Reference no: EM13986073
Consider a strategic setting in which two geographically distinct firms (players 1 and 2) compete by setting prices. Suppose that consumers are uniformly distributed across the interval [0,1], and each will buy either one unit or nothing. Firm 1 is located at 0 and firm 2 is located at 1. Assume that the firms cannot change their locations; they can only select prices. Simultaneously and independently, firm 1 chooses a price p1 and firm 2 chooses a price p2 . Suppose that the firms produce at zero cost and that due to a government regulation, they must set prices between 0 and 6.
As in the standard location game, consumers are sensitive to the distance they have to travel in order to purchase. But they are also sensitive to price. Consumers get a benefit of 6 from the good that is purchased, but they also pay a personal cost of c times the distance they have to travel to make the purchase. Assume that c is a positive constant. If the consumer at location x ∈ [0, 1] purchases from firm 1, then this consumer’s utility is 6 − cx − p1 . If this consumer instead purchases from firm 2, then her utility is 6 − c(1 − x) − p2 . If this consumer does not purchase the good, her utility is 0.
(a) Suppose that for given prices p1 and p2, every consumer purchases the good. That is, ignore the case in which prices are so high that some consumers prefer not to purchase. Find an expression for the “marginal consumer” who is indifferent between purchasing from firm 1 or firm 2.
Denote this consumer’s location as x*( p1, p2 ).
(b) Continue to assume that all consumers purchase at the prices you are analyzing. Note that firm 1’s payoff (profit) is p1 x*( p1, p2 ) and firm 2’s payoff is p2[1 − x*( p1, p2 )]. Calculate each firm’s best response as a function of the other player’s strategy. Also graph the best-response functions for the case of c = 2.
(c) Find and report the Nash equilibrium of this game for the case in which c = 2.
(d) As c converges to 0, what happens to the firms’ equilibrium profits?
(e) What are the rationalizable strategies of this game for the case in which c = 2?
(f) Find the Nash equilibrium of this game for the case in which c = 8.
|
Cause our balance of payments issues
: High spending and low savings in the U.S. helps cause our balance of payments issues. President Carter took us off the gold exchange standard. Most economists support a return to fixed exchange rates, such as the gold standard. If the U.S. government..
|
|
What is balls velocity just before it strikes the floor
: What is in m/s its velocity just before it strikes the floor? What is in m/s its velocity just after it leaves the floor on its way back up?
|
|
What is the incumbent first-mover advantage
: or this sequential entry game, the incumbent firm can make an advertising expenditure (i.e., sunk cost) to potentially deter entry. First, please determine the entrant's optimal decision if the incumbent advertises and if the incumbent does not ad..
|
|
Create an original example to demonstrate how an individual
: Create an original example to demonstrate how an individual or firm acting out of self interest
|
|
What happens to the firms equilibrium profits
: Consider a strategic setting in which two geographically distinct firms (players 1 and 2) compete by setting prices. Suppose that consumers are uniformly distributed across the interval [0,1], and each will buy either one unit or nothing. Firm 1 is l..
|
|
Explain the instances and the importance of a financial
: In your opinion, which of the given analyses is the most beneficial one for decision-makers: Analysis of balance sheet, Analysis of income statement, Analysis of statement of cash flow. Cite two instances where your chosen analysis stands more benefi..
|
|
What rotation period will provide an earth-like gravity
: An astronaut orbits planet X in his spaceship. To remain in orbit at above the planet's center, he maintains a speed of What is the mass of planet X? Note: the constant of universal gravity (G) equals 6.674 Af- 10 -11 N m2/kg2.
|
|
What is the bearings impact speed
: If a bearing needs 4.50s to solidify enough for impact, how high must the tower be? What is the bearing's impact speed?
|
|
Statistical discrepancy what is the capital account
: What is the current account for the economy below? If there is no statistical discrepancy what is the capital account?
|