Question

A weapons producer sells guns to two countries that are at war with each other. The guns can be produced at a constant marginal cost of $20. The demand for guns from the two countries can be represented as:

Q_A = 240 – 2P

Q_B = 180 – P

a. Suppose the weapons producer can group price discriminate, and charge both countries separate prices for guns. What price does the weapons producer charge each country? How many guns does the weapons producer sell to each country? What is the weapon producer’s profit from group price discrimination?  

b. Suppose the two countries resolve their differences and ally to wage war on a third country. Unable to prevent resale across borders, the weapons producer can no longer price discriminate. What is the demand of the aggregate market of countries A and B. What is now the weapons producers’ profit-maximizing price and quantity? What is the weapon producer’s profit in this scenario?  

c. If this weapons producer could perfectly price discriminate, what would be the producer surplus, consumer surplus and deadweight loss be in this market? (A careful graph can help guide you through this part, but it is not required)  

d. Does the weapons producer prefer to perfectly price discriminate, group price discriminate, or set a single price for both countries? Why?  

e. Does group price discrimination make Country A better off, worse off, or have no impact on them? How about Country B?  

Answer 1

A) In country A,

Qa=240-2p

P=120-0.5qa

MRa=120-qa

Profit Maximizing quantity at MR=MC

120-qa=20

Qa=100

Pa=120-0.5*100=70

Profit=(70-20)*100=5000

Country B,

Qb=180-p

P=180-qb

MRb=180-2qb

180-2qb=20

Qb=160/2=80

Pb=180-80=100

Profit=(100-20)*80=6400

Total Profit=5000+6400=11,400

B) Aggregate demand:Q=Qa+Qb=240-2q+180-q=420-3p

Profit=TR-TC=420p-3p^2-20*420+60p=480p-3p^2-20*420

∆profit/∆p=480-6p=0

P=480/6=80

Q=420-3*80=180

Profit=(80-20)*180=10,800

C)When seller do perfect price discrimination,then he charges the willingness tonlay by CONSUMERs for each QUANTITY.

So in that case CONSUMERs surplus will be zero.

Produer surplus=1/2*360*(140-20)=180*160=28,800

Deadweight loss =0( all perfect competition equilibrium surplus goes to seller)

D)As seller is earning highest Profit with perfect price discrimination ,so he will like to do perfect price discrimination.

E) Both country will be better with group pricing compare to perfect price discrimination. Because both countries are getting some CONSUMERs surplus with group pricing compare to perfect price discrimination where CONSUMERs surplus is zero.