Looking for the answer to #4.

. What do we mean by a "production function"? Interpret the following production functions. (a) Q = 4L%K (b) Q = 15cm;2 0.25K2L3 . What is the difference between short-run and long-run production? . What is the law of diminishing returns? What is the crucial assumption behind this law? Does the law hold in the long-run? Why or why not? . Short-run production: (a) Suppose capital is xed at K = 32. Write down the functional forms for the total product (TPL), marginal product (MP1,) and average product (APL) of labor for the production functions given in Question 1 (a and b]. (b) Plot the functions and identify (the ranges of output) for the three stages of production increasing, decreasing and negative returns. In which stage does the production take place for prot maximization? Why? (c) Looking at the plots, what can you say about the relationship between TPL and MP1,? What can you say about the relationship between APL and MPL? Prove these relationships mathematically