Question

1. (a) Describe all of the competitive equilibria in a market for a single item, with multiple buyers, each with a positive valuation for the item. (b) Now consider a modified market with k identical items and at least k + 1 buyers. Assume that each buyer has a positive valuation for the item and only wants a single item. Describe all of the competitive equilibria in such a market.

Answer 1

(a). Competitive equilibrium is a condition in which profit-maximizing producers and utility-maximizing consumers in competitive markets with freely determined prices arrive at an equilibrium price. At this equilibrium price, the quantity supplied is equal to the quantity demanded. In other words, all parties—buyers and sellers—are satisfied that they're getting a fair deal.

when prices are hiked, demand tends to fall and supply rises—and when prices are slashed, demand increases and supply declines.

Eventually, these two forces end up balancing out. The supply and demand curve intersects and a price that suits all parties is reached. Suddenly, what buyers are willing to pay equals what suppliers are willing to sell the goods they produce for.

At equilibrium prices, each agent maximizes his or her objective function subject to his or her technological limitations and resource constraints, and the market clears the aggregated supply and demand for the products in question.

(b). The market consists of many buyers. Any single buyer represents a very small fraction of all the purchases in a market. Due to its insignificant impact on the market, the buyer acts as a price taker, meaning the buyer presumes her purchase decision has no impact on the price charged for the good. The buyer takes the price as given and decides the amount to purchase that best serves the utility of her household.

The market consists of many sellers. Any single seller represents a very small fraction of all the purchases in a market. Due to its insignificant impact on the market, the seller acts as a price taker, meaning the seller presumes its production decisions have no impact on the price charged for the good by other sellers. The seller takes the price as given and decides the amount to produce that will generate the greatest profit.

Firms that sell in the market are free to either enter or exit the market. Firms that are not currently sellers in the market may enter as sellers if they find the market attractive. Firms currently selling in the market may discontinue participation as sellers if they find the market unattractive. Existing firms may also continue to participate at different production levels as conditions change.

The good sold by all sellers in the market is assumed to be homogeneous. This means every seller sells the same good, or stated another way, the buyer does not care which seller he uses if all sellers charge the same price.

Buyers and sellers in the market are assumed to have perfect information. Producers understand the production capabilities known to other producers in the market and have immediate access to any resources used by other sellers in producing a good. Both buyers and sellers know all the prices being charged by other sellers.