Consider a product that has network effects in the sense of our model from Chapter 17. Consumers are named using real numbers between 0 and 1; the reservation price for consumer x when a fraction z of the popuation uses the product is given by the formula r(x) f (z), where r(x) = 1 − x and f (z) = z.
(a) Let’s suppose that this good is sold at cost 
to any consumer who wants to buy a unit. What are the possible equilibrium numbers of purchasers of the good?
(b) Suppose that the cost falls to 
and that the good is sold at this cost to any consumer who wants to buy a unit. What are the possible equilibrium numbers of purchasers of the good?
(c) Briefly explain why the answers to parts (a) and (b) are qualitatively different.
(d) Which of the equilibria you found in parts (a) and (b) are stable? Explain your answer.
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