Consider the problem of utility over territory. Let’s start simply

with a one-dimensional representation. Consider two actors, 1

and 2, with utility functions defined over a single-dimensional

issue space X = [0, 1], but where the actors can own sections or

“provinces” of the interval. The boundaries between sections are

defined by a vector B = (b1, b2, b3, . . . , bn, 1).

Thus, there are n+ 1 provinces. Define a “size” vector containing the lengths of

each province, S = (b1, b2 − b1, b3 − b2, . . . , 1 − bn). Define for

each actor an “ownership” vector Oi with 1s in the place of the

provinces that it owns and 0s elsewhere.

1. Assume that each actor’s utility function is a simple sum of

how much of the space they own so ui=∑n+1,j=1, oj,sj

(a) Can the players both be made better off by exchanging

existing provinces?

(b) Can the players both be made better off by altering the

boundaries of the existing provinces while preserving the

ownership structure?

(c) Can the players both be made better off by reducing the

number of provinces – for instance, by consolidating

contiguous provinces that are owned by the same actor?

2. Now assume that the utility function is a function of the sum

of the squares of the provinces owned, indicating that there are

increasing returns to the size of a province ui=∑n+1,j=1, (oj,sj)^2

(a) Can the players both be made better off by exchanging

existing provinces (without doing anything else)?

(b) Can the players both be made better off by reducing the

number of provinces – for instance, by consolidating

contiguous provinces that are owned by the same actor?

(c) If the actors are free to adjust both the number of

provinces and the ownership structure, what set of

boundaries is Pareto optimal with this utility function?

2.2 (see formula in the attachments) Consider two states, state 1 and state 2, which can unilaterally

set their tariff rates on imported goods, ti ≥ 0. Each state has an

ideal level for its own tariff, and prefers that the other

side’s tariff be 0, Assume that each side’s utility declines

with the distance between the tariff levels and their ideal point,

as follows

1. Draw the t1, t2 quadrant and draw in the ideal points for each

player.

2. Draw in sample indifference curves for the two states around

their ideal points. What shape are they?

3. Draw in the contract curve between the two ideal points. What

shape is it and why? What equation describes it?

4. The contract curve divides the t1, t2 quadrant into two regions.

How do they differ in terms of how the players could realize

joint gains in each region?

2.3 Consider the utility function u(x) = xρ, where ρ > 0 and x ∈ [0,

1]. Under what conditions would a player with such preferences

be risk acceptant, risk neutral, and risk averse?

Answer:24

Step-by-step explanation:

Bet

Answer:

92

Step-by-step explanation:

Given

2n + t² ← substitute n = - 4 and t = - 10 into the expression

= 2(- 4) + (- 10)² = - 8 + 100 = 92

Answer: -28

Step-by-step explanation: 2x-4=-8 and -10x2=-20    -8+-20=-28

pls mark brainiest thanks

Answer:

Step-by-step explanation:

Answer:

1)2 x 10^27 kg

2)3.30 x 10^23 kg

3)Jupiter is 5,751.51 times more massive than Mercury

Step-by-step explanation:

1)Mass of Jupiter is 2 x 10²⁷ kg.

2)Mass of mercury is 3.30 x 10²³ kg.

3)Jupiter is 5,751.51 times more massive than Mercury.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using mathematical symbols.

1. Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.

The scientific notation is:- 2 x 10²⁷ kg.

2. Mercury, has a mass of about 330,000,000,000,000,000,000,000 kg.

The scientific notation is:- 3.30 x 10²³ kg.

Divide Jupiter's mass by the mass of mercury.

Jupiter / Mercury =  2 x 10²⁷  / 3.30 x 10²³

Jupiter / Mercury = 5,751.51

To know more about scientific notations follow

https://brainly.com/question/1767229

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Answer:

x = 9

Step-by-step explanation:

equation:

3x + 3x + x = x + x + x + x + 27

simplify:

7x = 4x + 27

3x = 27

x = 9

Answer:

$1.80, $2.90, $4.00, $10.90

Step-by-step explanation:

For 9/10 mile, the price will be $1.80. For 2 miles, the price will be $2.90. For 3 1/10 miles, the price will be $4.00, and for 10 miles, the price will be $10.90. The relationship between distance travelled and the price is not proportional because it costs $1.00 for the first 1/10 mile and then for every additional 1/10 mile, it only costs $0.10. Hope it helps!

Answer:

JK= 8x-4

Step-by-step explanation:

This is achieved by adding JM And MK because M is the midpoint of JK.

Answer:

Option B

m<1 + m<2 = 180-m<3

Explanation:

This is how you will find the third interior angle of a triangle when two angles are already given.

Answer:

55

Step-by-step explanation:

Answer:

5/4

Step-by-step explanation:

Answer: The difference between M and mu is due to the sampling error is -6.59 .

Step-by-step explanation:

As per given:  

in population, the average number of minutes spent in active play on weekends is μ = 65.87

In sample, the average number of minutes the children spend in active play on weekends is M = 59.28

Now, the difference between M and μ is due to the sampling error is M- μ

= 59.28  - 65.87

= -6.59

So, the difference between M and mu is due to the sampling error is -6.59 .

Answer:

x=-3

Step-by-step explanation:

h(x)=7

-4x-5=7

-4x=12

x=-3

Answer: -3

Step-by-step explanation:

Answer:

4.53 x 10^-5

Step-by-step explanation:

Answer:

A relation

Step-by-step explanation:

Answer:

A relation is a set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation and the set of all second components of the ordered pairs is called the range of the relation.

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...

  a + b + c = 108 . . . . . total number of liters

  .20a +.35b +.55c = 0.40·108 . . . . . liters of acid

  0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution

__

Solving these three equations by your favorite method gives ...

  (a, b, c) = (36, 18, 54)

The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.

_____

Comment on alternate approach

Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...

  (3(.55) +1(.35))/4 = 0.50 = 50%

So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.

Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.

__

* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...

  x(50%) +(1 -x)(20%) = 40%

  x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x

  x = (40% -20%)/(50% -20%)

The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.

Answer:

m = 1

Step-by-step explanation:

Slope is defined by the change in y over the change in x, [tex]\frac{\Delta y}{\Delta x}[/tex]. A trick here is to find where 2 points where the slope intersects a corner of the square grids. For example, here, it can be (0,1) and (1,0). Then, you count how many squares you needed to go up or down by and divide by the number of square you needed to move right or left by. If you move up or right, the value will be positive and vice versa for down and left. Which direction you go will depend on which point you start on. Here, we can see between (0,1) and (1,0), we need to move up 1 and right 1. Meaning 1/1 is the slope or m = 1. If this doesn't make sense, just ignore it but it may come in handy when you move to more complex problems where the slope is a fraction or something.

Answer:

b= -1

m=1

Step-by-step explanation:

the equation for a linear graph is y=mx+b

your y intercept would be -1 because thats where the line crosses on the y axis. The slope which would be 1 is because when you are on the point (0,-1) you go up one and one to the right and get (1,0)

therefore the equation would be

y=1x-1 or y=x-1

Answer:

1. n=-6

2. x=-17

Step-by-step explanation:

Answer:

n - 11 = 18n

Step-by-step explanation:

n−11=18n

Step 1: Subtract 18n from both sides.

n−11−18n=18n−18n

−17n−11=0

Step 2: Add 11 to both sides.

−17n−11+11=0+11

−17n=11

Step 3: Divide both sides by -17.

−17n−17=11−17

n=−1117

Answer:

n = −11/17

Answer:

correlation: positive, negative, none

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

the answer to that is 12

Step-by-step explanation:

1st, arrange the numbers from lowest to highest

2nd, group them into quarters

= 11, 12, 16, 16, 17, 18, 20

-lq. -mq. -uq.

Answer:

An equation in point-slope form that represents Byron’s  distance from home, y, after  x hours is y=4x+2

Step-by-step explanation:

Speed of Byron = 4 miles / hour

Distance traveled in x hours = [tex]Speed \times time[/tex]

Distance traveled in x hours = 4x

We are given that After half an hour of  running, he is 2 miles from home

So, Total distance = 4x+2

So, y = 4x+2

Hence an equation in point-slope form that represents Byron’s  distance from home, y, after  x hours is y=4x+2

Answer:

=25x-7

Step-by-step explanation:

Answer:

x=16

Step-by-step explanation:

(16*3)-2

48-2

46

134+46=180

Answer:

[tex]p = \frac{mn-rs - x}{2} [/tex]

Step-by-step explanation:

[tex]if \: mn-rs=x +2p \\ x +2p = mn-rs \\ 2p = mn-rs - x \\ p = \frac{mn-rs - x}{2} [/tex]

Answer:

omg yay congrats :)

Step-by-step explanation:

you can go to my profile page and answer 3 of my questions that only have one answer. you dont have to put a legit answer and i'll give you brainliest ❤️

Answer:

You are almost there!!

Step-by-step explanation:

Answer:

1: 2x + y = 24

2: x - 3y = 54

Step-by-step explanation:

Answer:

[tex] y = - 3. \\ x = - 13.5[/tex]

Step-by-step explanation:

[tex]equation 1: -x/3 - y/6 = -4 \: \: = - \frac{x}{3} - \frac{y}{6} = - 4 \\ \\

equation 2: -x/6 + y/2 = -9 \: \: = - \frac{x}{6} + \frac{y}{2} = - 9 \\ \\ - \frac{x}{3} - \frac{y}{6} = - 4 \\ - 6x - 3y = - 72 ...(eq3.) \\ \\ - \frac{x}{6} + \frac{y}{2} = - 9 \\ - 2x + 6y = - 9...(eq4.) \\ \\ \\ 2 \times - 6x - 3y = - 72 ...(eq3.) = > - 6y = -1 44 \\6 \times - 2x + 6y = - 9...(eq4.)= > - 36y = -54 \\ - 6y - ( - 36y) = - 144 - ( - 54) \\ 30y = - 90 \\ y = - \frac{90}{30} \\ y = - 3. \\ x = - 13.5

[/tex]