Increasing returns and imperfect competition: Suppose a new piece of computer software — say a word processor with perfect speech recognition — can be created for a onetime cost of $100 million. Suppose that once it’s created, copies of the software can be distributed at a cost of $1 each.

(a) If Y denotes the number of copies of the computer program produced and X denotes the amount spent on production, what is the production function; that is, the relation between Y and X?

(b) M ake a graph of this production function. Does it exhibit increasing returns? Why or why not?

(c) Suppose the ?rm charges a price equal to marginal cost ($1) and sells a million copies of the software. What are its pro?ts?

(d) Suppose the ?rm charges a price of $20. How many copies does it have to sell in order to break even? What if the price is $100 per copy?

(e) Why does the scale of the market — the number of copies the ?rm could sell — matter?