Final answer:
The market supply and demand curves are found by summing the individual producer's supply curves and consumer's demand curves, respectively. The equilibrium price and quantity, and the consumer and producer surpluses, are then found by integrating under these curves.
Step-by-step explanation:
To find the market supply curve, q = S(p), we add the quantities supplied by each producer at each price. Adding Producer 1's supply curve and Producer 2's supply curve gives us q = S1(p) + S2(p) = Sp + (q - 2 + 2p). After simplifying, the market supply curve is q = 2Sp - 2.
Similarly, the market demand curve, q = D(p), is obtained by adding the quantities demanded by each consumer at each price. Adding Consumer 1's demand curve and Consumer 2's demand curve gives us q = D1(p) + D2(p) = (5 - p) + (3 - p), which simplifies to q = 8 - 2p.
The market equilibrium is found by setting the market supply curve equal to the market demand curve and solving for p. This yields p = 5, which is the equilibrium price. Substituting p back into either the supply or demand market equation will give the equilibrium quantity, q. The consumer surplus and producer surplus are found by evaluating the areas under the demand and supply curves, respectively, up to the equilibrium price. Consumer surplus is the area under the demand curve, up to the price p = 5. It represents the additional benefits consumers receive because they would be willing to pay more for the goods than they actually have to. Producer surplus is the area above the supply curve, up to p = 5, and represents the additional benefits producers receive because they are able to sell their goods for more than they would be willing to accept.
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