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Theory of the Firm: A Reformulation with Primary Factors of Production and Procurement of Ingredient Inputs


  • Hiroaki HAYAKAWA

    () (School of Business and Economics, University Brunei Darussalam, Drunei Darussalam.)


This paper reformulates the neoclassical theory of the firm by distinguishing two types of inputs: (1) the primary factors of production (labor, capital, etc.) and (2) ingredient inputs (intermediate goods, raw materials, and services). The production function is defined on the space of the primary factors while ingredient inputs, as required by production technologies, are procured externally from other firms. Firms maximize profits subject to the production function as well as to the ingredient input requirement functions. We analyze how the optimal level of production and the optimal employment of factor services are determined when the cost of the acquisition of ingredient inputs is counted explicitly as part of the total cost of production. The first order condition of profit maximization requires that the marginal value-added product of an employed primary factor be equal to its price, and the second order condition is stated in terms of the negative definiteness of the Hessian of the value-added function. Cost minimization requires that the marginal cost of production be equal to the sum of an incremental cost of factor services and an incremental cost of ingredient inputs that are procured. The optimum level of production and the optimal use of the primary factors both respond to changes in the prices of ingredient inputs. The paper also shows: the zero degree homogeneity of factor demand and output supply functions, the linear homogeneity of the value-added function, Shephard’s lemma, the interpretation of the Lagrangian multiplier in cost minimization, the nonlinearity of the iso-cost surfaces, and the concavity of the cost function.

Suggested Citation

  • Hiroaki HAYAKAWA, 2016. "Theory of the Firm: A Reformulation with Primary Factors of Production and Procurement of Ingredient Inputs," Journal of Economics and Political Economy, KSP Journals, vol. 3(3), pages 418-439, September.
  • Handle: RePEc:ksp:journ1:v:3:y:2016:i:3:p:418-439

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    References listed on IDEAS

    1. Khang, Chulsoon, 1971. "An isovalue locus involving intermediate goods and its applications to the pure theory of international trade," Journal of International Economics, Elsevier, vol. 1(3), pages 315-325, August.
    2. Charles R. Hulten, 1978. "Growth Accounting with Intermediate Inputs," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 511-518.
    3. Diewert, W. Erwin, 1978. "Hick's Aggregation Theorem and the Existence of a Real Value Added Function," Histoy of Economic Thought Chapters,in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 2, chapter 2 McMaster University Archive for the History of Economic Thought.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Petia Topalova & Amit Khandelwal, 2011. "Trade Liberalization and Firm Productivity: The Case of India," The Review of Economics and Statistics, MIT Press, vol. 93(3), pages 995-1009, August.
    6. Moro, Alessio, 2012. "Biased Technical Change, Intermediate Goods, And Total Factor Productivity," Macroeconomic Dynamics, Cambridge University Press, vol. 16(02), pages 184-203, April.
    7. Charles I. Jones, 2011. "Intermediate Goods and Weak Links in the Theory of Economic Development," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(2), pages 1-28, April.
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    More about this item


    Primary factors; Ingredient inputs; Production function; Value-added function; Marginal value-added product.;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity


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