Write a 5 pages paper on on the production function for agriculture. The origin of the Cobb-Douglas production function can be traced to the 1928 seminal work of Paul Douglas and Charles Cobb in studying the United States manufacturing sector using the data set of 1899-1922 (Felipe and Adams 2005, p. 428). However, Felipe and Adams (2005, p. 428) also pointed out that several authors like Paul Samuelson have argued that Knut Wicksell should have taken the credit as well for its discovery. Nevertheless, Cobb and Douglas’s econometric or empirical estimation of an aggregate production function was the first in the profession of economics (Felipe and Adams 2005, p. 428). The production function is discussed in Gujarati (2004, p. 224). In its Cobb-Douglas form, it is possible to know or estimate whether we have an increasing, constant, or decreasing returns to scale (Gujarat 2004, p. 244). In a way, the production function reflects the technological constraints or the production feasibility set (Varian 2006, pp. 322-327).
Meanwhile, we can see in the literature that the production function estimation has been supplemented by several techniques to improve precision or correct perceived weaknesses. Mittlehammer et al. (1980) employed mixed estimation and principal component regression to mitigate the effects of severe multicollinearity that was preventing accurate through ordinary least squares. The methods improved precision as well as the theoretical reasonableness of estimated parameters. Just et al. (1983, p. 770) developed a technique for the estimation of multi-crop production functions. Their method employed all available information and they claim that their empirical results show that their approach is practical and inexpensive. Mittlehammer and Conway (1988, p. 859) developed a mixed estimation procedure of the production frontier that departs from the Theil-Goldberger model that had been questioned in the literature. Mittlehammer and Conway (1988, p. 865) introduced instead a prior integrated mixed estimator or the PIME that are based on generally accepted principles. . .