Q: Demand in an competitive industry is given by P=84-Q. Each of the six identical firms in this industry have TC=3q2. How much profit does 1 firm earn?
A: To determine profits we need to know the price and how many units each firm produces. The price is determined by the intersection of supply and demand. Demand is given but we need to find supply. Market supply is the horizontal sum of the firms' MC curves. Since TC=3q2, MC=6q. Because the firm will set MR=MC and MR=P for a competitive firm we have P=6q or q=P/6. Thus Market Q=q+q+q+q+q+q=P/6+P/6 +P/6+P/6 +P/6+P/6 =P. SO the supply curve is P=Q. Now we can find the market price and quantity be setting supply and demand equal. This gives 84-Q=Q or Qe=42 and Pe=42. Since there are 6 firms each makes 42/6=7 units. Hence profits are 42*6-3(6)2 = 144 .