4. A model of network externalities. Suppose that there are 50 potential consumers in the market for a new technology that exhibits network effects. There is a uniform distribution of consumers with individual valuations, v, ranging from $1, $2,..., $50. Consumer valuation from consuming the technology is given by vN, where N is the number of consumers adopting the technology. Consumers with purchase the product as long as their valuation is greater or equal to the price, so that the marginal consumer has a valuation such that p=yN. The number of consumers adopting the technology is given by the number of people with valuation greater than y, i.e. N = 50-y. a) Using the information above, derive the relationship between the price of the product and the number of consumers adopting the product, N. Characterize this relationship - does it reflect a typical market demand curve? b) If the price for the product is $600, find the three equilibrium number of adopters in the market. c) Graph this market, with the price of the product on the vertical axis and the number of adopters on the horizontal axis.