There are H consumers and n firms. The demand of each consumer is
x(p) = 1 - p and the cost function of each firm is c(y) = (y)^2/2.
1. Compute the competitive equilibrium price, quantity and the consumers' and producers' surplus as functions of H and n.
2. Define social welfare as the sum of consumers' and producers' surplus and establish a relation between social welfare and H and n. What happens when H = 10 and n tends to infinite?