Trends in Hardware and Software Costs as an Example of Structural Economics Dynamics

Empirical Trends in Costs for Computer Systems

1.0 Introduction¹

Over time, the proportion of the cost of computer systems consumed by software has tended to rise. Figure 1, originally in Boehm (1973) illustrates. In this post, I offer a theoretical explanation of this empirical observation. One might take this post as an illustration of an empirical use of the Labor Theory of Value.

2.0 The Model

Assume a computer system consists of equal amounts of hardware and software, both measured in some standard units^{1, 2}. Earlier computer systems delivered less units, while current computer systems deliver more. Next, assume that both hardware and software are produced directly from labor³.

2.1 Definitions and Assumptions

Let l_h be the staff-hours needed to produce a unit of hardware. Define ρ_h to be the rate of growth of labor productivity in the hardware industry:

ρ_h = - (1/l_h)(dl_h/dt)

Similarly, let l_s be the staff-hours needed to produce a unit of software, and define ρ_s to be the rate of growth of labor productivity in the software industry:

ρ_s = - (1/l_s)(dl_s/dt)

The last assumption is that the rate of growth of productivity is higher in producing hardware:

0 < ρ_s < ρ_h

One last variable must be defined. Let p be the ratio of labor costs to total system costs for a software system:

p = l_s/(l_h + l_s)

This completes the exposition of the model assumptions and variable definitions.

2.2 The Solution of the Model

Some algebraic manipulations with the above definitions yields the following differential equation:

(1/p) (dp/dt) = Δ(1 - p),

where Δ is the difference in the growth rates of labor productivities in hardware and software productivity:

Δ = ρ_h - ρ_s

This differential equation expresses the rate of growth of software cost, as a proportion of total system cost. The solution to this differential equation is:

p(t) = 1/[1 + c exp(-Δ t)]

where c is a constant determined by an initial value:

c = [1/p(0)] - 1

2.3 Numerical Values

Calibrating the model is the last step in the analysis presented here. Suppose 20% of the cost of a system is software in 1960, and that 80% of the cost of a system is software in 1995. The rate of growth of labor productivity is then 8% more in hardware than in software.

Δ = (1/35)[ln(4) - ln(1/4)] ≈ 7.9 %

The integrating constant for the initial value is:

c = 4/exp(-1960 Δ) ≈ 1.1 x 10⁶⁸

Figure 2 shows the relative proportion of system costs, as generated by the model with these parameters. Notice how closely Figure 2 resembles Figure 1. The model provides an explanation of the empirical observations.

Modeled Trends in Costs for Computer Systems

3.0 Conclusion

This post has presented a model, with its attendant idealizations. And that model shows how the empirical observation that productivity increases faster in hardware than software can account for the empirical observation that the cost of computer systems have become mostly software costs. Hardware costs, as a proportion of total system costs have been declining for decades.

Footnotes

1. This post draws on work I did elsewhere decades ago.
2. Floating Point Operations per Second (FLOPs) is a common measure of output in hardware. I suppose one should also specify the power at which these FLOPs are generated.
3. Source Lines Of Code (SLOC) is a common measure of software size. I have heard the analogy that measuring software in SLOC is like measuring the size of a house by the number of nails used in its construction. I guess one could always use Function Points (FPs) as a measure of software.
4. A natural extension would be to assume both hardware and software are produced solely from inputs of labor, hardware, and software. I am not sure if I ever stepped through such a model in this context.

References

• Barry W. Boehm (May 1973). "Software and Its Impact: A Quantitative Assessment", Datamation.
• Luigi L. Pasinetti (1993). Structural Economic Dynamics: A Theory of the Economic Consequences of Human Learning, Cambridge University Press.

Elsewhere

• Steve Denning, a writer for Forbes, describes Milton Friedman as being the source of "The world's dumbest idea". (I have written on Milton Friedman's confusion. incoherence, and lack of integrity, as well as Michael Jensen's (ir)responibility. See also Unlearning Economics.)
• Mike Konczal on Philip Mirowski's new book.
• Henry Scowcroft on the need for communicating economics to the public.
• Michael Lind on supposedly "Econ 101". Noah Smith complains about the public impression of what economists teach.
• Robert Neild on a 1981 anti-monetarism petition. I am especially amused about him losing his cool in a debate with Milton Friedman.
• Mark van Vugt and Michael Price, two psychologists, I gess, comment on Homo Economics. They link to a website which has David Sloan Wilson as editor in chief.
• Floyd Norris, in the New York Times, explains that Steve Keen foresaw the global financial crisis better than Ben Bernanke did.

Who Are The Nine People Prosecuted By The USA For Espionage For Leaking Secrets To The Press?

1.0 Introduction

This is a current affairs post, usually outside what I blog about.

I have found the count in the post title echoed in several publications, for example:

"...Historically, the vast majority of leak-related investigations have turned up nothing conclusive, and several of the nine that have been prosecuted — six already under the Obama administration, and just three more under all previous presidents — collapsed...

...Many people are surprised to learn that there is no law against disclosing classified information, in and of itself. The classification system was established for the executive branch by presidential order, not by statute, to control access to information and how it must be handled. While officials who break those rules may be admonished or fired, the system covers far more information than it is a crime to leak.

Instead, leak prosecutions rely on a 1917 espionage statute whose principal provision makes it a crime to disclose, to persons not authorized to receive it, national defense information with knowledge that its dissemination could harm the United States or help a foreign power." -- Charlie Savage, New York Times, 9 June 2012.

"Only three times in its first 92 years was the Espionage Act of 1917 used to prosecute government officials for leaking secret information to the press. However, the current administration has already brought six charges under this Act. The accused in all of these cases appear to represent whistleblowers, not those engaged in attempted espionage for foreign governments that 'aid the enemy.'" -- Association for Education in Journalism and Mass Communication

2.0 Possible List

Maybe these are those being discussed:

1. Daniel Ellsberg: Famous for the Pentagon Papers.
2. Anthony Russo: Also involved in disseminating the Pentagon Papers.
3. Samuel Loring Morison: Only person ever convicted, in a trial, for espionage for leaking classified information to the press.
4. John Kiriakou
5. William Binney.
6. J. Kirk Wiebe.
7. Ed Loomis.
8. Thomas Drake.
9. Bradley Manning: Involved with Wikileaks.

Apparently, Scooter Libby was not indicted and tried for espionage. The Espionage Act of 1917 was modified by the McCarran Internal Security Act of 1950, I guess.

3.0 Possible Future Additions

Possibly, Edward Snowden and Retired General James Cartwright (for leaking, maybe, about Stuxnet) will be added sometime to the above list.

(Somewhere in Democracy in America, as I remember it, Alexis de Tocqueville observes that political disputes in the United States almost always become legal disputes.)

Rate of Profits And Value Of Stock Independent Of Workers Saving

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1.0 Introduction

This post presents elements of a model of a smoothly reproducing economy, that is, of an economy growing along at the warranted growth rate. I have previously presented a more detailed exposition of a variant of this model. One could add, say, Harrod-neutral technical change to that exposition. I would find it easier to add biased technical change by assuming fixed, not variable, coefficients of production. Perhaps this model reflects conventions and the balance of class forces prevalent in Anglo-American economies after World War II and before the collapse of the Bretton Woods system.

Anyways, I am revisiting this model because, recently, I have noticed another mathematical property of this model. Not only are the determinants of the rate of profits along a warranted growth path independent of the decisions of the workers to save. So is the average stock price of corporations.

2.0 The Model

This model abstracts from the existence of government spending and taxation. It also treats foreign trade as negligible. National income is comprised of wages, W, and profits, P. The rate of profits, r, is the ratio of profits to the value of capital goods, K, used in producing national income.

2.1 The Corporate Sector

I begin with corporations. The corporations own the capital goods and hire the workers to produce output with these capital goods. Corporate managers decided on the level of investment, I, to achieve a target growth rate, g.

Investment, in this model, is financed by some mixture of retained profits and the issuance of new stock (also known as shares) on the stock market. Corporate managers decide on this mix. Let s_c be the proportion of profits that are retained to finance new investment. And let f be the proportion of investment financed by issuing new shares:

I = s_c P + f I

Some algebra yields:

P/K = [(1 - f)/s_c] (I/K)

Or:

r = [(1 - f)/s_c] g

Thus, the rate of profits consistent with a warranted rate of growth is determined by parameters characterizing decisions made by corporate managers.

2.2 Finances and Households

In this model, households do not own capital goods. Rather, corporations own capital goods, and households own stock in these corporations. The ratio of the market value of stock to the value of the capital goods owned by the corporations is called the valuation ratio, v. The valuation ratio is assumed constant along a warranted growth path. Variations in the valuation ratio reflect short-term speculation. Generally, the valuation ratio is above unity.

Households are divided into two classes in this model, workers and capitalists. Workers receive part of their income in the form of wages. Given a positive savings rate on the part of workers, they also receive dividends and capital gains from their stock. Capitalists do not labor; their households receive all their income from dividends and capital gains. The variable j is used to denote the proportion of stocks owned by the workers.

Dividends consist of profits received and not retained by the corporations. By assumption, the value of dividends is then (1 - s_c)P. Net investment, I, is the increase in the value over a year of the capital goods owned by corporations, while the increase in the value of stocks is vI. But the value of new shares is only fI. The difference, (v - f)I, is the value of capital gains.

The interest rate is the ratio of the returns to financial capital (that is, dividends and capital gains) to the value of stock. With a valuation ratio above unity the interest rate, i, falls below the rate of profits. The valuation ratio then becomes:

v = (r - g)/(i - g)

I assume workers typically save at the rate s_w, and capitalists typically save at the greater rate s_r. Table 1 shows sources of savings, based on these definitions and behavioral assumptions.

Table 1: Sources of Economy-Wide Savings

Source	Amount
Retained Earnings:	sc P
Capitalist Savings Out of Dividends:	(1 - j)sr(1 - sc)P
Minus Capitalist Consumption Out of Capital Gains:	- (1 - j)(1 - sr)(v - f)I
Worker Savings Out of Wages:	swW
Worker Savings Out of Dividends	j sw(1 - sc)P
Minus Worker Consumption Out of Capital Gains:	- j(1 - sw)(v - f)I

In adding up savings, one must be sure not to double-count retained earnings. Corporations decide to save retained earnings, but households can undo this decision by consuming capital gains. Total savings for capitalists, S_r, are:

S_r = (1 - j) s_r[(1 - s_c)P + (v - f)I]

Total savings for workers, S_w, are:

S_w = s_wW + j s_w[(1 - s_c)P + (v - f)I]

Along a warranted growth path, investment is always equal to savings. The following equation is based on the components in Table 1:

I = s_c P + (1 - j)[s_r(1 - s_c)P - (1 - s_r)(v - f)I]

+ s_wW + j [s_w(1 - s_c)P - (1 - s_w)(v - f)I]

A bit of algebra allows the investment-savings equality to be restated:

I = s_c P + S_r + S_w - (v - f)I

The last term (that is, capital gains) is subtracted to avoid double-counting.

Another condition of a warranted growth path in this model is that the corporate sector, capitalist households, and workers continue to endure. This condition requires that the rate of growth of the book-value of the capital goods held by the corporations, the rate of growth of the value of the stock held by capitalists, and the rate of growth of the value of the stock held by the workers all be equal. Thus, the rate of growth of the value of the stock held by capitalists is:

g = S_r/[(1 - j)v K]

The rate of growth of the value of the stock held by workers is:

g = S_w/(j v K)

This completes the exposition of the equations I need for my point here.

2.3 Some Algebra

I now report on some algebraic manipulations of these equations. The condition that the value of the stock held by capitalists and workers grows at the same rate yields the following condition:

S_w = S_r [j/(1 - j)]

Substituting in the investment-savings equality, one can obtain:

I = s_c P + [S_r/(1 - j)] - (v - f)I

Or, by expanding the definition of capitalist savings:

I = s_c P + s_r[(1 - s_c)P + (v - f)I] - (v - f)I

Regrouping yields:

[1 + (1 - s_r)(v - f)]I = [s_c + s_r(1 - s_c)]P

Dividing through by the book value of the capital goods owned by the corporations, one obtains:

r = {[1 + (1 - s_r)(v - f)]/[s_c + s_r(1 - s_c)]} g

Equating for the value of the rate of profits previously found, one obtains an expression for the valuation ratio in terms of model parameters:

v = {[s_r(1 - s_c)]/[s_c(1 - s_r)]} - {s_r/[s_c(1 - s_r)]} f

Notice the parameters on the right-hand-side characterize either corporate decisions or the decisions of capitalist households. The saving propensities of the workers do not enter into it. The more that corporations finance investment by issuing shares, instead of using retained earnings, the lower the valuation ratio is along a warranted growth path. If the proportion of profits distributed in dividends lies below the proportion of investment financed by issuing new stock, a smaller capitalist savings propensity is associated with a higher valuation ratio. In some sense, capitalists get what they spend.

3.0 Conclusions

This post has outlined some necessary properties of a warranted growth path in a model containing:

• Corporations, a capitalist class, and a class of workers.
• A stock market, in which ownership shares in the corporations are bought and sold.
• A growth rate determined by decisions of the corporate managers.

In this model, the decisions of the corporate manager as to the growth rate, retained earnings, and finance obtained by issues of new stock determine the rate of profits consistent with a warranted growth path. These decisions of the corporate managers, along with the savings propensities of the capitalists, determine the ratio of the price of stock to the book value of the capital goods owned by the corporations. A fortiori, these decisions also determine the interest rate. Within the limits where a warranted growth path exists, the savings propensities of the workers have no effect on the growth rate, the rate of profits, the price of stock, the interest rate, or the functional distribution of income. The savings decisions of the workers do affect, however, the personal distribution of income and the proportion of stock owned by the workers.

Appendix: Variable Definitions

• K is the book value of the capital goods, in numeraire units, owned by the corporations.
• I is investment, in numeraire units.
• P is corporate profits, in numeraire units.
• S_r is capitalist savings, in numeraire units.
• S_w is worker savings, in numeraire units.
• f is the proportion of investment financed by issuing new stock (also known as shares).
• g is the warranted rate of growth.
• i is the interest rate.
• j is the proportion of stock owned by workers.
• r is the rate of profits earned by the corporations on the book value of their capital stock.
• s_c is the proportion of profits retained by corporations.
• s_r is the (average and marginal) to save of the capitalists.
• s_w is the (average and marginal) to save of the workers.
• v is the valuation ratio, that is, the ratio of the value of the stocks of the corporations to their book value.

Reference

• Scott J. Moss (Dec. 1978). The Post-Keynesian Theory of Income Distribution in the Corporate Economy, Australian Economic Papers, V. 17, N. 31: pp. 302-322.

Against Biotechnological Determinism

1.0 Introduction

Perhaps arguments lasting between groups for decades have some underlying issues that are not immediately apparent by looking at the details. I often attempt to explain technical details of the Cambridge Capital Controversy (CCC). Is there something central, but hardly articulated by the participants and on-lookers, that helps in understanding the positions taken by economists on the CCC? I take the concept and the phrase biotechnological determinism from Stephen Marglin (1984).

2.0 Neoclassical Economics As Embodying Biotechnological Determinism

A naive neoclassical economics embodies biotechnological determinism. The biology is to be seen in population demographics and in preferences, including over intertemporal consumption plans and over choices between labor and leisure. The technology is to be seen in production functions and endowments.

From about 1870 up to the 1930, neoclassical economists emphasized incoherent models of long-run equilibrium. To maintain biotechnological determinism after the transition to very short-run models of temporary and intertemporal equilibrium, neoclassical economists must adopt a theory of the short-run. The most congenial short run models to this determinism will assume all markets always clear.

3.0 Post Keynesianism Rejects Biotechnological Determinism

Post Keynesians, as I see it, reject biotechnological determinism. Here are some characteristic ideas of Post Keynesianism that, at least, are in tension with such determinism:

• An emphasis on open models.
• A view that appropriate models might vary among countries, sectors, and decades.
• An emphasis on historical time and the acceptance or development of models in which history matters.
• The adoption of models in which corporations are taken as having power to make decisions on the rate of growth and the markup of prices over costs.
• The rejection of the descriptive accuracy of the autonomous utility-maximizing consumers.
• The rejection of the natural rate of unemployment.
• The rejection of the Wicksellian concept of the natural rate of interest, in all runs.
• The acceptance of the idea that fiscal policy can be effective.

4.0 Can Mainstream Economists Reject Biotechnological Determinism?

Of course, markets do not always clear in neoclassical economics. For decades, economists have been talking about, for example, sticky prices, asymmetric information, and multiple equilibrium. Nevertheless, I am often surprised by how willing many economists who have studied such matters seem to be willing to talk as if the economy is always trending towards a unique, given long-run equilibrium. Forces that prevent the economy reaching equilibrium in the short run seem to have no effect on the long run theory. Maybe a tension exists in neoclassical economics between the formal properties of the theories that have been developed and the underlying vision of many economists.

Some argue that mainstream economics is no longer neoclassical and, at least at the research level is open to a wide variety of ideas. Some recent ideas, such as evolutionary game theory, seem compatible with outcomes emerging that cannot be calculated in a closed-form solution as uniquely determined by the givens of the model.

I think older trends, emphasizing perfect competition and instantaneous adjustment to equilibrium, are still widely prevalent among economists and how economists portray their ideas to the public. A skeptic might argue that newer trends will never replace such ideas because of their incompatibility with this underlying vision of biotechnological determinism.

5.0 Conclusion

Do different views on biotechnological determinism underlie the visions of various economists? Can contrasting views on this issue ever be settled by empirical evidence, and if so, how?

Bibliography

• Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press.

Sraffa Prices As A Linear System

Figure 1: Two Equivalent Block Diagrams for a Linear System

1.0 Introduction

I have previously gone on about complex, out-of-equilibrium phenomena arising in certain non-linear models for economics. This post provides a contrast, by defining linear. Sraffa's system of equations for prices of production, from a certain perspective¹, is an example of a linear system.

I regard the mathematical manipulations expressed in this post as fairly trivial. Nevertheless, it will not surprise me if some find it difficult to read. I do not think any such reading difficulties result solely from defects in my expository powers. Rather, I am trying to echo the sort of abstract reasoning typical of advanced mathematics courses taught at many universities. I think I only gesture here at the advantages provided by such abstractions.

2.0 Definition of "Linear"

Functions can be characterized as linear or non-linear. A function, f(), maps elements in some set to elements in another, possibly different, set. The set of possible arguments² for a function is known as the domain of the function. The set that elements of the domain are mapped into is known as the range of the function. One assumes that elements of the domain can be added together, in some sense, to obtain another element of the same set. Furthermore, each element of the domain can be multiplied by a scalar³. Last, one makes the same assumptions about the elements of the range.

The function f is linear if the following two conditions are met:

f(x₁ + x₂) = f(x₁) + f(x₂)

f(a x) = a f(x)

These equations are illustrated, respectively, by Figure 1 above and Figure 2 below. The first condition states that when a linear function is applied to the sum of two elements, the summation can equally well be calculated after applying the function to the elements being summed. The second condition states that the order of scalar multiplication and the application of the function can likewise be interchanged, with no effect on the output.

Figure 2: Two More Equivalent Block Diagrams for a Linear System

Maybe the simplest example of a linear system is the equation of a straight line going through the origin:

y = f(x) = m x,

where x and y are real numbers⁴.

3.0 Sraffa's Price Equations

The above definition would not be worth much if the only example of a linear function was a straight line through the origin in a two-dimensional Cartesian space. Accordingly, I will describe an example for a function whose argument is a vector.

Suppose an economy is observed at a point in time. And, in this economy, at the observed scale, firms have adopted n processes to produce n commodities. The j-th process is characterized by its inputs and outputs. Its inputs consist of a_0,j person-years of labor, a_1,j units of the first commodity, a_2,j units of the second commodity, and so on. Its outputs consist of b_1,j units of the first commodity, b_2,j units of the second commodity, and so on⁵. A common rate of profits, r, is also among the givens in this model. These givens allow one to set up the following system of equations for the wage, w, and prices of production⁶, p₁, p₂, ..., p_n:

(p₁ a_1,1 + ... + p_n a_n,1)(1 + r) + a_0,1 w = p₁ b_1,1 + ... + p_n b_n,1

(p₁ a_1,2 + ... + p_n a_n,2)(1 + r) + a_0,2 w = p₁ b_1,2 + ... + p_n b_n,2

.
.
.

(p₁ a_1,n + ... + p_n a_n,n)(1 + r) + a_0,n w = p₁ b_1,n + ... + p_n b_n,n

The above system of n equations in n + 1 unknowns can be conveniently expressed in matrix form:

p A(1 + r) + a₀w = p B,

where a₀ and p are row vectors and A and B are square vectors. Some manipulations yields the following matrix equation:

p [B - A(1 + r)] - a₀w = 0

These manipulations suggest the definition of a linear function.

3.1 A Linear Function

Accordingly, consider the following function:

f(p, w) = p [B - A(1 + r)] - a₀w

This function maps a vector space with the dimension n + 1 to an n-dimensional vector space. Figure 3 illustrates for the case where n is two. The components of the vector calculated by this function are the extra profits earned in each process in use. Two, almost one-line, proofs demonstrate the linearity of this function.

Figure 3: A Linear Function for a Two-Commodity Economy

3.1.1. Proof of the First Condition

By definition, the value of the function for the sum of two elements of its domain is:

f(p + q, u + v) = (p + q) [B - A(1 + r)] - a₀(u + v)

Or:

f(p + q, u + v) = p [B - A(1 + r)] - a₀u + q [B - A(1 + r)] - a₀v

Or, by the definition of the function:

f(p + q, u + v) = f(p, u) + f(q, v),

which was to be shown.

3.1.2. Proof of the Second Condition

By definition, the value of the function for an argument consisting of the product of a scalar and an element of the domain of the function is:

f(c p, c w) = (c p) [B - A(1 + r)] - a₀(c w)

Or:

f(c p, c w) = c { p [B - A(1 + r)] - a₀w}

Or, by definition,

f(c p, c w) = c f(p, w)

which, again, was to be shown.

3.2 Observations and Questions

Consider all the elements of the domain of a function that map into the zero element in the range. This subspace of the domain is called the null space⁷. Figure 4 illustrates a null space for a linear function that, generically, does not arise for the Sraffa model. The three dimensions in the figure represent the domain of the function. For a linear model, the origin is in the null space. In this case, two non-zero independent vectors, represented by the two heavy arrows not along any of the three axes, map to zero. So the plane in which these two vectors lie represents the subset of the domain which maps to zero.

Figure 4: The Subspace of Zeros of a Linear Function

Wages and prices of commodities are positive in an economically meaningful solution to Sraffa's model. Thus, the null space should contain a ray leading from the origin through the first quadrant. Furthermore, if the extension of such a ray is all of the null space, the solution of this model is unique, up to multiplication by a constant. Choosing a numeraire for measuring prices and the wage specifies a location on this ray.

The economic setting of this model suggests conditions⁸ that might lead to the desired properties of the null space:

• No coefficients of production are negative, while direct labor inputs are always positive.
• Every process requires some commodities as inputs, and produces at least some commodities.
• Every commodity is produced as an output by at least some process.
• The economy hangs together, in some sense. One cannot find two or more sets of commodities where, for instance, no commodities from the first set enter as inputs into the second set and vice versa.
• The production processes are all distinct, in some sense. Technically, no production process is a linear combination of the other processes.
• The economy produces a surplus. The quantities of commodities required as inputs can be replaced out of the outputs, with some commodity output left over.
• With a notional rescaling of processes, a set of commodities can be found that, in some sense, enter into the production of all commodities and that are being produced at a same rate of surplus production.
• The rate of profits does not exceed that maximum rate of surplus production.

More is going on here than a counting of equations and variables.

4.0 Conclusion

Sraffa, in his book, does not present his sequence of models in these abstract terms. But many comments and sections, such as the appendix on "beans", demonstrate that he was aware of the mathematical issues arising with his models. One can read Sraffa as having an interest in computability not shown in my exposition.

Finally, this post proves that the use of models in which the solution illustrates the mutual interdependence of a system of equations is simply insufficient to demonstrate that economists think of the economy as a complex, non-linear system.

Footnotes

1. If one took the wage, instead of the rate of profits, as the independent variable, Sraffa's equations would define a non-linear system. Furthermore, since Sraffa's model is open, it is consistent with non-linearities in economic relationships not in the model, such as provided by Increasing Returns to Scale.
2. In this section, arbitrary elements of the domain are represented by x, x₁, and x₂.
3. Technically, the domain and the range are each examples of a vector space, also known as a linear space. The scalars are from a field. The sets of real and complex numbers are canonical examples of a field.
4. Although the graph of an affine function, y = m x + b, is a straight line, an affine function is, technically, non-linear when the y-intercept is non-zero.
5. Since more than one commodity can be produced as output for each process, this is a model of joint production. See Chapter VII, Sections 50-52 of Production of Commodities By Means of Commodities.
6. Prices of production allow for the outputs to be redistributed among industries such that the economy can continue (re)production undisturbed.
7. For a linear function, the null space is a linear space.
8. Such conditions are more obvious for the special case of no single-product industries. I do not fully understand the issues for joint production, especially when the processes in use are chosen from a larger set of possible processes.

Warren Mosler On Front Business Page Of New York Times

Anne Lowrey provides a profile of Warren Mosler and Modern Monetary Theory. I am sitting in my favorite coffee shop, when I open my newspaper to this article. I say, "Hey, I know this guy. I once sold him a book on-line." But I did not go on about economics. I know the fellow next to me is a fan of Formula 1 racing. So I say, "He has his own car company. He makes race cars, I think." And I skim forward to the third to last paragraph, skipping over quotes from professors at the University of Missouri at Kansas City and such like, to read about Mosler Automotive, which apparently he is looking to sell.

Elsewhere

• Frances Woolley claims that, nowadays, economics is more empirically grounded and better than it used to be.
• Edward Fullbrook says that academic success in economics is furthered by publishing papers that serve best as manure and hindered by publishing serious work.
• Noah Smith describes what he calls four levels of science.

(It would be nice to have a catalog of responses to Greg Mankiw's latest vicious tomfoolery, to be published in the Journal of Economic Perspectives.)