The Brady Corporation has eleven plants located around the world. In a recent year, the data for each plant gave the number of labor hours (in thousands), capital (total net plant assets, in millions), and total quantity produced:

The plants all operate at a similar level of technology so a production function can be derived from the data.
a. Use a Cobb-Douglas production function to calculate a regression, and discuss the important characteristics of your results, such as the form of the equation, R2, and the statistical significance of the coefficients.
b. Calculate the estimated production for each plant.
c. Does the result indicate constant, decreasing, or increasing returns to scale?
d. What are the elasticities of production of labor and of capital? What is the meaning of the elasticities?
e. Is the marginal product of labor decreasing?

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Capital 30 34 Labor 50 70 76 84 86 104 110 116 250 270 800 320 350 400 440 440 450 460 460 Quantity 245 240 300 320 390 440 520 520 580 600 600