Suppose a Canadian lumber company has a world monopoly on lumber. That is, imagi

Question

Suppose a Canadian lumber company has a world monopoly on lumber. That is, imagine that all lumber purchased by U.S. citizens is bought from this one Canadian lumber company. The inverse demand curve for U.S. consumers (note that “consumers” means any person or business that wants lumber, so construction firms are included) is p(Q) = 10q^(-1/3) and the lumber company has a constant marginal cost of 2.

a. Show that p = (3/2)m where p is price and m is marginal cost. (Hint: Lerner Index Rule)

b. (2 pts) Define p1 and Q1 as the price and quantity when marginal cost = $2, and p2 and Q2 as the price and quantity when marginal cost = $1.98. Find p1, Q1, p2, and Q2 (use a calculator and round to 2 decimals if necessary). Show that if the U.S. government subsidizes the Canadian lumber company by $0.02 per unit, US total surplus will actually increase!

Explanation / Answer

(p - m)/p = -1/Ed

q = 1000/p3

Ed = (dq/dp)*(p/q) = (-3000/p4)*p4/1000

= - 3

(p - m)/p = 1/3

3p - 3m = p

p = (3/2)m

b) p1 =(3/2)*2 = 3

q1 = 1000/27 = 37.03

p2 = (3/2)*1.98 = 2.97

q2 = 38.17

Total surplus will increase by (38 - 37) = 1

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.