Increasing returns and imperfect competition: (a) The production function for the word processor is Y = X – 100 million if X is larger than 100 million, and zero otherwise. By spending $100 million, you create the first copy, and then $1 must be spent distributing it (say for the DVD it comes on). For each dollar spent over this amount, you can create another
Increasing returns and imperfect competition:
(a) The production function for the word processor is
Y = X – 100 million
if X is larger than 100 million, and zero otherwise. By spending $100 million, you create the first copy, and then $1 must be spent distributing it (say for the DVD it comes on). For each dollar spent over this amount, you can create another copy of the software.
(b) The production function is plotted in Figure 6.5. Output is zero whenever X is less than 100 million. Does this production function exhibit increasing returns? Yes. We spend $100 million (plus $1) to get the first copy, but doubling our spending will lead to 100 million copies (plus 2). So there is a huge degree of increasing returns here. Graphically, this can be seen by noting that the production function “curves up” starting from an input of zero, a common characteristic of production functions exhibiting increasing returns. (Constant returns would be a straight line starting from zero; decreasing returns would curve down more sharply than a straight line.)
(c) If the firm charges a price equal to marginal cost (i.e., equal to $1) and sells a million copies, then revenues are $1 million, while costs are $101 million. Profits are therefore negative $100 million. That is, if the firm charges marginal cost, it loses an amount equal to the fixed cost of developing the software. (d) Selling at price p, revenue is pX and cost is $100 million + X dollars. To break even so that revenue is equal to cost, the firm must sell X copies, where
Atp = 20, this gives X = 5.26 million copies. Atp = 100, this gives X = 1.01 million copies. Notice that the answer is approximately 100 million divided by the price, since the marginal cost is small. (e) The fact that this production function exhibits increasing returns to scale is a strong hint that “scale matters.” Increasing returns to scale means that larger firms are more productive. In this case, everything is about covering the fixed cost of creating the software. If the software can be sold all over the world, it will be much easier to cover the large fixed cost than if the software can only be sold to a few people. If the firm could sell 100 million copies of the software at $2 each, it would break even. If it could sell 200 million copies at that price, it would make lots of money.
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