A competitive firm has estimated its average variable cost function as: AVC = 20 - 0.04Q + 0.00005Q2 ...

A competitive firm has estimated its average variable cost function as: 

AVC = 20 - 0.04Q + 0.00005Q2 

Its total fixed cost is $500. 

a) Calculate the short-run marginal cost function associated with the average variable cost function. 

b) Calculate the level of output at which average variable cost reaches its minimum and what value that is. 

c) Calculate the level of output this firm should produce in order to maximize profits, and what level of profit (loss) this firm would incur. 

d) Suppose the forecasted price of its product is $10, calculate the level of output and profit (loss) this firm would incur. Please explain.