In class, we discussed several numerical examples illustrating a rule-based judo strategy. Consider the following adaptation of the game. There are two players in the toothpaste market. P&G, the incumbent, has sufficient capacity to serve all potential toothpaste buyers in its market. Hello Product LLC is a second smaller company considering entering the market. The rule governing competition is one-price- to-all (i.e. price discrimination is not possible). ' Stage 1: Hello Product LLC decides whether or not to enter market. ' Stage 2: Hello Product LLC decides simultaneously on how many buyers to target (N) and on a single price (p) at which to offer its toothpaste to the buyers it is targeting ' Stage 3: P&G (the incumbent) decides on single price at which to offer its own toothpaste to all buyers ' Stage 4: buyers make purchase decisions, and each company serves the buyers that decide to purchase from it. To simplify the analysis, assume there are 2,000,000 potential buyers in the market. each buyer purchases at most one tube of toothpaste from either P&G or Hello Product, and only those buyers targeted by Hello Product have the option of purchasing its toothpaste. Each buyer has willingness to pay of $3 .00 for one tube of P&G toothpaste and of $3 .50 for one tube of Hello Product toothpaste. P&G has a $1.00 unit cost of serving buyers, and Hello Product has a $3.00 unit cost of serving buyers. 4c. (4 points) What is P&G's payo' if it accommodates in Stage 3 (as a function of p and N)? What is P&G's payo'if it ghts in Stage 3 (as a function ofp and N)? IfHello Product wants to ensure P&G accommodates at Stage 3, what condition must the target market size (N) and price (p) combination it selects at Stage 2 satisfy? 4d. (5 points) What target market size (N) and price (p) should Hello Product choose in Stage 2 of the game in order to ensure P&G accommodates and Hello Product maximizes its payoff? Be sure to show your work, including all calculations and conditions used. 4e. (2 points) Using your answer to (4d), show that if Hello Product chooses this target market size (N) and price (p), P&G would be indifferent between accommodating and ghting (i.e. payoff would be the same either way). 4f. (4 points) Based on your answer in (4d), does Hello Product add value (total surplus) by entering the game? If so, how much? If not, how much value does it destroy? Be sure to show your work, including all calculations. Clearly indicate the value (total surplus) of the game without entry and the value (total surplus) of the game with entry. In the game with entry, assume that Hello Product enters with the target market size (N) and price (p) indicated in your answer to (4d). 4g. (3 points) According to the articles, P&G is ghting, not accommodating, Hello Product. Is this outcome consistent with your analysis in 4c-4f'? Why or why not? If not, explain this inconsistency