Romer’s Assumptions; Their Context and Their Implications

Romer’s strategy was to formulate a process of economic growth in which a) the growth of economically-useful knowledge is endogenous, and b) there is an equilibrium which consists of a balanced, constant, exponential growth among key aggregate outputs in the very long run.  Useful knowledge A, total output Y, total capital K, and total consumption C would all grow at the same constant exponential rate.

Note in the next excerpt that his analysis is in terms of households and firms using a store of knowledge and a panoply of specialized producer durables, rather than in terms of interdependent functionings defining and conditioning one another.  Romer asserts how firms and households would behave in the constitution of a very-long-run equilibrium:

An equilibrium for this model will be paths for prices and quantities such that i) consumers make savings and consumption decisions taking interest rates as given; ii) holders of human capital decide whether to work in the research sector or the manufacturing sector taking as given the stock of total knowledge A, the price of designs PA, and the wage rate in the manufacturing sector wA; iii) final goods producers choose labor, human capital, and a list of differentiated durables taking prices as given; iv) each firm that owns a design and manufactures a producer durable maximizes profit taking as given the interest rate and the downward sloping demand curve it faces, and setting prices to maximize profits; v) firms contemplating entry into the business of producing a durable take prices for designs as given; and vi) the supply of each good is equal to the demand. [Romer 1990, S88]

And he outlines his strategy to formalize an equilibrium.

The strategy for characterizing the model that is followed here is to solve for an equilibrium in which the variables A, K, and grow at constant exponential rates.  This is generally referred to as a balanced growth equilibrium.  The intuition from the Solow model suggests that such an equilibrium will exist if grows at a constant exponential rate.  The intuition from the Uzawa model suggests that it is possible for to grow at an exponential rate  because equation (3) for Å is linear in A. It will grow at a constant rate if the amount of human capital Hthat is devoted to research stays constant.  Verifying that a balanced growth equilibrium exists therefore reduces to the problem of showing that prices and wages are such that Hand Hremain constant as Y, K, C, and grow.  [Romer, 1990, S90]

Interpretation of Romer’s Strategy:

“Prices” implies flows of money expended for purchases; and “wages” implies flows of outlays which become incomes to workers.  Therefore, Romer is postulating that flows in and between two interdependent sectors, 1) R&D and 2) production of producer durables, are such that the allocation of a fixed amount of human capital to the two sectors does not change over time; i.e. HA and HY are each constant.

For simplicity and pedagogy Romer will be assuming linearity of Hand when the other is fixed.  Since the evolution of AÅ = δHAA, with δ being a productivity parameter,  this productivity parameter δ carries a heavy burden, along with the parameters η and x-bar in achieving “constant exponential growth.”

For our placement of Romer’s firms in Lonergan’s framework of velocitous functionings, the R&D activities of firms and the manufacturing and service activities of firms must be interpreted as functional-flow activities, which, explicitly or not, they are.  Though Romer is less explicit than Lonergan regarding functioning, both deal in interdependent functional flows.

As Romer stated, his mathematicized equilibrium is dependent upon constant allocations of human capital and upon equal wages for human capital in both sectors: R&D and production of durables.

We must keep in mind as we compare and contrast Romer’s and Lonergan’s work that, in the real economy, a) a unit of enterprise may function simultaneously in more than one sector-circuit; corner-store managers selling products at retail (basic) have insights which are properly classified as functional R&D; and while a recipient of wage, salary, or fee, etc. may earn his/her living as a street vendor of retail (basic) items, he/she may be channeling part of this income into investing, and outlaying in a unit of enterprise doing biochemical research or making producer durables.  So, the analysis of the real economic world must be a functional analysis.  Recipients of higher or lower wages and salaries may be employed on any level; people having the same wage or salary will save at different rates and spend in different circuits.  Per Lonergan’s Diagram of Rates of Functional Flows, and for explanation at an adequate level of abstraction, we must think in terms of interdependent functionings, not in terms of rigidly interacting households and firms.

Romer made several strategic assumptions in order to demonstrate the possibility of endogenous growth at constant exponential rates.  His assumptions are his conceptual premises.  His “proof” is the logical expansion of these assumptions or conceptual premises.  Again, we quote his strategy:

The strategy for characterizing the model that is followed here is to solve for an equilibrium in which variables A, K, and Y grow at constant exponential rates. [Romer, 1990, S90]

Before listing the assumptions Romer made to bring him to his conclusions, let us preliminarily show again other lists in his analysis:

1. Three premises: (S72)

    1. Technological change lies at the heart of economic growth
    2. Technological change arises in large part in response to market incentives
    3. Instructions for working with raw materials are inherently different from other economic goods

2. Four fundamental inputs:  (S78, S89) Romer’s four fundamental inputs of his production function, applied at velocities, and therefore understood by us as velocitous functionings, are

    1. general capital, K = ηA(x-bar), may consist of a) specialized physical capital, b) a store of products supporting the manufacture of producer durables e.g. consumables such as carrots stored to feed the people producing durables, c) money set aside. Thus “general” means catch-all general.
    2. H, human capital– a measure of the cumulative effect of education and on-the-job training (The holders of human capital are a headcount, but the quantity of human capital held by this headcount is taken as a measured “cumulative effect.”)
    3. L, labor– consists of bodily coordination and eye-hand skills, quantified as a headcount
    4. A, an index of the level of technology – consists of the count of “designs”

 3. Four explanatory conjugates: implicitly defined by their functional relations to one another, and representing the velocities in his production function:

    1. HA, the velocitous functional application of compensated human capital (i.e. intelligence capable of insight) to the store of knowledge for the purpose of invention and design in R&D on level 1; the “design” is for a producer durable to be subsequently manufactured on level 2 (Note: the invention of a design is the production of a product having economic value.  Thus we give it a circuit of outlays and incomes.)
    2. HY, the velocitous functional application of compensated human capital on levels 2 and 3; because existing producer durables are assumed to represent cumulative forgone output, total capital being used on levels 2 and 3 equals ηΣ1xl = ηΣ1Axi (S82); therefore by Romer’s assumption and definition, equals cumulative forgone output.  Also, we note that per (7) (S89), total capital being used may be formulated in terms of total designs, A, times x-bar, which is assumed to be the “level of use” of all producer durables. (S88)
    3. L, Labor, the velocitous functional application of compensated human skills on levels 2 and 3
    4. x(i), the velocitous use of existing producer durables (index i) in quantities(x) on levels 2 and 3

4. Three “sectors” of the Diagram:  (S79) Romer names three sectors in the hierarchical system, each with its allocation of the inputs listed above.  We have represented each of these sectors as distinct circuits of outlays and incomes.  However, Romer does not analytically distinguish and classify the temporalities and elemental functional correspondences of these sectors to one another.  In particular, he groups – while we keep separate – sectors 2 and 3 into a single circuit (S81) (S82) because they have “the same functional form”; he does not consider temporality and elemental, functional, point-to-X correspondences. (N16) The final goods producers are assumed to operate in perfect competition and not be able to set prices.

      1. Research and development producing “designs” (an idealized concept)– Inputs: human capital, HA, and the stock of economically-useful knowledge, A.
      2. Production of producer durablesInputs: human capital, HYlabor, L; existing producer durables, x(i). (Romer’s formulation does not explicitly include the specific design as an input. See his “black box” description (S81). “Once it owns the design, the firm can convert η units of final output into one durable unit of good i.”

(S81)  “The correct interpretation of this formal description is that the foregone consumption is never manufactured. … The resources that would have been used to produce the forgone output are used instead to manufacture capital goods.  It is possible to exchange a constant number of consumption goods for each unit of capital goods if the production function used to manufacture capital goods has exactly the same functional form as the production function used to manufacture consumption goods.” (S81)

      1. Production of final productsInputs: human capital, labor, existing producer durables. Final output can be consumed or saved as new capital to be used to support future production of producer durables or final output. (N16) The final goods producers are assumed to operate in perfect competition and not be able to set prices.

Again, Romer’s sectors 2 and 3, rendered as circuits in the Diagram, use the same set of inputs, and are not adequately functionally distinguished. Rather than being two functionings distinguished by their different temporal and productive correspondence with outputs exiting the system, they resemble more a single versatile entity lacking precise norms or precepts of pure-cycle functioning.  The final goods producers are assumed to operate in perfect competition and not be able to set prices.  Perhaps, even though not quite willy-nilly, now the circuit acts out specialized producer durables; now it acts out final outputs.  According to what precise quantities and temporality?  While, in Lonergan’s analysis of the pure cycle, there is a rationale determining timing and quantity of particular production in a particular functioning, Romer’s analysis of the very long run can resort to some extreme assumptions regarding linearity, delta, eta, x-bar, and wages simply to make growth rates equal and time-of-arrival synchronized in the very long run.  Further, the classification of the final output of the final-goods sector – whether it is consumed as consumables or saved as general capital – is decided in the real economy by its recipient’s use, not by the recipient’s production sector. A desktop computer may function as business capital, remaining for accelerative use in the system, or as a consumable exiting the system into personal enjoyment.  And an inventory of food usually being consumed in the present may, in Romer’s scheme, function as part of the general capital panoply supporting workers producing producer durables in a future period.

We list Romer’s assumptions below, but separate his assumptions into a) assumptions acceptable for simplification of the demonstration, and b) assumptions problematic because contrary to macroeconomic principles and empirical facts. (page numbers for reference by the reader lead each assumption, with S indicating Romer’s essay and N indicating the Nobel Announcement’s commentary: Scientific Background on the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2018; See in Bibliography under Romer, Paul)

Acceptable assumptions:

  • (S73) Because there is free entry into research and development, R&D activities are in perfect competition and earn zero profits, but do recover their costs. Comment: Acceptable for the math of the proof, but in the real world biotech research activities do earn accounting profits when successful; and some researchers might choose to work at low wages on spec.
  • (S79) There are three sectors: 1) research and development of a “design”, dHAA, 2) production of durable goods, x(i); 3) production of other final-output goods, η.
  • (S78-79) “Capital is measured in units of consumption goods, η.
  • .” Comment: In Romer’s essay, η will be the fundamental unit of account for a) integral durable goods produced instead of so many units of consumer goods, b) consumer goods themselves, c) denomination of prices and loan amounts. Thus η serves generally as the fundamental production element and the fundamental measure of value.
  • (S79) The total population, its supply of labor L,and its count of persons possessing human capital are exogenously fixed and constant. Comment: a simplifying assumption critical to the mathematical result of constant, Cobb-Douglas, exponential growth.
  • (S79) The total stock of human capital, H, in the fixed population is itself fixed, and the fraction supplied to the market is also fixed. Human capital is defined by Romer as the cumulative effect of activities such as formal education and training. Comment: As Romer states, (S80) this assumption of fixity is made for technical reasons of simplification.
  • (S79) The rival component of knowledge H,  embodied as a cumulative effect in a (competitive, therefore rivalrous) person, is distinguished from the nonrival, technological component A, which is a count of disembodied “designs” comprising a total store of knowledge available to all researchers. By an assumption of linearity (S84 below), can grow without bound  at a constant, long-run rate (N15) and is always available to all researchers.
  • (S80) Attention will be directed to equilibria with constant growth rates for key aggregates. Comment: OK for simple demonstration of a very-long-run result, but not realistic for multiple intrinsically-cyclical expansions during and comprising that very long run.
  • (S80) Two sectors – the producer-durables sector and the final-output sector – “share” the same technology.  Thus,

(S80) “Forgoing consumption is then equivalent to shifting resources from the consumption sector into the capital sector.”

(S81) “Once it owns the design, the firm can convert η units of final output into one durable unit of good i. … The correct interpretation of this formal description is that the forgone consumption is never manufactured.  The resources that would have been used to produce the foregone output (consumption) are used instead to manufacture capital goods.  It is possible to exchange a constant number of consumption goods for each unit of capital goods if the production function used to manufacture capital goods has exactly the same functional form as the production function used to manufacture consumption goods.”

(JMC His thinking is functioning off the the functional form of the production function rather than the point-to-x correspondence)

Comment: Romer is saying that his criterion for distinguishing his producer-durables sector is merely descriptive.  Because they share the same inputs and indifferently produce combinations of η, there is no scientific distinction between them. They arefunctionally indistinguishable in terms of outputs and are organized as would be two sections of a single production floor. He is, simultaneously, operating within the textbooks’ undistinguished single circuit perspective, yet unscientifically asserting two circuitsreminiscent of Lonergan’s double-circuited framework. Also, because he is treating very-long-run inter-entity-ism rather than shorter intrinsically-cyclical, inter-function-ism, he does not treat either the temporality or the coefficients of the interactions between circuits

  • (S80) Only and Hare used in R&D to produce designs. Labor and physical capital are not used.  Comment: acceptable for simplification and formation of vivid proof of endogeneity, but researchers do in fact employ physical capital and labor.
  • (S80) Specialized capital goods are disaggregated into an infinite number of distinct types of producer durables. This simplifies matters by avoiding issues of neighboring capital goods which can be complementary or act as competing substitutes for one another.
  • (S80) Romer uses a type of Cobb-Douglas production function, a homogeneous equation of the first degree. This mathematical form a) assures constant returns to scale, b) by its combinations of measured conjugates (HY, L, x(i)) with their exponents (α, β,1-α-β( specifies each factor’s intensity overall, and c) in combination with the definition of producer durables as a quantity of forgone consumption (S80, S82) and their assumption of being additively separable, ultimately specifies, by the partial derivative of each conjugate with respect to total production, each sector’s share of productive contributions and possible “profits.”
  • (S81) Sector 3, comprised of many firms producing “final output,” can be described and a single. aggregate, representative, price-taking firm.
  • (S81) However, in Sector 2, there is a distinct firm i producing each durable good i.  The firm puts “never-manufactured” primitive units in on one side of a black box and produces one producer durable out the other side.
  • (S81) The functional form of both sectors 2 and 3 is the same Y)hY, L, K) =       , so the firm is indifferent as to what is produced and is, therefore, parallel to a one-sector model.
  • (S81) firm i will face a downward-sloping demand curve.
  • (S81-2) Durables do not depreciate; thus, no repair and maintenance of machines is required; thus all new physical capital is incremental. Comment: acceptable for simplification of demonstration, but not realistic. (See Bureau of Economic Analysis’ NIPA accounts for Consumption of Fixed Capital (Table 5.1, Saving and Investment by Sector, Lines 13-19)
  • (S82) Total capital evolves as new K = Yt) – C(t) and K = ηΣl=1xl ; K = ηΣi=1Axi 
  • (S82-83) indivisibility of  a specialized capital good is not important for this first-pass analysis; the different types of producer durables, i, are treated as a continuous variable, and the summation of x(i) is replaced by an integral, where “x must be interpreted as a function from an appropriately defined function space.”
  • (S83) “anyone engaged in research has free access to the entire stock of economically useful knowledge.”
  • )S83) the aggregate stock of designs evolves as Å = δHAA (3)
  • (S83) Today’s engineer has the same life span and has foregone the same participation in the labor market in order to manufacture producer durables; he/she has the same embodied human capital (“smarts”) as an engineer 100 years ago. Comment: acceptable for simplification, but while we may not have any more native intelligence than our forebears, we should have learned more from better teachers.
  • (S83) The stash of designs evolves according to Å= δHA(3).  Thus, the accumulation of designs is nonconvex due to continuous knowledge spillovers into A serving to increase A
  • (S83) devoting more human capital to research leads to a higher rate of production of new designs for physical capital. dA/dt = δHAA/dt
  • (S84) Labor as defined, L, and physical capital x(Ÿi) are not inputs to the invention of designs.  Again, (S80)  only and Hare used in R&D to produce designs. Comment: acceptable for simplification and formation of proof, but researchers do in fact employ technical capital.
  • (S84) “the output of designs is linear in each of HAand A when the other is held constant.” Comment: Linearity in A makes unbounded growth possible, “in this sense, unbounded growth is more like an assumption than a result of the model.  Romer acknowledges that this assumption is made for analytical convenience.  “… linearity is necessary for generating a constant, long-run, growth rate.” (N15)
  • (S84) The owner of a design for a machine has property rights for the manufacture of the machine, but not for research and development; i.e. by convenient assumption, R&D does not use physical capital.
  • (S85) There are no “neighboring” producer durables; this rules out the possibility of obsolescence and substitution. All producer durables are additively separable. (S80)
  • (S85) H = HA+ HY  Existing, fixed, human capital is allocated to either the invention of designs or the production of physical capital or consumables, but not simultaneously to both.
  • (S85) Spot prices are denominated as units of output, η. (in dollars, a single η would have a price of $1.00)
  • (S85) is the interest rate on loans which are denominated in goods, η. (A loan of $1,000 is equivalent in value to η1,000)
  • (S85) goods can be converted into “capital” one for one.

Because goods can be converted into capital one for one, the spot price for capital is one and its rate of return is r. … Each of these producer-durables firms takes the price Pfor designs, the price of one for capital goods, and the interest rate as given. (S85)  Comment: The producer-durable firms are, thus, doing market research.  So in Romer’s formalism, this function could actually be placed before R&D as constituting an initial and separate circuit spending money and producing a market-research report having economic value.

  • (S85) (9) (S91) wH, wage rental rate per unit of human capital in R&D, wHA = PAδA, and in production of durables or final products   [wH= PAδA = αHYα-1] (9) (S91)
  • (S86) It is assumed that there is a “representative” final output firm” which chooses a profit-maximizing quantity for each durable.  Comment: But where do the profits come from?  If HY,   L, and x, are paid their fair share of marginal costs, then profits are the rent r charged by durables-producers to themselves through incomes and outlays.
  • (S86) The producer of durables would have to assume two costs: the costs of the design purchased from cost-incurring R&D plus the marginal cost of its output which equals the forgone consumables. (See equation (5) (S86) the rightmost term -rηx)
  • (4) (S86) The demand value – forming a demand curve –  of an individual durable, i, may be formulated in terms of its marginal contribution to total output.  The more that is produced, the less the marginal value.  Comment: Hereby, the function of market research is being performed.  In a sense, this may be placed prior in time to R&D as a function resulting in a fourth circuit. Thus Lonergan speaks more abstractly and distinctly of n, n-1, n-2, and point-to-surface, point-to-line, and point-to point.
  • (S87) The flow of monopolist’s profit is π = (α+β)(p-bar)(x-bar). The flow of the monopoly profit of the producer durables considers a) his marginal cost of production of the durables (4), b) the interest cost of what he paid to R&D for rights to the design (5) -rηx
  • The producer of durables selects a production quantity.
  • (S87) Though the price, PAcharged by R&D to the producer of durables is given, the profits from rental of the durable to final goods producers will be bid up based upon the present value of revenues that a monopolist can extract.
  • (S87) The producer of a durable cannot monitor its use by those to whom it leases the durable.
  • (S88) Because of the symmetry in the model, all the durable goods x(i) that are available are supplied at the same level, henceforth denoted as (x-bar). Comment: We wish Romer were more clear regarding, for each producer durable, a) the amount of foregone consumption associated with producing it, versus b) the coefficient of future productivity of final outputs by the durable.
  • (S89) The spillover of knowledge results in knowledge available to all researchers as an external effect.
  • (S90) all producer durables previously produced are used at the same level, (x-bar)
  • (N15) all ideas (designs) are equally good and have identical costs of production. This would imply that unit quantity η and unit value η are the absolute primitives
  • (S91) Human capital, HA, allocated to R&D receives as incomes all the outlays of this research sector in which they work.

Problematic Assumptions:

  • (S78-80) Capital is measured in units of consumption foregone; it is a matter of a simple shift of resources between production of capital and production of final outputs; Thus, (S82) total capital, K = ηΣl=1xl ; K = ηΣi=1Axi  Comments:
    1. This assumption of choice suggests a sacrifice of some potential current output of the basic process for the benefit of the expansion of producer durables for future benefits. Without getting into issues of widening vs. deepening, we note that outlays for expansionary capital can be financed by credit.  It is not necessary to sacrifice consumption.  It is not an instead of; nor is it an either/or.  There is possible a both.
    2. Functionally, physical capital should be understood in analytical terms rather than merely described as a lathe, truck, or power hammer. Those are descriptive categories, not explanatory functional categories. Rather physical capital is an integral assembly of the compensated factors of its production having a specific future accelerative effect and involving a time lag until it is put into use.

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1  [CWL 15, 37]

  • (S79)  Human capital, H, ( a distinct measure of the “cumulative effect” of activities such as formal education and on-the-job training [S79]; thus not a headcount but rather a cumulative effect to be applied to R&D and other production) and Labor, L, are fixed, and rate of increase of each type of output and of total goods is the same. Comment: The real short-run and long-run hierarchical and sequential process involves a sequence, rather than a simultaneous equality, of rates of growth on different levels.  While in the long run, new ideas benefit basic and surplus equally (See next excerpt from CWL 15), still a) the actual measure of the productivity parameter δ will not be ruled by assumptions, and b) in the short and intermediate run, functionings precede and succeed others.  However, for the very long run, Lonergan and Romer do agree.  To quote Lonergan,

One may expect the increment of a volume to stand to the increment of a surface as the volume does to the surface.  To suppose the contrary leads to absurd conclusions…  If, for instance, dQ”/Q” were on a long-term aggregate much greater or much less than dQ’/Q’, then a series of long-term periods would make this difference multiply in geometrical progression to effect a convergence of Q” and Q’ or else a mounting divergence.  Such a convergence or divergence would imply that the more roundabout methods of capitalist progress were increasingly less efficient or increasingly more efficient in expanding the supply of consumer goods.  Neither view is plausible.  New ideas and new methods increase existing efficiencies in both the surplus and the basic stages; the ratio between the quantity of surplus and the quantity of basic products per interval is not a matter of efficiency but of the point-to-line correspondence involved in any more roundabout method, in the fact that a single surplus product gives a flow of basic products. [CWL 15, 124]

  • (S82) Romer cites the one-sector, single-circuit model of national income accounting (superseded by Lonergan’s double-circuited model.  Comment: See Lonergan’s Simple Move to two circuits and Revision of NIPAto define an accounting measure of  total capital K as cumulative forgone output. See Problematic (S78-80) above
  • (S83-84) Because of Romer’s assumptions and the selection of the Cobb-Douglas formalism, the output of new designs dA is linear in a) human capital, HA, allotted to R&D, and b) the stock of knowledge available to all, A, when the other is held constant. Linearity (obviating convexity and an exhausted petering-out) makes unbounded growth in the stock of knowledge possible.  Comment: As Romer admits, this assumption is made for analytical convenience. (S84)
  • (S85) and are supplied separately, rather than jointly. Comment: Given Romer’s purpose, and for simplification, this assumption is acceptable; however, any and every human worker is simultaneously using some combination of pure intelligence and bodily talent jointly.
  • (5) (S86) r is exogenously determined.  Not so.  r should be rationally formulated by internal productive and monetary relations.
  • (S86) Capital is putty-putty. Units of durables can be converted back into “general capital” at any time to avoid interest cost.
  • (S86-87) Producer of durables has a constant marginal cost and faces a constant-elasticity demand curve.
  • (S88) “At time 0, consumers own the existing durable-goods-producing firms; and the net revenues π of these firms are paid to these consumers as dividends.  Comment: Given Romer’s definite purpose and limited scope, this assumption is understandable, but it is unrealistic for an economy granting the right of private property and freedom of choice in spending.
  • (S88) The owners-consumers are endowed with fixed quantities of labor and human capital that are applied inelastically. … Final-goods firms earn zero profits and own no assets, so they can be ignored in the specification of endowments of Labor L and human capital H. Comment: On page (S85-6) Romer appears to contradict the above: Faced with a price (rental) list … for all the producer durables … the representative final-output firm, if it is an entity separate from the production of-durables entity chooses a profit-maximizing quantity x(i) for each durable.  Because it is a constant-returns-to-scale firm (because of the adopted Cobb-Douglas homogeneous equation of the first degree) its input demands for human capital Hand labor Lare defined only after the scale of operation is pinned down.  Again we are back to the issue of the ambiguity of a single unitary entity operating in two sectors-circuits.
  • (S88) By the long-run simultaneity of time-of-arrival of demanders’ receipts of all outlays and dividends and suppliers’ receipts back of these by sales, the physical supply of each good matches the monetary demand.  Comment: acceptable for this model, but unrealistic in an economy allowing private property and freedom of choice of expenditures.

To conclude this subsection, let us requote, first, Romer’s general specification of equilibrium and, second, the strategy he set and met in achieving his goal.  The reader should set aside all our critical observations about the intermediate, transitional dynamics which Romer deliberately bypassed; the reader should congratulate Romer and express his gratitude for Romer’s impressive contribution to our understanding of economic advancement.  Romer’s proof is admirable.

An equilibrium for this model will be paths for prices and quantities such that i) consumers make savings and consumption decisions taking interest rates as given; ii) holders of human capital decide whether to work in the research sector or the manufacturing sector taking as given the stock of total knowledge A, the price of designs PA, and the wage rate in the manufacturing sector wA; iii) final goods producers choose labor, human capital, and a list of differentiated durables taking prices as given; iv) each firm that owns a design and manufactures a producer durable maximizes profit taking as given the interest rate and the downward sloping demand curve it faces, and setting prices to maximize profits; v) firms contemplating entry into the business of producing a durable take prices for designs as given; and vi) the supply of each good is equal to the demand. [Romer 1990, S88]

The strategy for characterizing the model that is followed here is to solve for an equilibrium in which the variables A, K, and grow at constant exponential rates.  This is generally referred to as a balanced growth equilibrium.  The intuition from the Solow model suggests that such an equilibrium will exist if grows at a constant exponential rate. The intuition from the Uzawa model suggests that it is possible for to grow at an exponential rate  because equation (3) for Å is linear in A. It will grow at a constant rate if the amount of human capital Hthat is devoted to research stays constant. Verifying that a balanced growth equilibrium exists therefore reduces to the problem of showing that prices and wages are such that HY and HA remain constant as Y, K, C, and grow.  [Romer, 1990, S90]