Question

Consider the model of intra‐industry trade with increasing retu rns to scale and love of variety...

Consider the model of intra‐industry trade with increasing retu

rns to scale and love of

variety studied in class.

Consider a single country in isolation. Firms in this country p

roduce differentiated varieties.

The demand for each vari

ety is the following:

q(p) = S * [ (1/n) ‐ b* ( p – Pm ) ]

In this expression, p is the price of each variety. The average

industry price is Pm. The market

size is

S

= 100. The responsiveness of consumers' demand for this variety

to price deviations

from the average market price is given by a constant,

b

= 1.

Each firm's average total cost is given by

ATC = q=F/q+c

where marginal cost is constant

at

c

= 10 and fixed cost is

F

= 20.

a. Find an expression for each firm's average cost as a functio

n of the number of firms,

n

.

Graph this with cost on the vert

ical axis and the number of fir

ms on the horizontal axis.

b. Write the expression for a fir

m’s price as a function of the

number of firms. Graph this the

price on the vertical axis and t

he number of firms on the horiz

ontal axis.

c. Solve for the equilib

rium number of firms,

n.

d. True or false? If the market size quadruples to

S= 400, for instance, due to trade, the

number of firms will also quadr

uple. (Explain your answer.)

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