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:

Capital Labor Quantity 30 250 245 34 270 240 44 300 300 50 320 320 70 350 390 76 400 440 84 440 520 86 440 520 104 450 580 110 460 600 116 460 600 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? (See Appendix 6C to answer this question.)

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