Question

TV Azteca and Televisa control a large share of the Mexican multimedia market. As a manager of TV Azteca, you choose the number of broadcast hours of television programming of your hit shows (Lo que callamos las mujeres, Ventaneando, Hechos, Venga la Alegria, ...) to air 1 hour before your competitor, but Televisa does not have any way to know your broadcast hours before choosing their own broadcast hours. Advertisers consider all broadcast hours to be identical. The demand for broadcast hours is Q = 1.60 – 0.20 P; TV Azteca’s costs are C1(Q1) = 3Q1; and Televisa’s costs are C2(Q2) = 4Q2. Would it be mutually profitable for the companies to collude by setting TV Azteca’s and Televisa’s outputs to 0.35 and 0.15? Can TV Azteca trust Televisa to collude? Can Televisa trust TV Azteca to collude?

Answer 1

Yes, collusion is always profitable because playing alone in the market would lead either price competition or any other type of competition which may become unprofitable for both the firms. This may make either of the firms even leave the market.

it is given that

Q = 1.60 – 0.20 P;

TV Azteca’s costs are C1(Q1) = 3Q1; and

Televisa’s costs are C2(Q2) = 4Q2.

if they both collude by setting their quantity Q1 = 0.35 and  Q2 =0.15

then the total quantity supplied in the market will Q =Q1+Q2

so, Q = 0.50

Putting the value of Q in demand function for the price of television

0.50 = 1.60 - 0.20*p

p =(1.60-0.50 ) /0.20

p = 1.10/0.20

p = 5.5  

for the profit of firm 1

the total cost of firm1 = 3* 0.35 = $1.05

total revenue = p*q = 5.5 *0.35 =$ 1.925

profit = total revenue - total cost

profit = 1.925-1.05 = $0.875

for the profit of firm 2

total cost = 4*0.15 = 0.6

total revenue = 0.15 *5.5 = 0.825

profit = 0.825 - 0.6 =$ 0.225

it can be clearly seen that profit of firm 2 is less than firm 1 on the quantity is agreed by them . With less quantity firm 2 is getting less profit as compared to firm1 , this may induce the firm to break the agreement . This may happen in the case of firm1 also to increase the revenue they can increase the quantity . so, we can both of them can break the trust of each other .