1. A firm has the following total cost function
T C = 6Q2 - 12Q + 87.5 for Q > 2
(a) Find the break-even levels of output if the market price is $38.
(b) Show that the profit maximizing level of output is the average of the two break-even levels.
2. Assume all firms in a competitive industry have the following cost function
T C = Q3 - 40Q2 + 1600Q + 1500
(a) If the market price for this good is $1400 per unit, determine a typical firm's break-even level(s) of output.
(b) What is a typical firm's profit maximizing level of output.
(c) What is the market long run (normal profit) price?
3. All firms in a competitive market have the following total cost function:
T C = 0.5Q3 - 12.5Q2 + 125Q + 3200
The market demand and supply functions are given by
Qmd = 16500 - 60P Qms = -3500 + 40P
(a) What is a typical firm's optimal level of output?
(b) What is the firm's profit or loss?
(c) How many firms operate in this market?
4. Assume no change in the cost structure of the firms and in demand in the previous problem,
(a) Determine the long-run price established in this market.
(b) What is a typical firm's output in the long-run?
(c) In the long-run, how many firms enter or exit the market?
(d) What is the long-run equation of the supply function?