Pokémon Go is a location-based AR (augmented reality) mobile game. In this game players capture, battle, and train virtual creatures, called Pokémon, who appear on device screens as though in the real world. To play the game, First the player needs to create an avatar by selecting a hair, skin, eye color, and outfit. After the avatar is created, it is displayed at the player’s current location along with a map of the player’s immediate surroundings. Features on the map include a number of PokeStops and Pokémon gyms. PokeStops provide players with items, such as eggs, Poke Balls, and potions and can be equipped with items called lures, which attract wild Pokémon. Gyms serve as battle locations for team-based king of the hill matches. As players travel the real world, their avatar moves along the game’s map. Different Pokémon species reside in different areas of the world. During an encounter with a wild Pokémon, the player may throw a Poke Ball at it by flicking it from the bottom of the screen up toward the Pokémon. If the Pokémon is successfully caught, it will come under the ownership of the player. Factors in the success rate of capture include the right force, the right time and the type of Poke Ball used.
Suppose you have just created an app called NewtonTMfor Pokémon Go. When encountering a wild Pokémon, this app is able to calculate the force and the trajectory of the throw of a Poke Ball to maximize your chance to catch the Pokémon. You would like to launch this new app to the market, but you are not sure how much your targeted customers are willingly to pay for this app. You conduct a survey for 200 potential customers and find out that 160 customers are willing to buy the product when the price p = 1; and 120 of them are willing to buy when p = 2: You believe that the market demand has the following linear functional form: p = a-bq.
(a) Derive the market demand function and the marginal revenue function for your app Newton
(Note. if the market demand is p = a-bq; then the marginal revenue function is MR(q) = a-2bq).
Findthe profit-maximizing output q*and price p*.
(c) What is the elasticity of demand at p*? Denote the elasticity at p*by.png”>. Show that the Lerner Index (Price Markup).png”>is equal to.png”>.
Suppose now another new app comes out to the market called Super NewtonTM. Not only Super Newton allows the user to calculate the best force and trajectory of the throw of a Poke Ball, but also it provides the user the exact timing of throwing; hence, Super Newton gives a higher chance of catching a Pokémon than Newton does. After this new app is introduced to the market, the demand of Newton drops 50% at each price level.
(d) Derive the new market demand function and new marginal revenue function for Newton.?
(e) Find the new profit-maximizing output q*and price p*: Calculate the new Lerner Index.png”>.