03 Jun Question A country produces manufactured goods,
Question
A country produces manufactured goods, whose industry is characterized by increasing returns to
scale, monopolistic competition, and firms that differentiate their products. Firms are symmetric: all
firms have identical cost functions and demand functions given below.
1
Q S b P P
n
TC F aQ
where Q is the quantity demanded when the total industry demand is S , the number of firms in the
industry is n , the average price in the industry is P and the price charged by the firm is P . TC is
the total cost of producing Q units, where F is the fixed cost of production and a is the marginal
cost of production. Assume that S does not change with the price in the industry.
a) Derive an equation that relates average cost AC to n , F , S , and a . That is, derive an
equation with AC on the left-hand side and n , F , S and a on the other. Hint: firm
symmetry implies that each firm charges the same price. (20 pts)
b) Derive an equation that relates marginal revenue MR to P , n and b . Hint: use the
demand function to get P as a function of Q .Then, multiply it by Q to get total revenue as a
function of Q. Derive marginal revenue. Then use the demand function again, to substitute
for Q. (30 pts)
c) To maximize profits, firms set marginal revenue equal to ___________________. (5 pt)
d) Given your answers to b) and c) derive an equation that relates P to a , b and n . (10 pts)
e) Sketch the equations from a) and d) on a graph with the number of firms n on the X-axis
and the average cost and price on the Y-axis. (10 pts)
f) Suppose the country opens to trade, which leads to a larger market size, S . Show the effect
of this on your graph from e., labeling the new price p o and the new number of firms n o .
Clearly label any curves that shift, and in which direction they shift. (20 pts)
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