**Summary:**

Can I adapt Roemer's work, suitably taking into account later work by D'Agata and Zambelli, to found this approach to markup pricing? As a start, I here quote Roemer on a reproducible solution (RS), before he takes into account unequal rates of profits and a choice of technique. Given the role of endowments, is this a neoclassical approach, like Hahn's 1984 CJE paper? Even so, is it a valid justification for Sraffa's price equations? Notice there are no subscripts for time below. "There are N capitalists; the νth one is endowed with a vector of produced commodity endowments ων ... Capitalist ν starts with capital ων, which he seeks to turn in more wealth at the highest rate of return. Thus the program of capitalist ν is Facing prices p, to choose xν ≥ 0 to max (p - (p A + L)) xν

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Can I adapt Roemer's work, suitably taking into account later work by D'Agata and Zambelli, to found this approach to markup pricing? As a start, I here quote Roemer on a reproducible solution (RS), before he takes into account unequal rates of profits and a choice of technique. Given the role of endowments, is this a neoclassical approach, like Hahn's 1984 CJE paper? Even so, is it a valid justification for Sraffa's price equations? Notice there are no subscripts for time below.

"There areNcapitalists; the νth one is endowed with a vector of produced commodity endowmentsω^{ν}... Capitalist ν starts with capitalω^{ν}, which he seeks to turn in more wealth at the highest rate of return. Thus the program of capitalist ν isFacing pricesp, tochoosex^{ν}≥0tomax (p- (pA+L))x^{ν}s.t. ((The constraint says that the inputs costs can be covered by current capital.) Let us callpA+L)x^{ν}≤pω^{ν}A^{ν}(p) the set of solution vectors to this program." -- Roemer (1981: 18-19, I made changes for typesetting mathematics).

Roemer defines a RS:

"Definition 1.1: A price vectorpis a reproducible solution for the economy {A,L;b;ω^{1}, ...,ω^{N}} if:We shall also refer to the entire set {

- For all ν, there exists
x^{ν}inA^{ν}(p), such that (profit maximization)x= Σx^{ν}andx≥Ax+ (Lx)b(reproducibility)pb= 1 (subsistence wage)Ax+ (Lx) ≤ω= Σω^{ν}(feasibility)p,x^{1}, ...,x^{N}} as a reproducible solution." -- Roemer (1981: 19-20, with for math).

A RS can only exist if the elements of the endowment vector are in certain proportions:

"Theorem 1.2: Let the model {A,L,b} be given withAproductive and indecomposable, and the rate of exploitatione> 0. Let {p,x^{1}, ...,x^{N}} be a nontrivial RS. (i.e., Σx^{ν}=x≠0). Then the vector of pricespis the E[qual] P[rofit] R[ate] vectorp. Furthermore, a RS exists if and only if^{*}omegais an element ofC, where^{*}Cis a particular convex cone in [the space of^{*}n-dimensional real vectors] containing the balanced growth path of {A,L,b}. (Cis specified precisely below.)" -- Roemer (1981: 20, with changes for math).^{*}

Even though endoments are taken as given in defining the firm's LP, endowments are endogenous in the sense that they must lie close to those on a balanced growth path. I like to have labor advanced and wages paid out of the surplus, instead of vice versa as above. The above does not allow for a choice of technique. Roemer has at least some of this in later chapters.

**References**

- John E. Roemer. 1981.
*Analytical Foundations of Marxian Economic Theory.*Cambridge University Press.