Intra-Industry Trade Consider the model of intra-industry trade with increasing returns to scale and love of variety studied in class. Consider a single country in isolation. Firms in this country produce differentiated varieties. The demand for each variety 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 function of the number of firms, n. Graph this with cost on the vertical axis and the number of firms on the horizontal axis. b. Write the expression for a firm's price as a function of the number of firms. Graph this the price on the vertical axis and the number of firms on the horizontal axis. c. Solve for the equilibrium number of firms, n. = 400, for instance, due to trade, the d. True or false? If the market size quadruples to S number of firms will also quadruple. (Explain your answer.)
Intra-Industry Trade Consider the model of intra-industry trade with increasing returns to scale and love of variety studied in class. Consider a single country in isolation. Firms in this country produce differentiated varieties. The demand for each variety 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 function of the number of firms, n. Graph this with cost on the vertical axis and the number of firms on the horizontal axis. b. Write the expression for a firm's price as a function of the number of firms. Graph this the price on the vertical axis and the number of firms on the horizontal axis. c. Solve for the equilibrium number of firms, n. = 400, for instance, due to trade, the d. True or false? If the market size quadruples to S number of firms will also quadruple. (Explain your answer.)
Chapter35: International Trade Restrictions
Section: Chapter Questions
Problem 11E
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![Intra-Industry Trade
Consider the model of intra-industry trade with increasing returns to scale and love of
variety studied in class.
Consider a single country in isolation. Firms in this country produce differentiated varieties.
The demand for each variety 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 function of the number of firms, n.
Graph this with cost on the vertical axis and the number of firms on the horizontal axis.
b. Write the expression for a firm's price as a function of the number of firms. Graph this the
price on the vertical axis and the number of firms on the horizontal axis.
c. Solve for the equilibrium number of firms, n.
=
400, for instance, due to trade, the
d. True or false? If the market size quadruples to S
number of firms will also quadruple. (Explain your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeca2974-444a-4f04-907d-5f8874d40e92%2Fe3522fd8-bac7-4751-9f57-6d48f67c8a2c%2F0zcno7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Intra-Industry Trade
Consider the model of intra-industry trade with increasing returns to scale and love of
variety studied in class.
Consider a single country in isolation. Firms in this country produce differentiated varieties.
The demand for each variety 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 function of the number of firms, n.
Graph this with cost on the vertical axis and the number of firms on the horizontal axis.
b. Write the expression for a firm's price as a function of the number of firms. Graph this the
price on the vertical axis and the number of firms on the horizontal axis.
c. Solve for the equilibrium number of firms, n.
=
400, for instance, due to trade, the
d. True or false? If the market size quadruples to S
number of firms will also quadruple. (Explain your answer.)
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