**Industrial organization**

- The critical discount factor to sustain collusion using grim punishment strategy if detection for diversion requires two periods.

P=300-Q

MR=10

P= (300-Q)-10)Q

dP/dQ= 290-Q

Q=290 P=10

In this case, at equilibrium point p1=p2=10

If we assume that both firms charge the same prices, then they will be an evenly market split.

- Expected value of the critical discount factor if detection requires three periods

The value of the critical discounting factor will not be higher since the high-cost firm makes zero profits, and also the lower cost firm profit will be;

(p1-c1)q1=(10-6)(5000-200(10)=12000

- Effect of the value of critical discount factor if the firms increase to five

If the number of firms increases to 5, the discounting factor will be lower since there is increased competition in the market. There are new entrances which possess more threat to existing firms calling for change on production strategies, and hence the outcome will not be efficient.