Charlies cattle farm produces q heads of cattle and a feedlot buys Charlies cattle at p dollars per head. His farm is characterized by the following economic terms.

Production function: q = L^0.5 + K^0.5, where L and K are labor and capital.

Total cost function: C = q² + 10q + 9

Does Charlies farm have increasing, decreasing, or constant return to scale? [Hint: Chapter 18] (7 points)

3.2 [This is a bonus question. Do not attempt unless you have time left.] If the production function is q = L^0.5 + K^{0.5 + N}, where N is a non-zero constant, calculate and comment on the return to scale. (3 points) 3.3 What is Charlies: [Hint: Chapter 21] (8 points) 3.3.1 Variable cost? 3.3.2 Fixed cost?

3.3.3 Average total cost? 3.3.4 Average variable cost?

3.4 If Charlie is operating in a competitive market, will Charlie supply in the short run? Why? If the market price equals 30 (P = 30), how many heads of cattle will Charlie supply? [Hint: To decide whether Charlie will supply or not, we need to consider the shutdown point in short run; to decide quantity of the supply, please consider the profit maximization condition under competitive market] (10 points)

3.5 If Charlie is operating in a competitive market, what is the long run equilibrium market price of his cattle? [Hint: Chapter 23 and remember, in the long run, a competitive producer should have zero profit.] (10 points)