In the cloth industry, assume the following:Q=S[1/n-b(P-P )], where Q represents
ID: 1223662 • Letter: I
Question
In the cloth industry, assume the following:Q=S[1/n-b(P-P )], where Q represents sales by an individual firm, s = total sales, n = Number of firms. Fixed costs = 100 dollars, Marginal cost = 5, Total sales in an industry = 50 units, Average price for a unit of cloth = 30, assume all firms are subject to the same demand and costs and b = 1/10
A) Derive the number of firms that exist in this market in equilibrium.
B) Now assume that firms in this industry are allowed to trade (export and import cloth across borders). This means that the firms do not have to produce in both countries and can thus make use of economies of scale. If the size of the market triples as a result, how many varieties of products are available in the market?
Explanation / Answer
a) Total cost linear equation: C = F + cQ
Total cost is equal to the sum of fixed costs (F) and variable costs cQ. Note that the parameter cis constant marginal cost.
Average cost are: AC = F/Q + c
Also, Q = A - BP,
then by simple algebra - A = Q + BP.
The inverse linear demand curve is P = A/B - Q/B. MR from this is MR = (A -2Q)/B. Substitute in for A, MR = (Q + BP- 2Q)/B = (BP - Q)/B,
therefore MR = P - Q/B
Given demand curve: Q=S[1/n-b(P-P )]
Each firm takes P as exogenous. We can rewrite the firm' demand curve
as: Q= (S/n + SbP ) -SbP
the firm's marginal revenue can be written as: MR = P - Q/Sb ( as explained above)
Profit maximization requires the equality of MR and MC, therefore:
P - Q/Sb = c,
which rearranged leads to :
P = c + Q/(Sb),
but with each firm charging the same price then Q is an equal share of the market, S/n, thus: P = c + 1/(bn)
5 = 5 + 1/ (1/10 * n)
1 = 10/n
n = 10
B) With international trade the size of the market increases. This enters in the average cost equation as S. An
increase in S shifts the average cost curve downwards thus lowering the price of the good while increasing the
number of viable firms. The greater the number of firms the more the number of differentiated products, thus
international trade provides consumers with greater variety and lower prices.
Now, S' = 150
P= AC
30 = 100n/150 +5
30 = 2n/3
n = 45