The market for pencils is easy to enter, but entry takes time. In the short run, the number of firms (and plants) in the industry is fixed. Production occurs in standard sized plants with each plant having an annual total cost of 2 TC = 400 + q (this includes a normal return on the plant's capital). Currently, no firm owns more than one plant. Pencils are a completely homogenous good and pencils is a perfectly competitive industry.
a. You own one plant among more than a hundred in the industry. Currently, the price of a pencil is P = 100. How many pencils do you produce each year? What price do you charge? What are your annual profits?
b. The demand in the market is Q = 50000 - 200P. As stated in part a, the price is P = 100. If the market is in short-run equilibrium (meaning each firm is maximizing its profits given that the number of plants is fixed in the short run), how many firms are in the market?
c. Explain why this market is not in long-run equilibrium. Derive the long-run equilibrium in this market. What is the equilibrium price? What is the equilibrium quantity sold by each firm? How many firms are in the market?
d. If the number of firms is equal to the number that you found in part b, what is the short run industry supply function?
e. What is the long run industry supply function?
f. Now you find a way to produce pencils more cheaply. Your total cost function is now 2 200 2 q TC = + . Your technology is unique and cannot be reproduced by others or replicated by you. In the long run, does this discovery increase your profits? Does it lower the market price? Does in change the number of firms in the market?