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



Abstract. 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.

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

JEL. D01, D21, D24.


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

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Arrow, K.J. (1974). The measurement of real value added. In P. David, & M. Reder (Eds.), Nations and households in economic growth: Essays in honor of Moses Abramovitz (pp, 3-19). New York: Academic Press. doi. 10.1016/B978-0-12-205050-3.50006-3

Bruno, M. (1978). Duality, intermediate inputs and value-added. In M. Fuss, & D. McFadden (Eds.), Production economics: A dual approach to theory and applications Vol. 2, pp. 3-16. Amsterdam: North-Holland. doi. 10.1016/B978-0-444-85013-3.50008-5

Ciccone, A. (2002), Input chains and industrialization. Review of Economic Studies, 69(3), 565-587. doi. 10.1111/1467-937x.t01-1-00022

Cobbold, T. (2003). A comparison of gross output and value-Added methods of productivity estimation. Research Memorandum Cat No: GA511, Australian Government Productivity Commission.

Cobb, C.W., & Douglas, P.H. (1928). A theory of production. American Economic Review, 18, 139-165. Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association.

David, P.A. (1962). The deflation of value added. Review of Economics and Statistics, 44(2), 148-155. doi. 10.2307/1928197

David, P.A. (1966). Measuring real net output: A proposed index. Review of Economics and Statistics, 48, 419-425. doi. 10.2307/1924620

De Backer, K., & Yamano, N. (2011). International comparative evidence on global value chains. In A. Sydor (Ed.), Global value chains: Impacts and implications (pp. 103-126). Trade Policy Research. Foreign Affairs and International Trade Canada, Cat: FR2-5/2011E. doi. 10.2139/ssrn.2179937

Diewert, W.E. (1973). Functional forms for profit and transformation functions. Journal of Economic Theory, 6, 284-316. doi. 10.1016/0022-0531(73)90051-3

Diewert, W.E. (1974). Applications of duality theory. In M. D. Intriligator, & D. A. Kendrick (Eds.), Frontiers of quantitative economics Vol.2, pp.106–166. Amsterdam: North-Holland.

Diewert, W.E. (1978). Hicks’ aggregation theorem and the existence of a real value-added function. In M. Fuss, & D. McFadden (Eds.), Production economics: A dual Approach to theory and applications (Vol.2, pp.17-51). Amsterdam: North-Holland. doi. 10.1016/b978-0-444-85013-3.50009-7

Douglas, P.H. (1976). The Cobb-Douglas production function once again: Its history, its testing, and some new empirical values, Journal of Political Economy, 84(5), 903-916. doi. 10.1086/260489

Ferguson, C.E. (1969). The neoclassical theory of production and distribution. Cambridge: At the University Press. doi. 10.1017/cbo9780511896255

Globerman, S. (2011). Economic and policy issues. In A. Sydor (Ed.), Global value chains: Impacts and implications (pp. 17-42). Trade Policy Research. Foreign Affairs and International Trade Canada, Cat: FR2-5/2011E. doi. 10.2139/ssrn.2179533

Goldberg, P.K., Khandelwal, A.K., Pavcnik, N., & Topalova, P. (2010). Imported Intermediate inputs and domestic product growth: Evidence from India. Quarterly Journal of Economics, 125(4), 1727-1767. doi. 10.1162/qjec.2010.125.4.1727

Grossman, G.M., & Rossi-Hansberg, E. (2008). Trading tasks: A simple theory of offshoring. American Economic Review, 98(5), 1978-1997. doi. 10.1257/aer.98.5.1978

Halpern, L., Koren, M., & Szeidl, A. (2015). Imported inputs and productivity. American Economic Review, 105(12), 3660–3703. doi. 10.1257/aer.20150443

Henderson, J.M., & Quandt, R.E. (1980). Microeconomic theory: A mathematical approach (3rd ed.), New York: McGraw-Hill.

Hicks, J.R. (1946). Value and capital (2nd ed.). Oxford: At the Clarendon Press.

Hulten, C.R. (1978). Growth accounting with intermediate inputs. Review of Economic Studies, 45(3), 511-518. doi. 10.2307/2297252

Intriligator, M.D. (1971). Mathematical optimization and economic theory. Englewood Cliffs, NJ: Pretice-Hall.

Jones, C.I. (2011). Intermediate goods and weak links in the theory of economic development. American Economic Journal: Macroeconomics, 3(1), 1–28. doi. 10.1257/mac.3.2.1

Khandelwal, A., & Topalova, P. (2011). Trade liberalization and firm productivity: The case of India. Review of Economics and Statistics, 93(3), 995-1009. doi. 10.1162/rest_a_00095

Khang, C. (1971). An isovalue locus involving intermediate goods and its applications to the pure theory of international trade. Journal of International Economics, 1(3), 315-325. doi. 10.1016/0022-1996(71)90003-1

Kurz, C., & Lengermann, P. (2008). Outsourcing and US economic growth: The role of imported intermediate inputs. World Congress on National Accounts and Economic Performance Measures for Nations.

Leontief, W. (1936). Quantitative input and output relations in the economic systems of the United States. Review of Economics and Statistics, 18(3), 105-125. doi. 10.2307/1927837

Mas-Colell, A., Winston, M.D., & Green, J.R. (1995). Microeconomic theory. New York: Oxford University Press.

McFadden, D. (1967). A review of 'Manufacturing production functions in the U.S., 1957: An interindustry and interstate comparison of productivity. Journal of the American Statistical Association, 62, 295-300.

McFadden, D. (1978). Cost, revenue, and profit functions. In M. Fuss, & D. McFadden (Eds.), Production economics: A dual approach to theory and applications Vol.1, pp.3-109. Amsterdam: North-Holland.

Moro, A. (2012). Biased technical change, intermediate goods, and total factor productivity. Macroeconomic Dynamics, 16, 184-203. doi. 10.1017/S1365100510000532

Peng, S.K., Riezman, R., & and Wang, P. (2013). Intermediate goods trade, technology choice and productivity. CESifo Working Paper Series No. 5637.

Samuelson, P.A. (1947). Foundations of economic analysis. Cambridge, MA: Harvard University Press.

Shephard, R.W. (1953). Cost and production functions. Princeton, NJ: Princeton University Press.

Shephard, R.W. (1971). Cost and production functions. Princeton, NJ: Princeton University Press.

Sims, C.A. (1969). Theoretical basis for a double deflated index of real value added. Review of Economics and Statistics, 51, 470-471. doi. 10.2307/1926441

Solow, R.M. (1957). Technical change and the aggregate production function. Review of Economics and Statistics, 39, 312-20. doi. 10.2307/1926047

Sydor, A. (2011). Global value chains: Impacts and implications – Editor’s overview. In Sydor, A. (Ed.), Global value chains: Impacts and implications (pp. 1-16). Trade Policy Research. Foreign Affairs and International Trade Canada, Cat: FR2-5/2011E.

Uzawa, H. (1964). Duality principles in the theory of cost and production. International Economic Review, 5, 216-220. doi. 10.2307/2525564

Varian, H. (1984). Microeconomic analysis (2nd ed.). New York: Norton and Company.



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