model of “preference for variety”…

(Equation 2, as quoted in Helpman-Grossman, *Innovation and Growth in the Global Economy,* p. 46)

… and this function can be converted into a production function by substituting different types of capital for different types of goods. Cobb-Douglas, however, is a more standard way of modeling production, which may have empirical support of a sort in the observed regularities of capital and labor income shares. For this and some other reasons, I will for the moment use a modified Cobb-Douglas function to model the introduction of new goods. Production functions will take the form:

(Equation 3)

And utility functions:

(Equation 4)

where g_{1}…g_{n} refer to goods 1…*n*, L refers to labor, and R, r, and c relate to the *spatial* aspect of the model: R is the “rent bid” that each agent makes, r is the “average rent,” a function of all the rent bids and of the x- and y-coordinates where an agent or firm “lives,” which is returned by a land-market model which takes the locations and rent bids of agents and firms for inputs, and c is “commuting time,” a weighted average of the distances from where each consumer/worker “lives” to all the jobsites where he works, divided by an assumed speed of commuting.

If good g_{n} is not available, the term (1+g_{n})^{αn} will simple be 1, and the utility/production function is unaffected. When a new good becomes available, agents and firms can still go on consuming/producing the way they did before, but they *may* have an opportunity to consume the new good. This utility function avoids the unwelcome implication, common to both Cobb-Douglas and CES, that all agents will always consume positive amounts of every good. This will result in many “corner solutions” in which agents/firms would like to use negative amounts of a good, and the zero constraint must be imposed. These are mathematically inconvenient, but a computational model can handle that. Substantively, allowing agents to consume zero of some available goods is a welcome shift towards realism.

**Graphical, Mathematical, and Computational Economics**

When economists move beyond two-good models to many-good models, they reach the limits of what can be analyzed using geometry, and they have to rely on the *n*-dimensional possibilities of mathematics to go forward, using geometry to illustrate conclusions that are grounded in equations. In similar fashion, I suspect that as economists struggle to develop spatial models and models with new goods, there will be increasing pressure to supplement mathematical with *computational *approaches, and ultimately perhaps to embed general-equilibrium-style equations in computer simulations. At any rate, that is the approach contemplated in the agent-based, spatial, endogenous growth model contemplated here.

There is a map, which for starters will be a uniform square. Each period “bequeaths” to the next one at least three “spreadsheets” of information: (a) a goods spreadsheet, which contains all the goods available, their production functions, and a logistics cost index, and dummies for whether the good is a capital good and whether it has been “developed,” (b) an agents spreadsheet, recording the location where each agent “lives” and how many shares in an “index fund” he has (somebody has to own the firms; and there’s nobody to do it but the agents), and (c) a “firms” or “facilities” spreadsheet that records each location where production facilities exist, where a production facility consists of a bundle of capital goods dedicated to the production of some good *g*, which is owned by the “index fund” and will be operated to maximize profits in the next period by an implicit management: in addition to locations the firms spreadsheet records the capital inventory and product of each “firm” (or “facility”—for some purposes it may be better to imagine larger firms owning many facilities, which however may operate as competitors with each other). It may be necessary for each period to inherit *more* information from the previous one, in order to resolve multiple-equilibria problems; in that case the results would provide evidence for certain forms of path dependency.

The model contains no “representative agent” or “representative firm.” All agents have the same utility function. All firms producing a certain good have the same production function. They all solve their optimization problems in the same way. But agents have different locations and wealth, and firms have different locations, products, and capital stocks. What results will not be a model that can be solved, it will be a computer simulation which can be observed, with different initial conditions and parameter values. The model will contain randomness, not only in initial conditions but as an ongoing factor in its evolution over time. Certain generalizations can be anticipated, and other unanticipated ones may be observed. Hopefully intuitions will be apparent for all or at least many of the observed patterns. Moreover, the results will not be replicable by anyone with the mathematical skills and the patience to work through the equations—though it may be possible to make a computer application available online so that people can play with the model themselves. The cost to this approach is a loss of a certain kind of transparency, although it might lend itself to appealing and powerful graphical displays. But the approach seems necessary in order to avoid questionable assumptions.

On the other hand, my hope is that even if the results are not replicable by non-computational means, most of what the model will *do* will be intelligible in terms of traditional constrained maximization. Often computational models have imposed very simple rules of agent behavior. What they show is that complex patterns can emerge at the macro level from simple rules at the micro level. But by assuming sophisticated agents and firms, this model seeks to import the insights from mainstream economics into a computational framework.

**Market Power**

One of the properties of the utility and production functions above is that they may be characterized by *decreasing,* *constant*, or *increasing* returns (though constant returns are very unlikely), depending on β + γ + ∑α_{i}; if β + γ + ∑α_{i}<1, the production process has decreasing returns, whereas if β + γ + ∑α_{i}>1, the production process has increasing returns. (The story is in fact a bit more complicated than in the traditional Cobb-Douglas function, because if g_{i} is small relative to 1 a change in g_{i} will lead to a proportionally much smaller change in (1+g_{i})^{α}—a tiny bit of a new input is not enough to transform the production process—but this doesn’t affect the conclusions substantially.)

Increasing returns are a chronic challenge for economics, because although all kinds of intuitions and empirical evidence points towards them, they are incompatible with the assumption of perfect competition, which underlies all kinds of rule-of-thumb results which the discipline has great difficulty dispensing with. In this model, there is no perfect competition; instead, market power is assumed. For simplicity, all sellers (including workers, “sellers” of labor) have market power, while all buyers (including employers) are price takers. Again for simplicity, agents and firms optimize myopically: if they find they are at a local maximum, they take it as optimal, without looking to “jump” to distant equilibria. Each seller queries her buyers, finds the tangent lines of their demand curves, and uses that as an input into her own optimization.

**The Land Market**

For the model’s spatial element it is necessary to create a land market, and some definite way for it to clear. Each agent and firm needs land, and prefers to have as much as possible. This creates a *centrifugal* force, pulling away from “cities” (population concentrations) where land is scarce. At the same time, transport costs, economies of scale, and gains from specialization and trade give agents and firms a reason to concentrate and create cities.

*Rent—*the use-cost of land—should clear the land market by taking high values where population and income are concentrated, low values where population and income are rarefied. A model developed by von Thunen, which is still influential in urban economics, *assumes* a monocentric city; in many versions there is a “central business district” where firms must send representatives in order to do business with other firms. But if the monocentric city is assumed, the model can’t explain it. Still less can it explained cities like

Los Angeles

where a more sprawling and decentralized pattern has emerged.

My approach to the problem is to envision an array of agents (and firms) distributed on a map, to assume a given “rent bid” from each agent, and to decide how the land market might most realistically clear. What conditions should a reasonable market-clearing outcome meet? The first is obvious:

(Equation 5)

Where L_{1 }is the amount of land rented/used by agent 1, L_{2} by agent 2, etc. Equation (5) simply states that the amount of land used by all agents equals the total area of the map. Agents cannot use more land than there is, of course, but Equation (5) also (unfortunately, but for the moment it’s the best I can do) introduces a “no frontier” condition, i.e., there can be no land which remains unused because it is worth no one’s while to use it. Each L_{i} should satisfy:

(Equation 6)

Where R_{i} is agent *i*’s rent bid, while *r*_{i} is the value of the rental function at the (x,y) where agent *i* “lives.” What Equation (6) states is, if anything, even simpler than Equation (1): the amount of land agent *i* has/holds/uses equals his total rent bid divided by the local unit cost of land, yet there are subtleties hidden in it. We will regard the rental cost of land as a continuous function which takes a value at *every *(x,y) on the map. This is necessary, among other reasons, so that later in the model we can model agents’ choices about whether to move and where to live as a “constrained optimization” problem. But that implies that the rental cost of land may vary over the land that agent *i* holds. We will nonetheless assume that agent *i* “lives” at a single point, and rents land “in the vicinity of” that point.

The next task is to discover, or invent, the rent function. One task for the rent function is to ensure that “the market clears,” i.e., that the land used is no more and no less than the land available. But many functions can perform task. The other, more complicated task is to allocate land in a manner that is intuitively plausible and doesn’t involve too much distortion of the shapes of rental plots. We want to avoid a “pizza slices” solution, in which agents can cluster at a single point and purchase plots shaped like pizza slices, radiating outward from the center. We want high urban land rents to operate as a brake on concentration of population. The function I present does these things, but I will not definitely claim that it is the best or simplest such function, or that it is empirically valid in detail, and there may be room to discover better rent functions. Nonetheless, it will do for now:

(Equation 7)

As messy as this appears, it is a composite of simpler elements. The first we may called the “adjusted rent bid”: R – 1 + 1/(R+1). This has the properties that

(Equation 8)

(Equation 9)

Equation (8) ensures that very small landholders will be *price takers*, while Equation (9) ensures that as a landowner’s bend bid becomes very large, it will increasingly be channeled into driving up his own rent, and the landholder will not be able to completely dispossess other agents/firms.

The second element of the rent function is “adjusted distance squared,” *a* is needed because in some terms the denominator is the agent’s squared distance to *himself*, so without the *a*, this zero denominator causes the function to blow up.

From these two elements we can construct the “unscaled rent”:

(Equation 10)

By equation (10), an agent’s unscaled rent equals the sum of all the adjusted rent bids divided by the corresponding adjusted squared distances to himself. The numerators of the terms in equation (10) are the same for all agents, but the denominators are different, and urban rents are higher because many of these denominators—these distances to other agents—are very small. Equation (10) sets the rents in the correct proportion to one another, but does not ensure that the agents collectively will use the right amount of land. So a scaling factor must be introduced of the form

(Equation 11)

where Ur_{i} is the unscaled rent of agent *i*. The result is the rent function shown in Equation (7).

The results of land market clearing under this functional form may be best shown by a picture:

**Figure 1: Land Market: Centered Random Population Distribution, 500 Agents, Uniform Rent Bids**

In a Java program, I generated a random population distribution, but skewed so as to create a concentration of population in the center, then applied the rent function to it, and allocated the land accordingly. The results are shown in Figure 1. Each of the circles represents an agent, and the size of the circle represents the amount of land the agent has. The radius of each circle is proportional to the agent’s landholdings, but one-and-a-half pixels have been added to each radius, otherwise the landholdings of the agents in the center would be so small that they would not be visible at all.

As Figure 1 shows, landholdings become larger—because rents are lower—further from the population concentration in the center of the map. In a more complete version of the model, rent bids will be allowed to vary, and there may be multiple concentrations of population, but the pattern of larger landholdings in areas of low population density will presumably continue to be observed. Utility from landholding, and land as a factor of production, will function as the main force opposed to concentration of population.

**Defining an Equilibrium**

In each period, “the market clears.” What does this mean in the context of a spatial model with market power? Under conditions of perfect competition, the condition of “market clearing” is in game-theoretic terms a *Nash equilibrium*, that is, a state in which each “player” (each agent or firm) has chosen the best possible move, conditional on the other players’ moves. In order to define the same condition in the context of this model, we must define what each agent’s and firm’s moves are. The dilemma is: should an agent’s/firm’s “move” be defined as a *price*, a *quantity,* or perhaps as some sort of *decision rule,* e.g. a demand curve which states quantity demanded as a function of price.

If we define the moves as prices and quantities demanded and supplied of every good, the Nash equilibrium becomes trivial. Given the moves of all other agents and firms, agent *j* __cannot__ purchase more of any good, because firms have already decided the quantity they will produce, and they have nothing extra to supply to him. He cannot bid for more of the good because they have already fixed the price. Any decision set constitutes a Nash equilibrium in this sense, so this type of Nash equilibrium is not informative. It also hardly seems to constitute rationality, for why should a firm refuse to increase supply if agents are willing to bid up the price? For a more interesting and rationality-compatible definition of equilibrium, agents’ moves must be defined more subtly.

A supplier’s *price* is one kind of decision rule: I will supply whatever quantity agents are willing to buy from me at price *p*. A buyer’s demand curve is another kind of decision rule: I will buy some *q* units of good *g* for any price *p*, where *q*(*p*) is some (typically decreasing) function. How do agents decide what decision rule to use? Buyers can derive demand curves from their utility functions. __Then, faced with a given demand function, a supplier can determine his optimal price.__ (In bargaining models, a player who can observe the other’s preferences (demand function) and commit to a price has a strategic advantage, which can be called “first-mover advantage” or “market power.” Thus, by defining the moves in this way, we give market power to all suppliers. We could do the reverse, allowing buyers to observe sellers’ supply functions and choose their offer price accordingly, but in real markets suppliers seem to define prices most of the time.)

Each agent maximizes utility by making the following decisions:

(a) which goods to buy (and from whom) *as a function of* the available prices, and how much of each;

(b) which employers to work for, and what wage to demand, given the (observable!) labor demand functions of each employer;

(c) how much land to rent, given the *marginal *rental cost of land (that is, *not the value of the rent function at his own (x,y), but the partial derivative of the rent function with respect to his own rent bid at his own (x,y)…* this is one place where the model is a bit complicated);

(d) whether to move, and, if so, where to move to;

(e) whether to go into business for himself by establishing one or more firms.

Each firm maximizes profits by making the following decisions:

(a) how much of all inputs (including land and labor) to purchase (and from whom) *as a function of* the available prices (which also determines the quantity of its product that it will produce; the “price” of land is not the value of the rent function at the firm’s (x,y), but its partial derivative with respect to the firm’s rent bid);

(b) what to charge for its product, given the (observable) demand functions of all buyers (no price discrimination allowed, however).

A set of decision set for the economy consists of decision sets for every agent and firm over the set of decisions listed above (which is a lot more than five for agents and two for firms, because there are many goods, employers, etc.). That decision set is a Nash equilibrium if each agent’s and firm’s decision represents the solution of a constrained optimization problem given the decision sets of all other agents and firms.

**Seeking an Equilibrium**

How to find the type of equilibrium described above I don’t know right now. I’m guessing that there is probably some way to do it, if such an equilibrium exists. How many Nash equilibriums are there? I see three possibilities:

Case (b) corresponds to “market clearing” in the most orthodox sense. Case (a) might be described as *chaos,* but if there is no equilibrium of the type defined above, I can probably redefine the equilibrium so that at least one equilibrium exists. Case (c) represents *multiple equilibria,* and in that case the method for seeking an equilibrium matters, because different methods might take us to different equilibria. Since the model should seek equilibrium in some definite way, it may be necessary for the model to inherit more information from the previous period in order to determine *which* equilibrium the model will converge on; in this case, interesting path-dependency stories may emerge.

**Challenges**

Apart from how to find the Nash equilibrium, at least three aspects of the model present outstanding challenges that I haven’t solved yet: (a) mobility, (b) entrepreneurship, and (c) the design frontier.

*Mobility.* Each agent must decide, in each period, whether to stay put or move, and, if they move, where to. It seems realistic to assume that moving involves fixed and variable costs. From this it follows that the optimality of the location decision is differently defined for agents who have moved and for agents who have not. The former have already incurred the fixed costs of moving, so they will make sure that their destination location represents a local maximum of their optimized utility function with respect to their *x-* and *y-*coordinates. The latter do not need to be at a local maximum, because fixed costs prevent very small moves. But they do need some way of checking whether better places to live exist somewhat further away, such that the utility gain exceeds the fixed costs of moving. I am not sure how to solve this type of maximization problem mathematically, and unfortunately, this would need to be part of the *checkForNashEquilibrium* procedure which would likely be run over and over again during the process of seeking the Nash equilibrium. An alternative is to allow a random subset of agents to move at zero cost in each period. This will make the Nash equilibrium easier to define but it turns the mobility of the population into an exogenous parameter. Mathematically, locational optimization involves taking partial derivatives of the rent function, and of value and profit functions, with respect to the *x*- and *y*-coordinates where agents “live.” I can foresee more or less how this should be done, but I have not undertaken this so far and do not know how challenging it will prove to be.

*Entrepreneurship.* Because capital in the model must be produced in the previous period and, once produced, is immobile, no new capital-using firms can be created within-period in response to emerging market conditions. However, the production function implies that *it is possible to produce goods without using capital.* In fact, every good can be produced (perhaps very inefficiently) using land and labor alone; capital, at most, enhances productivity. There may, moreover, be some goods for which the α’s of all capital goods are zero, i.e., goods in the production of which capital plays no role at a given point in time (though capital goods useful in the production of the good may be invented later). There are, therefore, opportunities for agents to start new firms, creating what we may call an “informal sector,” purchasing goods and hiring workers (including themselves) at the available prices, and benefiting by taking home profits, or perhaps through the effects on their wages and/or by making goods available to themselves at lower prices. The independent sector has a very interesting and important interpretation, because it may represent not only entrepreneurship in the usual sense, but also “non-market” activities: home-cooked meals, do-it-yourself home improvement, and all sorts of “cottage industries.” But I haven’t figured out so far how to write an algorithm by which agents can look for opportunities for informal-sector entrepreneurship.

In the model, unlike in the real world where time is continuous, entrepreneurship which employs capital goods, which must used in the next period after they are produced, is quite distinct from the non-capital-using within-period entrepreneurship of the informal sector. “Formal sector” entrepreneurs face a problem which hasn’t been introduced into this model yet, the problem of optimizing *over time.* To do so, they need to have some way of forecasting the future. The “rational expectations” school argues that it is not good practice to assume that people have systematically mistaken expectations, so agents’ assumptions about the future should be the same as the modelers’ conclusions about the most probable future given all information available at the time. Can I meet this standard, and how? I haven’t figured that out yet, and the problem of the intellectual frontier makes it more complicated. Also needed is some model of capital markets. To develop a model of individual saving consistent with rational expectations and the life-cycle hypothesis is not a priority; for the time being I may take savings to be exogenous. But formal-sector entrepreneurs do have to generate some kind of demand curve for investment that will make capital markets clear. Only then will this become a multi-period model which may be able to shed light on economic growth.

*The design frontier.* The advance of knowledge is modeled through the expansion of the goods “spreadsheet,” but how does the goods spreadsheet expand? Two processes must be distinguished here: (a) the process by which new design possibilities are recognized which were not previously imagined, and (b) the process by which those design possibilities are researched-and-developed, executed, commercialized, in short, made real.

Process (a) is taken to be exogenous, but it is not simply an exogenous parameter. Rather, each period the program must executed the following: add *n* rows to the goods spreadsheet *and the same number of columns* to both the goods spreadsheet and the utility function; fill the new rows with random coefficients that comprise the good’s production function, as well as the transport cost coefficient, a random Boolean value for whether the good is capital or not, a dummy to indicate that the good has not yet been developed, and some kind of indicator of the cost of developed the good; and fill the new columns with random coefficients indicating the potential effect of the new good on the utility function and all production functions. Obviously a lot rides on the precise manner in which these coefficients, which may number tens, or hundreds, or thousands, are randomized.

Process (b) is endogenous: agents or firms—I haven’t figure out which makes the most sense—incur research-and-development costs in return for a patent of one-period duration, during which time they can earn monopoly profits selling the good. R&D-oriented firms will have to compete in the same capital markets with firms planning to produce currently-available goods. After one period, the patent expires, and the good and its production function become public knowledge. Goods which are in the process of development should not affect the behavior of agents, because it is assumed that the public, including both agents and firms, is not aware of the parts of the goods spreadsheet that are not yet developed.

The concept of the design frontier has usually been interpreted as the advance of technology, but it seems to me equally applicable to the arts.

**Emergent Scenarios**

__Malthusian Scenario__

The model can readily produce the scenario described by Thomas Malthus, in which natural population increase outpaces economic productivity, ensuring that many or most people live on the brink of starvation. To introduce reproduction—in each period, some agents “split” into two agents, which then have reason to move to gain more/cheaper land—and death—agents disappear with probably *p*, 0 < *p *< 1, if utility falls below a certain threshold—is straightforward. If there are few “industrial” (increasing returns) goods to encourage concentration and drive long-run growth, and if development of new goods is sluggish or non-existent, population growth can cause falling living standards, to the point where only widespread starvation may hold population in check. Arguably, much of world history exhibits Malthusian patterns.

__Ricardian Scenario__

David Ricardo thought that the fruits of economic growth went entirely to landowner-rentiers. Workers were caught in a Malthusian trap, while manufacturers competed away all profits, and the gains from technical progress and population growth went exclusively to landowners. Such a scenario is likely to emerge when population growth is allowed, and under certain structures of technological change. Many of the great civilizations of the past seem to exemplify the Ricardian scenario, generating opulence which, however, was restricted to the rich, while the lot of peasants, serfs, slaves, and even artisans was arguably little or no better than that of many uncivilized peoples.

__Smith-Young Scenario and the Industrial Revolution__

If technological progress is fast enough, and increasing returns are sufficiently common, we can anticipate a situation in which the goods spreadsheet keeps expanding; a few goods keep **crossing the threshold from decreasing to increasing returns** and thus “industrialize”; there is a steady **expansion of cities** as factories draw workers, and urban land rents rise steadily; the cost of new goods keeps falling as they reap increasing returns, as they generate “derived demand” for upstream goods which are invented and/or industrialized as a result, and as their low costs spur “downstream” industries to expand. This story of growing specialization, urbanization, and ever-advancing technology is the story told by Adam Smith early in *The Wealth of Nations,* a theme revived by Allyn Young. This scenario more or less describes the modern age.

__Solow Scenarios__

The Solow growth model focuses on the role of capital accumulation, and shows that a certain amount of economic growth can be driven by capital accumulation alone, but in the long run economic growth is attributed to an exogenous “Solow residual” which is usually interpreted as the advance of knowledge. To isolate the Solow phenomenon of growth through capital accumulation, we can alter the rules of the model so as to disallow the development of new goods. In that case, savings will be invested, and the capital stock will increase, driving economic growth. Moreover, if at least some goods’ production functions are characterized by increasing returns, we might observe economic growth indefinitely. But decreasing-returns goods will constrain the growth of utility.

If we then allow the development of new goods, these will drive an ongoing rise of productivity which will likely mimic the Solow residual, except that there will be a certain randomness, originating in the randomized expansion of the goods spreadsheet. Also, this quasi-“Solow residual” will have different effects on different sub-groups in the population, and may be influenced by policy, population, wealth distribution, and other variables.

__“Roundaboutness”__

A theme of Austrian economics is the growing “round-aboutness” of production which is observed in developed economies. Stages of production more and more remote from the ultimate needs of the users of goods are continually appearing. The demand for many goods is a “derived demand” coming from downstream industries. In the model, I anticipate that supply chains will become ever more complex as the economy grows, as goods that are invented or industrialized create potential demand for “upstream” goods, triggering their development.

__Interesting Questions__

To exhaust the interesting questions raised, or reframed, by this model would be difficult, but some large questions can be mentioned:

*What is the effect of different patent arrangements on the pace of technological change?* Patent laws affect technological change in two offsetting ways. On the one hand, they increase the incentive for entrepreneurs to incur the costs of developing new technologies. On the other hand, they lengthen the time during which a new good is a “monopoly” product, likely to be more expensive, which makes it less effectively available as an input to other goods, or as a source of demand for other goods as production inputs. There may be some optimum patent duration, depending on the parameters used in the model.

*If we impose mobility restrictions, what is the effect on inequality? *Since this is a spatial model, it is a good opportunity to study the effects of migration restrictions on distribution. Since there is no human capital in this model, we should in general expect wages to be quite equitable, varying only to compensate workers for living in places that are unattractive in some way. Some inequality will emerge from random variations in entrepreneurship and from location effects. But if mobility restrictions are imposed, real wages may settle to quite different levels in different “countries,” a process that may be exacerbated as some of the arbitrary borders isolate pieces of the map that are fail to emerge as magnets for economic activity.

*What is the effect of a new transportation technology?* Transportation technologies enter this model differently than other technologies: they cannot simply be entered into the goods spreadsheet, but must affect

*parameters*, namely those associated with commuting and transport of goods. If we reduce the transportation cost parameter, or the commuting cost parameter, how will this affect the distribution of population? How will it affect welfare? How will it affect the exploitation of economies of scale? The rate of technological change? (In a more sophisticated version of the model, I would introduce an

*economic distance density map*so that economic distance would not be a linear function of physical distance. In an even more sophisticated version, I could introduce

*modes*of transport… But for now I have enough on my plate!)

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Posted by: dissertation writing help | July 04, 2009 at 12:59 AM