Question 3 Krugman Model: Suppose that the elasticity of substitution between vari- eties of a differentiated good iso = 3. The marginal cost of production is c = 2, the fixed cost of operating a business is f = 10. There are two countries, H and F, that initally do not trade. The countries differ only in the size of their economies with EH = 100 EF = 50. All the Krugman model assumptions hold regarding preferences, monopolistic competition, free entry, etc. Starting from the closed economy, answer the following. a. Profits: Using A to denote the level of demand preceived by a typical firm in H, write the typical firm's profit function. Plug in the relevant numbers for the elasticity of substitution, the marginal cost, and the fixed cost, leaving AH as a constant. b. Profit Maximization: Take the derivative of the profit function and solve the first order condition for the optimal price. What is the optimal price charged? c. Free Entry: Now solve for the total number of entrants sold in each country and in the quantity sold in equilibrium in the closed economy case. d. Welfare: In which country is the standard of living higher? Now suppose that the two countries allow for free trade between them. Assume that T = 1. e. Trading pattern: describe the pattern of trade between the two countries? If you were a firm in H what share of your sales would be in F and what share in H? f. Gains from trade: in which country did trade have the biggest impact on welfare? Explain. g. Impact of a tariff: Suppose that F were to put a tariff of 10% (7 = 1.1) on goods from H. How does this tariff affect the price charged to customers in F by H firms and how does this affect the sales revenue of H firms on their export sales to F?
Question 3 Krugman Model: Suppose that the elasticity of substitution between vari- eties of a differentiated good iso = 3. The marginal cost of production is c = 2, the fixed cost of operating a business is f = 10. There are two countries, H and F, that initally do not trade. The countries differ only in the size of their economies with EH = 100 EF = 50. All the Krugman model assumptions hold regarding preferences, monopolistic competition, free entry, etc. Starting from the closed economy, answer the following. a. Profits: Using A to denote the level of demand preceived by a typical firm in H, write the typical firm's profit function. Plug in the relevant numbers for the elasticity of substitution, the marginal cost, and the fixed cost, leaving AH as a constant. b. Profit Maximization: Take the derivative of the profit function and solve the first order condition for the optimal price. What is the optimal price charged? c. Free Entry: Now solve for the total number of entrants sold in each country and in the quantity sold in equilibrium in the closed economy case. d. Welfare: In which country is the standard of living higher? Now suppose that the two countries allow for free trade between them. Assume that T = 1. e. Trading pattern: describe the pattern of trade between the two countries? If you were a firm in H what share of your sales would be in F and what share in H? f. Gains from trade: in which country did trade have the biggest impact on welfare? Explain. g. Impact of a tariff: Suppose that F were to put a tariff of 10% (7 = 1.1) on goods from H. How does this tariff affect the price charged to customers in F by H firms and how does this affect the sales revenue of H firms on their export sales to F?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Question 3 Krugman Model: Suppose that the elasticity of substitution between vari-
eties of a differentiated good is o = 3. The marginal cost of production is c = 2, the fixed
cost of operating a business is f = 10. There are two countries, H and F, that initally do not
trade. The countries differ only in the size of their economies with EH 100 > EF = 50.
All the Krugman model assumptions hold regarding preferences, monopolistic competition,
free entry, etc.
=
Starting from the closed economy, answer the following.
a. Profits: Using A to denote the level of demand preceived by a typical firm in H,
write the typical firm's profit function. Plug in the relevant numbers for the elasticity of
substitution, the marginal cost, and the fixed cost, leaving AH as a constant.
b. Profit Maximization: Take the derivative of the profit function and solve the first
order condition for the optimal price. What is the optimal price charged?
c. Free Entry: Now solve for the total number of entrants sold in each country and in
the quantity sold in equilibrium in the closed economy case.
d. Welfare: In which country is the standard of living higher?
Now suppose that the two countries allow for free trade between them. Assume that
T = 1.
e. Trading pattern: describe the pattern of trade between the two countries? If you
were a firm in H what share of your sales would be in F and what share in H?
f. Gains from trade: in which country did trade have the biggest impact on welfare?
Explain.
g. Impact of a tariff: Suppose that F were to put a tariff of 10% (7 = 1.1) on goods
from H. How does this tariff affect the price charged to customers in F by H firms and how
does this affect the sales revenue of H firms on their export sales to F?
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