Estimation of production and cost functions involves collecting data, assuming a mathematical form for the functions, and using estimation methods like regression analysis to determine parameter values. While data collection can be difficult due to issues like measuring capital usage, functions like the Cobb-Douglas and quadratic forms are commonly used in empirical work due to their flexibility and ability to capture concepts like diminishing returns. Long-run cost functions estimated via regression analysis or engineering methods are used for investment planning to determine optimal scale.

6. Quadratic Production Function continued Q L L AP MP MP AP a) b)

8. Cubic Production Function continued Q L L AP MP MP AP a) b)

10. Power Function continued Q L b<1 b=1 b>1

25. Cubic cost function $ TC Q

26. First marginal and average costs decrease and then increase: $ MC Q AC

28. Costs increasing at increasing rate $ TC Q

29. No decreasing marginal cost! $ MC Q AC

31. No Law of Diminishing Marginal Returns $ TC Q $ MC Q AC