Calculating price elasticity of demand, profit-maximizing, sketching marginal cost and average cost curves

1. Huntsville, Alabama is engaging in a bumper sticker advertising campaign. Monthly sales data suggest that the following demand relationship exists:

Q = 6,000 - 2,000P

Where: Q = bumper-sticker sales
P = price

A. How many bumper stickers could be sold at $2 each?
B. What would the price have to be in order to sell 5,000 bumper stickers?
C. At what price would bumper sticker sales equal zero?
D. How many bumper stickers could be given away?
E. Calculate the point price elasticity of demand at a price of $1.

2. Pile Buffers, Inc., has enjoyed substantial economic profits derived from patents covering the manufacturing of a special shock absorber used in driving piles at construction sites. Market demand relations for the shock absorber are:

P = $5,000 - $0.05Q

Fixed costs are zero, because research and development expenses have
been fully amortized during previous periods. Average variable costs are
constant at $4,000 per unit.

A. Calculate the profit-maximizing price/output combination and economic profits if Pile Buggers enjoys an effective monopoly on shock absorber due to patent protection
B. Calculate the price/output combination and total economic profits that would result if competitors offer clones that make the pile driver shock absorber market perfectly competitive.

3. Increased productivity is the main way in which individuals, firms, and entire economies can improve their real economic situation. Please address the following questions regarding productivity.

A. What is implied by "increased productivity?"
B. How is productivity measured and what problems are generally encountered when attempting to quantify changes
C. Discuss "productivity in the 1990s,"?reasons for dramatic increases and the effect of this on keeping inflation very low with low unemployment rates
4. Theoretically a firm in a perfectly competitive market cannot make above "normal profits" in the long run.

A. Discuss reasons why this is the case and how the long run adjustment process takes place
B. Given a cost function of: TC = Q2 address the following

1) Sketch the marginal cost and average cost curves
2) In perfect competition, what it the theoretical final outcome of such a cost function

5. Can monopolies lose money?

A. Graph this possibility and explain what action a monopoly can take to remedy the problem
B. Discuss two reasons why a monopoly, acting in their self-interest, might elect to charge a lower price and produce more output than the theoretical model to maximize profits would suggest.

See attached file for full problem description.