Question: 1) Consumers are uniformly distributed along a unit-length road. An incumbent gas station is located at the middle of the road. Soon, two identical gas

1) Consumers are uniformly distributed along a unit-length road. An incumbent gas station is located at the middle of the road. Soon, two identical gas stations selling gasoline at the same price enter the market and set up shop on both ends. The consumer's transportation cost per unit-length is c.

a) What proportion of the consumer market is controlled by the incumbent and entrants? [3 marks]

b) The entrants are now allowed to relocate anywhere they want on the 1-kilometre road. However, the incumbent remains at the middle. Assuming that the relocation cost is zero, where would the entrants relocate to and what is their market share? [4 marks]

c) Assuming that the incumbent is also free to relocate to anywhere on the road and the relocation cost is zero. Would the incumbent and entrants set up shop in the middle of the road? Explain whether this configuration constitutes a Nash equilibrium. [3 marks]

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