2. Reciprocal Dumping with transport costs. Consider two countries, i = {Spain, France}, each having the following inverse demand function: P = 20 – 2(qi+qi) where P is the price in Spain, qi is the quantity sold by the Spanish firm in Spain, and q is the quantity sold by the French firm in Spain. By analogy, the inverse demand function in France is: P 3D 20 — 2(ф2 + q2) where P* is the price in France, q2 is the quantity sold by the Spanish firm in France, and q5 is the quantity sold by the French firm in France. In each country there is only one firm. The cost function of the Spanish firm is: TC = 2(q1 + q2) %3D The cost function of the French firm is: TC* 2(qi + 2) To transport one unit from one country to the other, there is a transport cost t per unit. (There is no transport cost within countries.) 1 a) Start by considering a situation of autarky. Determine the equilibrium quantity and price in Spain. b) Compute total welfare in Spain under autarky (the sum of the consumer and producer surpluses). c) Now suppose that Spain opens up to international trade. Firms compete in quantities. In equilibrium determine (i)the quantity sold by the Spanish firm in Spain; (ii) the quantity sold by the French firm in Spain; (iii) the quantity sold by the Spanish firm in France; and (iv) the price of the good in Spain. Write down all these expressions as a function of t (the transport cost). d) Compute total welfare in Spain for t = 0 and t = 4.
2. Reciprocal Dumping with transport costs. Consider two countries, i = {Spain, France}, each having the following inverse demand function: P = 20 – 2(qi+qi) where P is the price in Spain, qi is the quantity sold by the Spanish firm in Spain, and q is the quantity sold by the French firm in Spain. By analogy, the inverse demand function in France is: P 3D 20 — 2(ф2 + q2) where P* is the price in France, q2 is the quantity sold by the Spanish firm in France, and q5 is the quantity sold by the French firm in France. In each country there is only one firm. The cost function of the Spanish firm is: TC = 2(q1 + q2) %3D The cost function of the French firm is: TC* 2(qi + 2) To transport one unit from one country to the other, there is a transport cost t per unit. (There is no transport cost within countries.) 1 a) Start by considering a situation of autarky. Determine the equilibrium quantity and price in Spain. b) Compute total welfare in Spain under autarky (the sum of the consumer and producer surpluses). c) Now suppose that Spain opens up to international trade. Firms compete in quantities. In equilibrium determine (i)the quantity sold by the Spanish firm in Spain; (ii) the quantity sold by the French firm in Spain; (iii) the quantity sold by the Spanish firm in France; and (iv) the price of the good in Spain. Write down all these expressions as a function of t (the transport cost). d) Compute total welfare in Spain for t = 0 and t = 4.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:2. Reciprocal Dumping with transport costs.
Consider two countries, i =
{Spain, France}, each having the following inverse demand
function:
P = 20 – 2(qi+qi)
where P is the price in Spain, qi is the quantity sold by the Spanish firm in Spain, and q
is the quantity sold by the French firm in Spain. By analogy, the inverse demand function
in France is:
P 3D 20 — 2(ф2 + q2)
where P* is the price in France, q2 is the quantity sold by the Spanish firm in France, and
q5 is the quantity sold by the French firm in France. In each country there is only one firm.
The cost function of the Spanish firm is:
TC = 2(q1 + q2)
%3D
The cost function of the French firm is:
TC*
2(qi + 2)
To transport one unit from one country to the other, there is a transport cost t per unit.
(There is no transport cost within countries.)
1
Transcribed Image Text:a) Start by considering a situation of autarky. Determine the equilibrium quantity and
price in Spain.
b) Compute total welfare in Spain under autarky (the sum of the consumer and producer
surpluses).
c) Now suppose that Spain opens up to international trade. Firms compete in quantities.
In equilibrium determine (i)the quantity sold by the Spanish firm in Spain; (ii) the
quantity sold by the French firm in Spain; (iii) the quantity sold by the Spanish firm
in France; and (iv) the price of the good in Spain. Write down all these expressions
as a function of t (the transport cost).
d) Compute total welfare in Spain for t = 0 and t = 4.
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