Roger and Zoë spend their vacation time at a nice cottage that they own in the countryside. Farmer Torti lives next door and normally lets his twelve sheep graze in his field. The sheep eat so quickly that it causes them to burp loudly, a very disruptive sound for Roger and Zoë vacationing next door. Torti is willing to remove sheep from the field when Roger and Zoë are there, but his marginal cost of doing so is $1 for the first sheep he removes, $2 for the second sheep, $3 for the third, etc. Roger and Zoë derive a (combined) marginal benefit of $12 for the first sheep Torti removes, $11 for the second sheep he removes, $10 for the third sheep he removes, etc.

a. Calculate the efficient number of sheep in the field if Roger and Zoë stay at the cottage.

b. Calculate the maximum amount Roger and Zoë would be willing to pay Torti to reduce his sheep to the efficient number.

c. Calculate the minimum amount Torti would be willing to accept to reduce his sheep to the efficient number.

d. Calculate the range of prices per sheep that Roger and Zoë could pay Torti to achieve the efficient number.

The following table shows the number of wins eight teams had during a football season. Also shown are the average points each team scored per game during the season. Construct a​ 90% prediction interval to estimate the number of wins for teams that scored an average of 27 points a game

Determine the upper and lower limits of the prediction interval.

UPL=

LPL=

1.) Consider the discrete Bertrand game described in the Oligopoly lecture notes/video. According to the rules of this game each student selects a number from the set {0,1,2, 3, 4, 5, 6, 7, 8, 9, 10} and is randomly matched with another student. Whoever has the lowest number wins that amount in dollars and whoever has the high number wins zero. In the event of ties, each student receives half their number in dollars. What number would you select if you played this game in our online class? Explain your reasoning.

2) Continue to consider this discrete Bertrand model, but now assume that each student has a constant cost of 5 that is deducted from all payoffs. So whoever has the low number wins their number, minus 5. Whoever has the high number loses 5 total. In the event of a tie, each student wins an amount equal to their number divided by two, then minus five. Find any Nash equilibria in this game. Explain your reasoning. Hint: It is perfectly fine for both players to have losses in equilibrium! There are more than 1 Nash equilibria. (The answer isn't none)

An elevator packed with people has a mass of 1900 kg.

The elevator accelerates upward (in the positive direction) from rest at a rate of 1.95 m/s² for 2.4 s. Calculate the tension in the cable supporting the elevator in newtons.

The elevator continues upward at constant velocity for 8.1 s. What is the tension in the cable, in Newtons, during this time?

The elevator experiences a negative acceleration at a rate of 0.75 m/s² for 2.8 s. What is the tension in the cable, in Newtons, during this period of negative accleration?

How far, in meters, has the elevator moved above its original starting point?

6 similar cars are entered in a race. The cars all have an equal chance of winning and there are no ties. Spectators are invited to complete a single prize ticket with their guesses for which cars will finish in first, second, and third place. The spectators who correctly guess the first, second, and third place finishers will get a small prize.

• How many different ways can a prize ticket be completed?
• What is the probability that a spectator will wins the small prize?
• Suppose spectators are allowed to complete 7 different prize tickets. What is the probability that a spectator, with 7 prize tickets, will wins the small prize?

Every time a certain basketball team wins, the players become over-confident. In that case, their chance of winning the next game is only 35%. Every time the team loses, the players become angry with themselves and more focused. In that case, their chance of winning the next game is 75% Assuming that the team wins the 1st game, calculate the probability they win the 4th game. Find the equilibrium distribution as well.

Every time a certain basketball team wins, the players become over-confident. In that case, their chance of winning the next game is only 35%. Every time the team loses, the players become angry with themselves and more focused. In that case, their chance of winning the next game is 75% Assuming that the team wins the 1st game, calculate the probability they win the 4th game. Find the equilibrium distribution as well.

Every time a certain basketball team wins, the players become over-confident. In that case, their chance of winning the next game is only 35%. Every time the team loses, the players become angry with themselves & more focused. In that case, their chance of winning the next game is 75%. Assuming that the team wins the first game, calculate the probability they win the fourth game. Find the equilibrium distribution as well.

A ball of mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator. The vertical motion of the elevator as it travels up and down is described in the statements below. Indicate for each of the situations described the relation between value of the tension in the cable, T, and the weight of the ball, Mg, or whether one Cannot tell. (Assume that there is no air, i.e., neglect the buoyancy effect of the air.)T > Mg, T < Mg, T = Mg​, cannot tell

1.The elevator is traveling upward and its upward velocity is increasing as it begins its journey towards a higher floor.

2. The elevator is traveling upward at a constant velocity.

3.The elevator is traveling downward and its downward velocity is decreasing as it nears a stop at a lower floor.

4. The elevator is traveling upward and its upward velocity is decreasing as it nears a stop at a higher floor.

5.The elevator is traveling downward and its downnward velocity is increasing

6. The elevator is stationary and remains at rest.

an elevator starts from rest and moves upward with a constant acceleration 1.2 abolt of mass m in the elevator celling above the elevator nworks loose and falls dowen assume g = 9.8 what is the velocity of the bolt at is it hit the flor relative to the ground?

what is the velocity of the bolt as it hits the floor relative to the elevator