Phillip J. Bryson David S. Lincoln Fellow Lincoln Institute for Land Policy

1. Henry George’s Theory of Distribution Phillip J. Bryson David S. Lincoln Fellow Lincoln Institute for Land Policy

2. Rent Line and Margin of Cultivation • Wealth produced in every community is divided into two parts by what may be called the rent line, which is fixed by the margin of cultivation, or the return which labor and capital could obtain from such natural opportunities as are free to them without the payment of rent. From the part of the produce below this line wages and interest must be paid. All that is above goes to the owners of land. Progress and Poverty, p. 163.

3. The Rent Line National Product Rent Rent Line Wages and Interest The Margin of Cultivation

4. Capital and Labor • Capital is “all wealth used to produce more wealth. Its return in distribution is called interest. • Labor is all human exertion. Its return in distribution is called wages.

5. Wages and Interest Combined • George provided extensive rationale for the determination of wages and the determination of interest, returns to labor and capital. • Analytically, he pooled them together as a single share or proportion in national distribution, the other share being rent. • The mechanism that kept their proportion roughly constant functioned as follows.

6. Interest and wages rise and fall together • “…interest and wages must rise and fall together, • …interest cannot be increased without increasing wages; nor wages lowered without depressing interest.” Progress and Poverty, 186

7. Interest and wages rise and fall together • For if wages fall, interest must also fall in proportion, else it becomes more profitable to turn labor into capital than to apply it directly; while, if interest falls, wages must likewise proportionately fall, or else the increment of capital would be checked. (186)

8. Interest and wages rise and fall together • If wages fell and interest didn’t fall in proportion, relatively cheap labor would be used to produce capital with its higher return. (Turn cheap labor into high-return capital rather than to apply labor directly.) while, if interest falls, wages must likewise proportionately fall, or else the increment of capital would be checked. (186)

9. Interest and wages rise and fall together • Conversely, if interest falls proportionate to wages, and wages don’t follow, capital is now offering lower returns. So investments would slow ( “the increment of capital would be checked,” p.186).

10. Wages and Interest Combined • Any tendency on the part of interest to rise above the equilibrium with wages must immediately beget not only a tendency to direct labor to the production of capital but also the application of wealth to the uses of capital; Progress and Poverty, p. 187

11. Wages and Interest Combined • …while any tendency of wages to rise above the equilibrium with interest must in like manner beget not only a tendency to turn labor from the production of capital, but also to lesser the proportion of capital by diverting from a productive to a nonproductive use some of the articles of wealth of which capital is composed. Progress and Poverty, p. 187

12. The Georgian Model rent The Margin of Cultivation w + i As the margin of cultivation declines, i.e., as wages and interest decline, rent increases.

13. Speculation pushes the Margin of Cultivation Line to the Left “…the speculative advance in land values tends to press the margin of cultivation, or production, beyond its normal limit, thus compelling labor and capital to accept of a smaller return, or (and this is the only way they can resist the tendency) to cease production.” Progress and Poverty, 238, 239

14. The Georgian Model rent The Margin of Cultivation w + i Speculation pushes the margin of cultivation line to the left, so wages and interest decline and rent increases beyond what would normally hold.

15. Progress, by George! • In George’s view, progress results in both increasing population and land use. There is a functional relationship between pop/land use expansion and the growth of rent, the return to the factor land. That can be shown in our simple model as follows.

16. Progress, by George! • In George’s view, progress results in both increasing population and land use. There is a functional relationship between pop/land use expansion and the growth of rent, the return to the factor land. That can be shown in our simple model as follows.

17. The Georgian Model rent Progress So as progress occurs, rent rises while wages and interest fall. w + i Pop/Land use As the population grows and Land use increases, rent increases as well. (Rent = f(Population, land use)

18. Social forces automatically push society up the pop/land use curve, although more capital intensive production, promoting greater output through the adoption of new techniques, saves labor. • Pop/land use = f(increased population, but also to the adoption of labor-saving improvements).

19. Capital and Technology rent w + i P/L The growth of capital-intensive production can be visualized through a capital curve which is a function of growth and development along with increasing population and land use. Investment Capital

20. Labor-saving capital investmentsand Improvements in Technique • The effect of inventions and improvements in the productive arts is to save labor—that is, to enable the same result to be secured with less labor, or a greater result with the same labor. Progress and Poverty, p. 223

21. Capital and Technology rent w + i P/L When development and technical change encourage more capital- intensive production, managers will automatically move in that direction Greater labor-saving investments can be seen as shifting the investment curve downward Capital

22. Capital and Technology rent w + i P/L Movement along the progress Line or left along P/L, is a function of increasing population, but also of the adoption of labor- saving improvements. More capital working with labor causes the returns to all factors to increase, i.e., it causes the factor returns curve to shift out. Capital

23. Let’s go back now to an earlier slide where a part of a passage from George was quoted.

24. Labor-saving capital investmentsand Improvements in Technique • The effect of inventions and improvements in the productive arts is to save labor—that is, to enable the same result to be secured with less labor, or a greater result with the same labor. This continues… And thus, while the primary effect of labor-saving improvements is to increase the power of labor, the secondary effect is to extend cultivation, and, where this lowers the margin of cultivation, to increase rent.

25. Capital and Technology rent w + i P/L All of this progress requires increasing land use, but now the workers are better off and adopt a life-style that uses more land. Movement along the progress Line or left along P/L, is a function of increasing population, but also of the adoption of labor- saving improvements. Capital

26. Capital and Technology rent w + i P/L So in the long run, the margin of cultivation declines, being pulled back to the left. Wages and interest are not improved, but rent increases. In the long run, increasing land use by successful workers who seem to become landowners implies subsequent movement up the progress curve. Capital

27. Rent Rises Wages Fall(Progress) (Poverty) • But labor cannot reap the benefits which advancing civilization thus brings, because they are intercepted. Land being necessary to labor, and being reduced to private ownership, every increase in the productive power of labor but increases rent—the price that labor must pay for the opportunity to utilize its powers; and thus all the advantages gained by the march of progress go to the owners of land, and wages do not increase. Progress and Poverty, p. 255

28. The Marshallian Analysis of Factor Shares

29. Marshall did not see the shares of national income accruing to the factors of production as determined simply by macro processes. • In classical economics, factor shares generally appear to interact as though at an aggregate level, to determine the distribution of the national income.

30. In the simple model presented above, this classical simplification was seen as the bundling of wages and interest. • The two factors were not a function of the individual land and capital markets which actually determine prices and quantities. • Rather, they were simply a function of the aggregate of land rent.

31. In contemporary economics each factor’s share in national income is the aggregate of what happens in individual factor markets. • For George, labor’s wages and capital’s interest were simply a residual. Labor and capital collected what was left over after the landlords collected their rent. • For Marshall it was all a question about the individual factor markets underlying factor returns.

32. The Marshallian Analysis • For factors generally (not merely for land) any earnings in excess of a factor’s transfer price (opportunity cost) constitute rent. • If the supply of a productive resource is strictly limited and it can be used for only one productive use, transfer earnings would be zero and the entire return would count as rent.

33. The Marshallian Analysis • Since no agent is incapable of being reproduced or of being adapted to other productive tasks, we must look at the time frame in which such flexibility is to be achieved. Fixed capital earns quasi-rents rather than interest in the short run. In that period the supply of machines cannot be augmented.

34. The Marshallian Analysis • In the long run new machines can be employed and old machines modified to perform new tasks, so “quasi-rents are always in the process of being eroded. • Thus, other factors of production earn quasi-rents on the same basis that land earns rent.

35. Contemporary economics no longer recognizes any need for special treatment of the factor land or for a theory of ground rent. • On this basis, Marshall’s objection to the ‘single tax’ becomes sensible. It is that all productive factors, not simply land, earn short-term ‘rents.’

36. Neoclassical Theory of Factor Pricing • In making the decision to hire additional units of any productive factor, the firm maximizes the return associated with those additional units. The firm will equate the marginal revenue product (MRP) of factor A to the product of that factor’s marginal productivity and the marginal revenue derived from the sale of that output. In other words, • MRPa = MPa x MRx in imperfect competition.

37. Neoclassical Theory of Factor Pricing • In perfect competition, this accrual of additional revenues from the hiring additional units of the productive factor is referred to as the Value of the Marginal Product, defined as VMPa = MPa x Px in pure competition.

38. Neoclassical Theory of Factor Pricing • According to Marshall, “the medium through which the principle of substitution so adjusts the employment of each agent that, in its marginal application, its cost is proportionate to the additional net product resulting from its use.” • The modern analysis can be derived directly from Marshall’s writings.

39. Marshallian Factor Pricing, Note XIV • Let α1, α2, α3, . .. αnrepresent different kinds of labor to be used in constructing a home. β, β,’β”, etc., represent different kinds of rooms for the home. • V will represent total outlays for productive factors,so V, β, β’,β”, etc., are all functions of α1, α2, α3.

40. Marshallian Factor Pricing, Note XIV • H, the housing utility or benefit anticipated from the rooms to be constructed, is a function of β, β’,β”, etc., and also of α1, α2, α3. • For simplicity, let H = total receipts from the sales of products A will help produce.Marshall seeks to find the marginal investments of each kind of labor for each kind of use with the following expressions. dV = dHdβ= dHdβ’ = dHdβ”= … dα1 dβ dα1 dβ’ dα1 dβ” dα1 dV = dHdβ= dHdβ’ = dHdβ”= … dα2 dβ dα2 dβ’ dα2 dβ” dα2

41. Marshallian Factor Pricing, Note XIV • These equations represent a balance of effort and benefit. The real cost to the producer of some small additional amount of labor employed to cut and process timber will be neatly balanced by the benefit accruing to their completed labors. If the principal here decides to pay a carpenter instead of doing the work himself, V will represent not his personal total effort, but his expenditures for the labor employed.

42. Marshallian Factor Pricing, Note XIV • The rate of pay carpenters will receive for their additional effort (the marginal demand price for their labor), is dV/da. • dH/dβ, dH/dβ’ are the monetary value to him of the marginal utilities of extra rooms constructed, (his marginal demand prices for them). • dβ/da and dβ’/da are the marginal efficiencies of carpenters’ labor in this project.

43. Marshallian Factor Pricing, Note XIV • According to the equations, the demand price for carpenters’ labor tends to be equal to the demand price for extra rooms in the home, being multiplied for each room by the marginal efficiency of the carpenters’ work in providing that extra accommodation.

44. Marshallian Factor Pricing, Note XIV • Generalizing this, the marginal demand price for hired labor is the marginal efficiency of the labor times the marginal demand price for the product. • In other words, wages here tend to be equal to the value of the output produced, i.e., the marginal efficiency of a unit of the labor times the value of the additional product generated.

45. Marshallian Factor Pricing, Note XIV • Marshall referred to this as the “net product” of the labor employed. Marshall declares this proposition to be very important, containing “within itself the kernel of the demand side of the theory of distribution.”

46. Marshallian Factor Pricing, Note XIV In more current notation, Marshall’s β, β1, …βn = X, X1, …Xn, α = f, f1,… fn for factor inputs. Let V = C (cost), H = R (revenues, receipts or benefits). TC, and X1, …Xn, are functions of f, f1,… fn. H = g(X1, X2,X3) and H = g(f1, f2 , f3). The equality of marginal returns and costs associated with each input type is expressed thus: (1) MC/df1 = dC/df1 = dR/dX1 ∙ dX1/df1 = MRx2/df2 = MRx3/df3

47. Marshallian Factor Pricing, Note XIV • This expression is a balance of effort (input cost) and benefit (productivity of an additional unit of an input). • We would express this today in a form which Marshall would have understood immediately. • For the competitive case, the value of the marginal product of input a will tend to equal the wage of input a, or more generally, the value of the marginal product of any input, will be equal to the price (cost) of that input.

48. As we saw above, the value of the marginal product of input a, VMPa, is the price of the commodity x times the marginal product of input a, MPa. • The firm’s optimization is achieved by setting VMPa = wa. Rewriting, px= wa/ MPa, or 1/px = MPa/pa or MPa/wa.