Question

In: Economics

required info: Question 1: Rebel without a cause Two drivers speed head-on toward each other and...

required info:

Question 1: Rebel without a cause Two drivers speed head-on toward each other and a collision is bound to occur unless one of them deviates at the last minute. If both deviate, everything is okay (they both win 1). If one deviates and the other does not, then it is a great success for the driver with iron nerves (he wins 2) and a great disgrace for the deviating driver (he loses 1). If both drivers have iron nerves, disaster strikes (both lose 2).

Question 2: Simultaneous quantity choice Two firms F1 and F2 produce a homogeneous product and compete on the same market. The market price is described by the inverse demand curve P = 11 − 2Q, where Q is total industry output and P is the market price. To keep things simple, suppose that each firm can produce either 1 or 2 units (these are the only possible choices of production). Further suppose that both firms have a constant marginal cost equal to 2, so that the total cost of firm i = 1, 2 producing quantity qi ∈ {1, 2} is given by C(qi) = 2qi . Further suppose that firms’ production choices are simultaneous.

question to be answered:

Question 3: Sequential quantity choice Now consider exactly the same firms, inverse demand function, cost function, and quantity choices as above. In contrast to before, however, suppose that firm 1 chooses its quantity q1 first, then firm 2 observes firm 1’s quantity choice and chooses its quantity q2.

1. Draw the game tree for this game (using the payoffs you found above).

2. What is Firm 1’s strategy set? What is Firm 2’s strategy set? (For F2, bear in mind that a strategy is a complete contingent plan for how to play the game!)

3. Using backward induction, predict the outcome of this game. Discuss your answer. Does moving first benefit Firm 1?

Solutions

Expert Solution

Calculating the payoffs of this choice of units available to Firm 1 and Firm 2,

The profits earned from the choice of the units of goods produced will be the payoffs of both the firms,

Now, profits are calculated as TR - TC.

Market inverse demand funtion given as P = 11 - 2Q

TR = P.Q = (11 - 2Q).Q = 11Q - 2Q2

TC = 2Q

Profits = 9Q - 2Q2

Profits for both the firms when Q = 1, Profit = 7

Profits when Q = 2, Profit = 10

___________________________________________________

(a) From the above payoffs, the game in the form of tree will be as

___________________________________________________

(b)  

Both the firms would want to maximise their profits given all the variables.

So, Firm 1's strategy set will be to choose, 2 units of the quantity to produce.

And Firm 2 would also want to produce 2 units. Hence, strategy set will be to choose 2 units.

___________________________________________________________

(c) Since, both the firms would wants to maximise their profits, they both would want to produce 2 units of the good.

The nash equilibria for the following game would be ( 2 units, 2 units) where the outcomes of both the firms are maximum.

But when firm 1 gets to choose first, it would want to maximise its outcome and would try to make its market share higher than the other firm. This will be possible when Firm 2 would choose to produce 1 unit. Thus, to maximise its profit Firm 1 would choose 2 units and want Firm2 to Choose 1 unit and expect the outcome to be (10, 7).

But when, firm 1 would choose 2units and maximise its profits, firm 2 would want to compete neck to neck with firm 1 and would also try to maximise the profits. And hence choose 2 units only making the equilibrium output to again turn out to be (2 units, 2 units).

Thus, sequential choice and benefit of first choice to firm 1 does not change the outcome.

________________________________________________________


Related Solutions

Two protons, each having a speed of 0.910c in the laboratory, are moving toward each other....
Two protons, each having a speed of 0.910c in the laboratory, are moving toward each other. a) Determine the momentum of each proton in the laboratory in GeV/c. b) Determine the total momentum of the two protons in the laboratory GeV/c. c) Determine the momentum of one proton as seen by the other proton GeV/c.
Two titanium spheres approach each other head-on with the same speed and collide elastically. After the...
Two titanium spheres approach each other head-on with the same speed and collide elastically. After the collision, one of the spheres, whose mass is 200 g, remains at rest. (a) What is the mass of the other sphere? (b) Assume that the initial speed of each sphere was 2.2 m/s. What is the speed of the two-sphere center of mass?
a. Two air-track gliders with equal and opposite speeds of 10.00 cm/s head toward each other...
a. Two air-track gliders with equal and opposite speeds of 10.00 cm/s head toward each other and collide, sticking together. Glider A, coming from the left, has a mass of 250.g, while glider B, coming from the right, has a mass of 500. g. What is the final velocity of the stuck-together pair, and in which direction? (The gliders are constrained to move only along the x-axis. Ignore friction.) Show your work completely b. Using the values above (both given...
In an experiment, two protons are shot directly toward each other, each moving at half the...
In an experiment, two protons are shot directly toward each other, each moving at half the speed of light relative to the laboratory. a What speed does one proton measure for the other proton? b What would be the answer to part (a) if we used only nonrelativistic Newtonian mechanics? c What is the kinetic energy of each proton as measured by an observer at rest in the laboratory? d What is the kinetic energy of each proton as measured...
Two trains, each having a speed of 30 km/h, are headed at each other on the...
Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 67 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the...
1. there are two types of drivers. Speed racers with %5 chance of accident per year...
1. there are two types of drivers. Speed racers with %5 chance of accident per year and low racers with %1 chance of accident per year. There are twice more speed racers than low racers and the cost of each accident is $12000. Assume that the pre-accident income for both types of drivers is $12,000 and that they all have utility function U(c)=√??. Also suppose, that the insurance company is offering full insurance (i.e. $12,000 payout in case of an...
Two 1.0 metric ton cars crash into each other. Both collide head-on, and each was travelling...
Two 1.0 metric ton cars crash into each other. Both collide head-on, and each was travelling 27 mi/hr when the collision occurred. The wreckage is at rest after the collision. How much thermal energy was gained by the cars and road in the collision? (in case you are worried, these were driverless vehicles with no passengers inside! Recall that a 100 W lightbulb uses up 100 Joules of energy in 1 second. If there was a way that the thermal...
At a county fair, two children ram each other head on while riding on the bumper...
At a county fair, two children ram each other head on while riding on the bumper car attraction. Jill and her car, traveling left at 3.50 m/s, have a total mass of 325 kg. Jack and his car, traveling to the right at 2.00 m/s, have a total mass of 290 kg. Assuming the collision to be elastic, determine their velocities after the collision.
. Two masses travel toward each other across a horizontal, frictionless surface. They collide, resulting in...
. Two masses travel toward each other across a horizontal, frictionless surface. They collide, resulting in 100 Joules of kinetic energy being lost. Below is a list of the known quantities. Mass#1 = 5.00 kg and has an initial velocity of 10.0 m/s to the right and a final velocity of 3.00 m/s to the right. Mass#2 = unknown and has an initial velocity of 4.00 m/s to the left and a final velocity that is unknown. What is the...
Two trains (on separate tracks) travel toward each other, the first at 60.0 km/s and the...
Two trains (on separate tracks) travel toward each other, the first at 60.0 km/s and the second at 40.0 km/s. Both turn on their whistle, the first one emitting a frequency of 200 Hz and the second one emitting a frequency of 220 Hz. What frequencies do they each receive if the speed of sound in air is 330 m/s? Hint: Draw a diagram or do this one in steps. Is the source or the observer moving?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT