Can you please answer the following question as soon as possible!!~~ Thank you!

(a) Given the profits of two firms in a duopoly with a choice of price per cup of coffee as below: Ruckin $20 per cup $30 per cup Sunbucks $20 per cup ($50m, $50m) ($100m, $30m) $30 per cup ($30m, $100m) ($80m, $80m) (Note: m for million dollars) (i) Show that ($30 per cup, $30 per cup) is not a Nash Equilibrium in this game. (2 marks) (ii) If the two firms can make an agreement to maintain a high price ($30) together, and an enforceable punishment of SY million dollars is required to be transferred to the other company if one company lowers the price to $20 per cup instead. Propose a possible size of SY, write down the new payoff matrix and show that now ($30 per cup, $30 per cup) is a Nash Equilibrium. (4 marks) (b) Suppose in a university far from the city center, Ruckin is the only coffee shop. Its marginal cost of producing a cup of coffee is constant $10, while there are other substantial costs independent of the number of cups of coffee sold. Originally, Ruckin sells the coffee at $30 per cup. Now, it is considering a membership pricing system where every customer needs to be a member and pays a membership fee, and then for each cup of coffee, each customer can pay a price lower than before. (i) Under what conditions a consumer will increase their consumption of coffee in this store under the new pricing scheme? Under what conditions a consumer will reduce their consumption of coffee in this store under the new pricing scheme? Explain your answers. (Hint: customers generally have a diminishing marginal benefit and thus a lower reservation price for the last unit when more cups of coffee are consumed.) (4 marks) (ii) What are the pros and cons for Ruckin to set a high membership fee? What are the pros and cons for Ruckin to set a low new (marginal) price of a cup of coffee? Explain your answers