The Pricing Strategy Assume

International Economics
Problem 1
Part 1
The Pricing Strategy
Assume that firm I generates profits as given by :
⫪i=[P(Yi)-C]Yi
You can maximize the profit output with respect to Yi
Let Qj be the profits generated by other firms.
d ⫪i
dYi =P(Y)-c +yi
dPdY
dQdYi =0
But dY
dYi =1 and dYj
dYi =0
Hence the reaction curve for the firm is P(Y) +Qi
dP
dY =c
Since there equal sizes of firms which in n number,
Yi= Y
n ,Thus
P(Y)= YdP
ndY =c
And P−c
p = 1
n
YdP
PdY = −1
nED
But Ed =nED
Proof of Profit Maximizing Price
Consider either a linear or isoelastic demand curve.
Assume that the demand curve is given by;
Log Yi=σ -b log P +βlog q

But q is the perceived sales that is made i.e demand funcrion.
Yi is the actual total demand
Beta is positive i.e β>0 when the network effect is a negative.
Yi=q at the equilibrium point,Hence;
Log Yi = σ
1−β - b
1−β log P
b
1−β log P= σ
1−β –log Yi
At the equilibrium, Marginal Cost =Marginal revenue.
Hence P= σ
σ−1MC= σ
1−σ Yiβ
Part 2
Consider The total return to be Yi
You will realize that at a positive beta of β>0,the network effect is
equal to a negative, hence the returns Yi would be low.
But B<1 of a kind of an isoelastic demand curve.
Hence at B<1, the elastic demand curve can make sense as the
marginal revenue is equal to the marginal.Yi is at its optimal level
Problem 2.
Average cost of an individual firm is the cost per unit of inputs
during production.
For a higher output to be achieved in the short-run,a firm have to
use more labor and more inputs to facilitate the production.

However higher implementation of inputs during production
increases the overall total cost i.e. cost is directly proportional to
the level of inputs as expressed below ;
C= F(L,w,r,e.t.c) i.e. Cost being a function of inputs.
Total Cost=Fixed Cost +Average Cost
Total cost is the sum of all cost of inputs of production.
Suppose the total number of inputs is Q,then it means,
TC
Q =TFC
Q = TAC
Q
And
ATC=AFC +AVC
Problem 3
Profit of a firm is the gain a for firm from the sale of goods and
services’ firm will be more satisfied with a higher profits rather
than just a sale.
Profit=Total Revenue-Total Cost.
P=TR-TC
TR –is the total gain for a firm from the sale of a given amount of
goods.
TR=pq
Where p is price is quantity sold.
Average Revenue is revenue per unit of goods sold.
AR= TR
q =p