Final answer:
The Nash Equilibrium for two hot dog vendors who are competing on a linear street where customers are uniformly distributed is option c: (1/4, 3/4), as this positioning prevents either vendor from unilaterally capturing more customers by relocating.
Step-by-step explanation:
The question at hand involves finding the Nash Equilibrium location for two competing hot dog vendors on a street. The customers are uniformly distributed along the street, which is modeled as a line segment from 0 to 1. The goal of the vendors is to position themselves in such a way that they maximize the number of customers nearest to them, thus optimizing their sales.
To find the Nash Equilibrium, we analyze the options given. In a Nash Equilibrium, no vendor can unilaterally change its location to gain more customers, assuming the other vendor's location is fixed. The equilibrium is thus option c: (1/4, 3/4). If one vendor is at 1/4, and the other is at 3/4, they split the street into three equal segments, maximizing coverage and ensuring no vendor benefits from moving. Both options a. (0, 1) and (1, 0) do not form an equilibrium because each vendor could move closer to the center to capture more customers. Option b. (1/2, 1/2) is not an equilibrium because one vendor would benefit by moving slightly away from the midpoint, capturing over half the street's customers.
Understanding the concept of equilibrium price and quantity is essential for this economic question. When trade is allowed between countries, the equilibrium price and quantity adjust to a level where the quantity demanded by consumers equals the quantity supplied by producers. To determine these new levels of equilibrium, one would compare the supply and demand curves of both countries and find the point at which they intersect when open trade is established.