1, What do we mean by a "production function"? Interpret the following production functions.

(a)Q=4L3/5*K2/5

(b)Q= 192KL2-0.25K2L3

2, what is the difference between short-run and long-run production?

3, 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?

4, Short-run production:

(a)Suppose capital is fixed atK= 32:Write down the functional forms for the total product(TPL), marginal product (MPL)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 profit maximization? Why?

(c)Looking at the plots, what can you say about the relationship betweenTPLandMPL?What can you say about the relationship betweenAPLandMPL?Prove these relationships mathematically.