Biology Forums - Study Force

Consider a weapons producer that is selling guns to two countries that are at war with one another. Guns can be produced at a constant marginal cost of $10 per gun. The demand for guns in each of the countries is given by:
      p = 50 - 0.5Q (Country A)
      p = 20 - 0.25Q (Country B)
a.   If the weapons producer can charge different prices to each country, what price and quantity will it sell to each?
b.   If the weapons producer cannot price discriminate, what price and quantity of guns will it sell to each country?
c.   Will the weapons manufacturer make more profit from price discriminating? Briefly explain. Why is it that the manufacturer will likely be able to price discriminate?
d.   Which country will benefit from price discrimination? Which country will be worse off from price discrimination? Explain briefly.
e.   Is the deadweight loss higher under price discrimination or a single-price? Show mathematically.

a.      QA = 40, PA = 30
      QB = 20, PB = 15
b.    Write demand curves as
   QA = 100 - 2p
   QB = 80 - 4p
   Total demand is
   Q = 180 - 6p (for p < 20)
   Write inverse demand:
   p = 30 - Q/6
   MR = 30 - Q/3 = 10 = MC
   Q = 60, p = 20(!)
   But at p = 20, the firm is only selling to country A. The firm is better selling at p = 30 since only country A is buying! On a graph:



NOTE: It's always possible to simply charge the monopoly price to the higher demanders, thereby pricing the low demanders out of the market. The optimal pricing will be based on whether it's more profitable to price out the low demand or price so both types purchase.

c.   Price discriminating is more profitable because the weapons seller can now sell to country B. Countries at war with each other typically don't trade arms, so resale is not a problem.
d.   Country A is indifferent, Country B is better because they can now purchase weapons.
e.   It's easy to see in this case—the DWL to country A is no different. The DWL to country B was 200 w/out price discrimination (they didn't purchase weapons), but with price discrimination it is 50.
   This is a case where price discrimination can actually reduce deadweight loss.