[Solved]Consider Product Network Effects Consumers Named Using Real Numbers 0 1 Reservation Price Q37243703

Consider a product that has network effects. Consumers are namedusing real numbers between 0 and 1; the reservation price forconsumer x when a z fraction of the population uses the product isgiven by the formula r(x)f(z), where r(x) = 1 − x and f(z) = z.

(a) Let us suppose that this good is sold at cost 1/4 to anyconsumer who wants to buy a unit. What are the possible equilibriumnumber of purchasers of the good?

(b) Suppose that the cost falls to 2/9 and that the good is soldat this cost to any consumer who wants to buy a unit. What are thepossible equilibrium number of purchasers of the good?

(c) Briefly explain why the answers to parts (a) and (b) arequalitatively different.

(d) Which of the equilibria you found in parts (a) and (b) arestable?

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