1) The president of Mighty Soft software company is about to introduce a new computer operating system called Roorknobs. Because it is easier to swap files with people who have the same operating system, the amount people are willing to pay to have Roorknobs on their computers is greater the larger they believe Roorknobs's market share to be. The perceived market share for Roorknobs is the fraction of all computers that the public believes is using Roorknobs. When the price of Deorknebs is p, then its actual market share is the fraction of all computer owners that would be willing to pay at least $p to have DoorKnobs installed on their computers. Market researchers have discovered that if Roorknobs's perceived market share is s and the price of Roorknobs is $p, then its actual market share will be x, where x is related to the price p and perceived market share s by the formula p=256s(1x) In the short run, Mighty Soft can influence the perceived market share of Roorknobs by publicity, advertising, giving liquor and gifts to friendly journalists, and giving away copies in conspicuous ways. In the long run, the truth will emerge, and Roorknobs'sperceived market share s must equal its actual market share x. (a) If the perceived market share is s, then the demand curve for Doorknobs is given by Equation (1). Draw the demand curve relating price to actual market share in the case in which QoorKnobs's perceived market share is s=1/2. Label this curve s=1/2 (b) On the demand curve that you just drew with s=1/2, mark a dot on the point at which the actual market share of Doorknobs is 1/2. What is the price at which half of the computer owners actually want to buy Reorknobs, given that everybody believes that half of all computer owners want to buy Reorknebs? (c) On the same graph, draw and label a separate demand curve for the case where Roorknobs's perceived market share s takes on each of the following values: s=1/8,1/4,3/4,7/8,1. (d) On the demand curve for a perceived market share of s=1/4, put a dot on the point at which the actual market share of Roorknobs is 1/4. If the perceived market share of Roerknobs is 1/4, at what price is the actual market share of Roorknobs also 1/4 ? 1) The president of Mighty Soft software company is about to introduce a new computer operating system called Roorknobs. Because it is easier to swap files with people who have the same operating system, the amount people are willing to pay to have Roorknobs on their computers is greater the larger they believe Roorknobs's market share to be. The perceived market share for Roorknobs is the fraction of all computers that the public believes is using Roorknobs. When the price of Deorknebs is p, then its actual market share is the fraction of all computer owners that would be willing to pay at least $p to have DoorKnobs installed on their computers. Market researchers have discovered that if Roorknobs's perceived market share is s and the price of Roorknobs is $p, then its actual market share will be x, where x is related to the price p and perceived market share s by the formula p=256s(1x) In the short run, Mighty Soft can influence the perceived market share of Roorknobs by publicity, advertising, giving liquor and gifts to friendly journalists, and giving away copies in conspicuous ways. In the long run, the truth will emerge, and Roorknobs'sperceived market share s must equal its actual market share x. (a) If the perceived market share is s, then the demand curve for Doorknobs is given by Equation (1). Draw the demand curve relating price to actual market share in the case in which QoorKnobs's perceived market share is s=1/2. Label this curve s=1/2 (b) On the demand curve that you just drew with s=1/2, mark a dot on the point at which the actual market share of Doorknobs is 1/2. What is the price at which half of the computer owners actually want to buy Reorknobs, given that everybody believes that half of all computer owners want to buy Reorknebs? (c) On the same graph, draw and label a separate demand curve for the case where Roorknobs's perceived market share s takes on each of the following values: s=1/8,1/4,3/4,7/8,1. (d) On the demand curve for a perceived market share of s=1/4, put a dot on the point at which the actual market share of Roorknobs is 1/4. If the perceived market share of Roerknobs is 1/4, at what price is the actual market share of Roorknobs also 1/4