Question

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.)

Answer 1