Consider two countries, A and B each with a monopolist that owns the only coal m
ID: 1139135 • Letter: C
Question
Consider two countries, A and B each with a monopolist that owns the only coal mine in the country, and it produces coal. Let firm 1 be the one located in country A, and firm 2 the one in country B. Let qij, i {1,2}, j {A,B}denote the quantity that firm i sells in country j. Consequently, let qi = qiA + qiB be the total quantity sold by firm i {1, 2} and let qj = q1j + q2j be the total quantity sold in country j {A,B}. The demand for coal in countries A and B is given respectively by,
pj =90qj, j{A,B},
vi(s1,...,sn) = csi + sj.
and the costs of production for each firm is given by,
ci(qi) = 10qi, i {1, 2}.
(a) Assume that the countries do not have a trade agreement and, in fact, imports in both countries are prohibited. This implies that q2A = q1B = 0 is set as a political constraint. What quantities q1A and q2B will both firms produce?
Explanation / Answer
Answer
a) A firm produces that quantity at which MR = MC i.e. Marginal Revenue = Marginal Cost
For Firm A
As it is given that q1B = 0
Marginal revenue = dTR/dq1 = d(p1q1)/dq1 = d(90q1 - q12)/dq1 = 90 - 2q1
MC = d(c1)/d(q1) = 10
Hence , 90 - 2q1 = 10 => q1 = 40
Similarly as above
For Firm B
As it is given that q2A = 0
Marginal revenue = dTR/dq2 = d(p2q2)/dq2 = d(90q2 - q22)/dq2 = 90 - 2q2
MC = d(c2)/d(q2) = 10
Hence , 90 - 2q2 = 10 => q2 = 40
Hence,Both firm 1 will produce q1A = 40 and Firm 2 will produce q2B = 40