Children’s Toys and Gucci Products: In most of our development of consumer theory, we have assumed that tastes are independent of what other people do. This is not true for some goods. For instance, children are notorious for valuing toys more if their friends also have them—which implies their marginal willingness to pay is higher the more prevalent the toys are in their peer group. Some of my snooty acquaintances, on the other hand, like to be the center of attention and would like to consume goods that few others have. Their marginal willingness to pay for these goods thus falls as more people in their peer group consume the same goods.
A. The two examples we have cited are examples of positive and negative network externalities.
(a) Consider children’s toys first. Suppose that, for a given number N of peers, demand for some toy x is linear and downward sloping—but that an increase in the “network” of children (i.e. an increase in N) causes an upward parallel shift of the demand curve. Illustrate two demand curves corresponding to network size levels N1 < N2.
(b) Suppose every child at most buys one of these toys which are produced at constant marginal cost. For a combination of p and x to be an equilibrium, what must be true about x if the equilibrium lies on the demand curve for network size N1?
(c) Suppose you start in such an equilibrium and the marginal cost (and thus the price) drops. Economists distinguish between two types of effects: A direct effect that occurs along the demand curve for network size N1, and a bandwagon effect that results from increased demand due to increased network size. Label your original equilibrium A, the “temporary” equilibrium before network externalities are taken into account as B and your new equilibrium(that incorporates both effects) as C. Assume that this new equilibrium lies on the demand curve that corresponds to network size N2.
(d) How many toys are sold in equilibrium C? Connect A and C with a line labeled . Is  the true demand curve for this children’s toy? Explain.
(e) If you were a marketing manager with a limited budget for a children’s toy company, would you spend your budget on aggressive advertising early as the product is rolled out or wait and spread it out? Explain.
(f) Now consider my snooty acquaintances who like Guuci products more if few of their friends have them. For any given number of friends N that also have Gucci products, their demand curve is linear and downward sloping — but the intercept of their demand curve falls as N increases. Illustrate three demand curves for N1 < N2.
(g) Assume for convenience that everyone buys at most 1 Gucci product. Identify an initial equilibrium A under which N1 Gucci products are sold at some initial price p—and then a second equilibrium C at which N2 Gucci products are sold at price p′ < p. Can you again identify two effects—a direct effect analogous to the one you identified in (c) and a snob effect analogous to the bandwagon effect you identified for children’s toys? How does the snob effect differ from the bandwagon effect?
(h) True or False: Bandwagon effects make demand more price elastic while snob effects make demand less price elastic.
(i) In exercise 7.9 we gave an example of an upward sloping demand curve for Gucci products, with the upward slope emerging from the fact that utility was increasing in the price of Gucci products. Might the demand that takes both the direct and snob effects into account also be upward sloping in the presence of the kinds of network externalities modeled here?
B. Consider again the positive and negative network externalities described above.
(a) Consider first the case of a positive network externality such as the toy example. Suppose that, for a given network size N, the demand curve is given by p = 25N1/2 −x. Does this give rise to parallel linear demand curves for different levels of N, with higher N implying higher demand?
(b) Assume that children buy at most one of this toy. Suppose we are currently in an equilibrium where N = 400. What must the price of x be?
(c) Suppose the price drops to $24. Isolate the direct effect of the price change — i.e. if child perception of N remained unchanged, what would happen to the consumption level of x?
(d) Can you verify that the real equilibrium (that includes the bandwagon effect) will result in x = N = 576 when price falls to $24? How big is the direct effect relative to the bandwagon effect in this case?
(e) Consider next the negative network externality of the Gucci example. Suppose that, given a network of size N, the market demand curve for Gucci products is p = (1000/N1/2)−x. Does this give rise to parallel linear demand curves for different levels of N, with higher N implying lower demand?
(f) Assume again that no one buys more than one Gucci item. Suppose we are currently in equilibrium with N = 25. What must the price be?
(g) Suppose the price drops to $65. Isolate the direct effect of the price change — i.e. if people’s perception of N remained unchanged, what would happen to the consumption level of x?
(h) Can you verify that the real equilibrium (that includes the snob effect) will result in x = N = 62? How big is the direct effect relative to the snob effect in this case?
(i) Although the demand curves for a fixed level of N are linear, can you sketch the demand curve that includes both direct and snob effects?