Consider the washing machine industry in America. There are many differentiated brands in the industry and they are all

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Consider the washing machine industry in America. There are many
differentiated brands in the industry and they are all
monopolistically competitive. For all these brands, manufacturing
each additional washing machine costs $300 while setting up a
manufacturing plant costs $1 billion. New brands can enter freely
if they deem profitable and existing brands can exit the market
when they do not find it profitable to continue producing. In
total, the industry sells 32 million washing machines every
year.
A.) What is the average cost of producing Q washing
machines? How does the average cost of producing washing machines
change with number of brands in the industry? Derive the
relationship and provide economic intuition for it.
B.) When a washing machine is sold, the additional revenue
that a firm in the industry makes is P − Q/bS where P denotes the
price at which the washing machine is being sold, Q denotes the
quantity, S denotes the market size, and b denotes the sensitivity
of demand with respect to price. Provide the definition markups
charged by producers. How do markups change when the number of
firms in the industry increases? Derive the relationship and
provide economic intuition for it.
C.) Suppose b = 1/1000, how many firms operate in the
industry in equilibrium and what markups do firms charge when
selling washing machines? Show your answers through calculations
and through a suitable diagram.