Consider the facemask industry which is a monopolistically competitive industry in Home country. First, we assume all fi

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Consider the facemask industry which is a monopolistically
competitive industry in Home country. First, we assume all firms
have the same cost function for producing masks: 𝐶 = 𝐹 + 𝑐𝑄, with
fixed cost 𝐹 = $15,000 and the marginal cost 𝑐 = $20 per package of
masks. Moreover, for a monopolistically competitive firm, we assume
the demand in Home is given by 𝑄 = 𝑆[ 1/𝑛 − 𝑏(𝑃 − 𝑃̅)] where Q is
an individual firm’s sale, S is the total sales of the industry, n
is the number of firms in the industry, P is the price charged by
the firm itself, and 𝑃̅ is the average price charged by its
competitors. 𝑏 represents the intensity of competition and is
assumed to be 0.6.
a) List two conditions to solve the optimal price of the
monopolistically competitive firm. Without trade, the total sales
of facemasks in home are 324,000 packages, calculate the
equilibrium number of firms and equilibrium price and quantity in
Home country.
(b) Consider a world with four symmetric countries. In other
words, the facemask industry in other three countries is exactly
the same as Home country, although they produce different variety
of facemasks. Now assume countries have free trade among them. What
is total number of firms in the facemask industry in the world? How
trade affects the price and output of each firm?
(c) Following (b), the outbreak of Covid-19 dramatically
increased the world demand of facemasks, so the world market size
of facemasks increased by 25 times. Compared with the price in part
(b), does the rising demand of facemasks increase the price of
facemasks and why?