F

We operate a business with no competitors where our total costs are given by the function: (I (x) = FC + 5::2 Where 1: represents our output and F6 is a xed cost of production. We face an inverse market demand curve of: Mac) = 1000 1th Where 3?: is the price. a) Assuming we face no competition, derive the profit maximising price and quantity {3 marks] b} How much profit does your company earn at this price and quantity combination? {3 marks] c) Assuming that individual demand functions satisfy all conditions required for aggregation as a representative consumer, what is the level of consumer surplus in this market when you are the only supplier? {3 marks} Now suppose a competitor enters the market which has exactly the same cost structure as your firm and supplies an identical product. Assuming you simultaneously compete in quantities (you both choose your optimal quantity simultameously}, where the new inverse demand function is: p(X) = 1000 10X where X = x1 + x; d} Derive the reaction function for your rm (firm 1) and by symmetry also for rm 2 {3 marks} 9) Plot these on a graph with rm 1 on the horizontal axis aid rm 2 on the vertical. Indicate the equilibrium outputs for both rms {2 marks) f) In the equilibrium where you compete in quantity, how much does each rm produce? What is the market price? {4 marks) g} Assuming again that the conditions in part 0} still hold, what is the consumer surplus in this market now that there is a second supplier? {3 marks} h} How high would fixed costs need to be to dissuade the new entrant from entering, but where you would still be happy to remain as the sole producer? {4 marks]